We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

10aDispersive equations10aEnergy method10aLocal wellposedness10aNLS10aPara-differential calculus10aQuasi-linear PDEs1 aFeola, Roberto1 aIandoli, Felice uhttp://www.sciencedirect.com/science/article/pii/S029414491830042801637nas a2200217 4500008004100000022001400041245007700055210006900132300001400201490000800215520097100223653002001194653001501214653001701229653001701246100001901263700002201282700002301304700002101327856007101348 2019 eng d a0022-123600aReducibility of first order linear operators on tori via Moser's theorem0 aReducibility of first order linear operators on tori via Mosers a932 - 9700 v2763 aIn this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ⋅∂xu+a(ωt,x)⋅∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

10aHyperbolic PDEs10aKAM theory10aNash–Moser10aReducibility1 aFeola, Roberto1 aGiuliani, Filippo1 aMontalto, Riccardo1 aProcesi, Michela uhttp://www.sciencedirect.com/science/article/pii/S002212361830379300814nas a2200121 4500008004100000245006700041210006000108260001000168520042500178100002200603700001900625856004800644 2019 en d00aOn the topological degree of planar maps avoiding normal cones0 atopological degree of planar maps avoiding normal cones bSISSA3 aThe classical Poincaré–Bohl theorem provides the exis-tence of a zero for a function avoiding external rays. When the do-main is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having in-ward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be di˙erent from ±1.1 aFonda, Alessandro1 aKlun, Giuliano uhttp://preprints.sissa.it/handle/1963/3533000612nas a2200169 4500008004100000245015500041210006900196300001100265490000800276100002200284700002000306700002000326700002300346700001700369700001900386856003700405 2018 eng d00aIterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments0 aIterative mapmaking with twolevel preconditioning for polarized a1–140 v6181 aPuglisi, Giuseppe1 aPoletti, Davide1 aFabbian, Giulio1 aBaccigalupi, Carlo1 aHeltai, Luca1 aStompor, Radek uhttps://arxiv.org/abs/1801.0893701341nas a2200133 4500008004100000245011300041210006900154260003400223520083400257100002301091700002301114700001901137856005101156 2018 en d00aPositive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree0 aPositive solutions for supersublinear indefinite problems high m bAmerican Mathematical Society3 aWe study the periodic boundary value problem associated with the second order nonlinear equation u''+(λa+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m−1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526401233nas a2200133 4500008004100000245007600041210006900117300001200186490000700198520080200205100002301007700002301030856004601053 2018 eng d00aPositive subharmonic solutions to nonlinear ODEs with indefinite weight0 aPositive subharmonic solutions to nonlinear ODEs with indefinite a17500210 v203 aWe prove that the superlinear indefinite equation u″ + a(t)up = 0, where p > 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt < 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo uhttps://doi.org/10.1142/S021919971750021300517nas a2200109 4500008004100000245011200041210006900153100001900222700002200241700002100263856012300284 2018 eng d00aReducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation0 aReducibility for a class of weakly dispersive linear operators a1 aFeola, Roberto1 aGiuliani, Filippo1 aProcesi, Michela uhttps://www.math.sissa.it/publication/reducibility-class-weakly-dispersive-linear-operators-arising-degasperis-procesi00361nas a2200109 4500008004100000245005600041210005300097100002100150700001900171700002400190856003700214 2018 eng d00aOn some rigorous aspects of fragmented condensation0 asome rigorous aspects of fragmented condensation1 aDimonte, Daniele1 aFalconi, Marco1 aOlgiati, Alessandro uhttps://arxiv.org/abs/1809.0358601022nas a2200121 4500008004100000245005500041210005500096520063900151100002100790700002300811700001800834856004800852 2018 en d00aTransmission conditions obtained by homogenisation0 aTransmission conditions obtained by homogenisation3 aWe study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems.1 aDal Maso, Gianni1 aFranzina, Giovanni1 aZucco, Davide uhttp://preprints.sissa.it/handle/1963/3531000564nas a2200133 4500008004100000245012900041210006900170260008500239300001400324490000700338100002300345700001900368856004300387 2017 eng d00aAn application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators0 aapplication of coincidence degree theory to cyclic feedback type bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a683–7260 v501 aFeltrin, Guglielmo1 aZanolin, Fabio uhttps://doi.org/10.12775/TMNA.2017.03800875nas a2200193 4500008004100000022001400041245006900055210006600124300001600190490000800206520024700214653002900461653002400490653002300514653003300537100002200570700001800592856007100610 2017 eng d a0022-039600aAn avoiding cones condition for the Poincaré–Birkhoff Theorem0 aavoiding cones condition for the Poincaré–Birkhoff Theorem a1064 - 10840 v2623 aWe provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincaré–Birkhoff fixed point Theorem for Poincaré maps of Hamiltonian systems.

10aAvoiding cones condition10aHamiltonian systems10aPeriodic solutions10aPoincaré–Birkhoff theorem1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S002203961630327801631nas a2200181 4500008004100000022001400041245007600055210006900131300001400200490000800214520106600222653001401288653001601302653001701318653002501335100001801360856007101378 2017 eng d a0021-999100aComputer simulations of phase field drops on super-hydrophobic surfaces0 aComputer simulations of phase field drops on superhydrophobic su a247 - 2590 v3443 aWe present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

10aMultigrid10aPhase field10aQuasi-Newton10aSuper-hydrophobicity1 aFedeli, Livio uhttp://www.sciencedirect.com/science/article/pii/S002199911730356X01736nas a2200181 4500008004100000022001400041245010800055210006900163300000900232490000700241520106900248653003901317653002301356653004001379653003601419100002301455856007601478 2017 eng d a1534-039200aMultiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities0 aMultiple positive solutions of a sturmliouville boundary value p a10830 v163 aWe study the second order nonlinear differential equation

\begindocument $ u'' + \sum\limits_i = 1^m α_ia_i(x)g_i(u) - \sum\limits_j = 1^m + 1 β_jb_j(x)k_j(u) = 0,\rm $ \enddocument

where $\alpha_i, \beta_j>0$, $a_i(x), b_j(x)$ are non-negative Lebesgue integrable functions defined in $\mathopen[0, L\mathclose]$, and the nonlinearities $g_i(s), k_j(s)$ are continuous, positive and satisfy suitable growth conditions, as to cover the classical superlinear equation $u"+a(x)u.p = 0$, with $p>1$.When the positive parameters $\beta_j$ are sufficiently large, we prove the existence of at least $2.m-1$positive solutions for the Sturm-Liouville boundary value problems associated with the equation.The proof is based on the Leray-Schauder topological degree for locally compact operators on open and possibly unbounded sets.Finally, we deal with radially symmetric positive solutions for the Dirichlet problems associated with elliptic PDEs.

10aLeray-Schauder topological degree;10apositive solutions10aSturm-Liouville boundary conditions10aSuperlinear indefinite problems1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a101598nas a2200217 4500008004100000022001400041245010600055210006900161300001600230490000800246520083500254653002301089653002501112653003601137653003201173653002601205653003601231100002301267700001901290856007101309 2017 eng d a0022-039600aMultiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree0 aMultiplicity of positive periodic solutions in the superlinear i a4255 - 42910 v2623 aWe study the periodic boundary value problem associated with the second order nonlinear differential equationu″+cu′+(a+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill's equation. We prove the existence of 2m−1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin's coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.

10aCoincidence degree10aMultiplicity results10aNeumann boundary value problems10aPositive periodic solutions10asubharmonic solutions10aSuperlinear indefinite problems1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961730021900849nas a2200109 4500008004100000245006100041210005900102260002000161520048400181100002300665856005100688 2017 en d00aA note on a fixed point theorem on topological cylinders0 anote on a fixed point theorem on topological cylinders bSpringer Verlag3 aWe present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skii ones.

1 aFeltrin, Guglielmo uhttp://urania.sissa.it/xmlui/handle/1963/3526300711nas a2200181 4500008004100000245009900041210006900140300001400209490000700223100002400230700002000254700002000274700002200294700002100316700002000337700002200357856015000379 2017 eng d00aNumerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts0 aNumerical modeling of hemodynamics scenarios of patientspecific a1373-13990 v161 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aIppolito, Sonia1 aScrofani, Roberto uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd001478nas a2200169 4500008004100000022001400041245008500055210006900140260000800209300001200217490000700229520096100236100002301197700002101220700002101241856004601262 2016 eng d a1424-066100aConstruction of Real-Valued Localized Composite Wannier Functions for Insulators0 aConstruction of RealValued Localized Composite Wannier Functions cJan a63–970 v173 aWe consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca uhttps://doi.org/10.1007/s00023-015-0400-600590nas a2200157 4500008004100000245009800041210006900139300001400208490000700222100001600229700001700245700001400262700001700276700001400293856012500307 2016 eng d00aError Estimates of B-spline based finite-element method for the wind-driven ocean circulation0 aError Estimates of Bspline based finiteelement method for the wi a430–4590 v691 aRotundo, N.1 aKim, T., -Y.1 aJiang, W.1 aHeltai, Luca1 aFried, E. uhttps://www.math.sissa.it/publication/error-estimates-b-spline-based-finite-element-method-wind-driven-ocean-circulation01717nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100002401305700002001329700002001349700002101369700002201390700002001412700002201432700001801454856005101472 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.1 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524000945nas a2200157 4500008004100000022001400041245007900055210007200134260000800206300001600214490000800230520046300238100002200701700001800723856004600741 2016 eng d a1618-189100aGeneralizing the Poincaré–Miranda theorem: the avoiding cones condition0 aGeneralizing the Poincaré–Miranda theorem the avoiding cones con cAug a1347–13710 v1953 aAfter proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

1 aFonda, Alessandro1 aGidoni, Paolo uhttps://doi.org/10.1007/s10231-015-0519-600961nas a2200133 4500008004100000245014200041210006900183260003100252520042800283100002300711700002300734700001900757856005100776 2016 en d00aPairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case0 aPairs of positive periodic solutions of nonlinear ODEs with inde bCambridge University Press3 aWe study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526200883nas a2200157 4500008004100000245005000041210005000091260001500141300001400156490000600170520040100176100002200577700002300599700001800622856008500640 2016 eng d00aPeriodic perturbations of Hamiltonian systems0 aPeriodic perturbations of Hamiltonian systems bDe Gruyter a367–3820 v53 aWe prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

1 aFonda, Alessandro1 aGarrione, Maurizio1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/periodic-perturbations-hamiltonian-systems02865nas a2200121 4500008004100000245007000041210006900111260001000180520240500190653002302595100002302618856010202641 2016 en d00aPositive solutions to indefinite problems: a topological approach0 aPositive solutions to indefinite problems a topological approach bSISSA3 aThe present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.10apositive solutions1 aFeltrin, Guglielmo uhttps://www.math.sissa.it/publication/positive-solutions-indefinite-problems-topological-approach00553nas a2200145 4500008004100000245008000041210006900121260002200190300001600212490000700228100002000235700002200255700001800277856011200295 2016 eng d00aSymmetry properties of some solutions to some semilinear elliptic equations0 aSymmetry properties of some solutions to some semilinear ellipti bClasse di Scienze a1209–12340 v161 aFarina, Alberto1 aMalchiodi, Andrea1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/symmetry-properties-some-solutions-some-semilinear-elliptic-equations00906nas a2200157 4500008004100000022001400041245004500055210004400100260000800144300001400152490000700166520048600173100002300659700002000682856004600702 2016 eng d a1572-909500at-Structures are Normal Torsion Theories0 atStructures are Normal Torsion Theories cApr a181–2080 v243 aWe characterize $t$-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

1 aFiorenza, Domenico1 aLoregian, Fosco uhttps://doi.org/10.1007/s10485-015-9393-z01400nas a2200169 4500008004100000022001400041245007000055210006900125260000800194300001600202490000800218520089300226100002301119700002101142700002101163856004601184 2016 eng d a1432-091600aZ2 Invariants of Topological Insulators as Geometric Obstructions0 aZ2 Invariants of Topological Insulators as Geometric Obstruction cMay a1115–11570 v3433 aWe consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca uhttps://doi.org/10.1007/s00220-015-2552-001837nas a2200145 4500008004100000245007900041210006900120520133000189100002201519700002901541700002001570700002901590700002101619856005101640 2015 en d00aA class of Hamiltonians for a three-particle fermionic system at unitarity0 aclass of Hamiltonians for a threeparticle fermionic system at un3 aWe consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3446901084nas a2200121 4500008004100000245013700041210006900178260002300247520059900270100002300869700001900892856005100911 2015 en d00aExistence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems0 aExistence of positive solutions in the superlinear case via coin bKhayyam Publishing3 aWe prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://projecteuclid.org/euclid.ade/143506451801364nas a2200181 4500008004100000022001400041245009900055210006900154300000800223490000900231520072700240653002700967653002300994653004101017653002501058100002301083856007601106 2015 eng d a0133-018900aExistence of positive solutions of a superlinear boundary value problem with indefinite weight0 aExistence of positive solutions of a superlinear boundary value a4360 v20153 aWe deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

10aboundary value problem10aindefinite weight10aPositive solution; existence result.10asuperlinear equation1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc4847802601820nas a2200169 4500008004100000245015600041210006900197520118400266100002401450700002001474700002001494700002001514700002201534700002101556700002201577856005101599 2015 en d00aFast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization0 aFast simulations of patientspecific haemodynamics of coronary ar3 aIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.1 aBallarin, Francesco1 aFaggiano, Elena1 aIppolito, Sonia1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aScrofani, Roberto uhttp://urania.sissa.it/xmlui/handle/1963/3462301899nas a2200133 4500008004300000245010100043210006900144520142800213100002101641700001701662700001701679700001801696856005101714 2015 en_Ud 00aFEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows0 aFEM SUPG stabilisation of mixed isoparametric BEMs application t3 aIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

1 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca1 aFormaggia, L. uhttp://urania.sissa.it/xmlui/handle/1963/3446601194nas a2200121 4500008004100000245008200041210006900123260001300192520077400205100002300979700001901002856005101021 2015 en d00aMultiple positive solutions for a superlinear problem: a topological approach0 aMultiple positive solutions for a superlinear problem a topologi bElsevier3 aWe study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3514700827nas a2200193 4500008004100000022001400041245005300055210005100108300001200159490000800171520026300179653002100442653001500463653002000478653002400498100002200522700001800544856007100562 2015 eng d a0362-546X00aA permanence theorem for local dynamical systems0 apermanence theorem for local dynamical systems a73 - 810 v1213 aWe provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition.

10aLotka–Volterra10apermanence10aPredator–prey10aUniform persistence1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S0362546X1400333200719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515701443nas a2200133 4500008004100000245015900041210006900200300001400269490000700283520085800290100001401148700002101162856012601183 2014 eng d00aEfficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems0 aEfficient geometrical parametrisation techniques of interfaces f a158–1690 v283 aWe present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid–structure applications in several fields. The examples provided deal with aeronautics and wind engineering.1 aForti, D.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/efficient-geometrical-parametrisation-techniques-interfaces-reduced-order-modelling01351nas a2200133 4500008004100000245008400041210007000125260003900195520087300234100001901107700001901126700002101145856005101166 2014 en d00aFinite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians0 aFinite dimensional KadomtsevPetviashvili τfunctions I Finite Gra bAmerican Institute of Physics Inc.3 aWe study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function.1 aBalogh, Ferenc1 aFonseca, Tiago1 aHarnad, John, P. uhttp://urania.sissa.it/xmlui/handle/1963/3495201169nas a2200145 4500008004100000245008500041210006900126260001000195520065500205653006700860100002100927700001900948700002000967856003600987 2014 en d00aSecond Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional0 aSecond Order Asymptotic Development for the Anisotropic CahnHill bSISSA3 aThe asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.10aGamma-convergence, Cahn-Hilliard functional, phase transitions1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/739001521nas a2200133 4500008004100000245009100041210006900132260001000201520106100211653003701272100002001309700002201329856003601351 2013 en d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in bSISSA3 aWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/661501048nas a2200145 4500008004100000245010400041210006900145260001300214520050500227653007400732100002100806700001900827700002000846856003600866 2013 en d00aAnalytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces0 aAnalytical validation of a continuum model for epitaxial growth bSpringer3 aIn this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].10asingular nonlinear parabolic equations, Hilbert transform, thin films1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/724501565nas a2200169 4500008004100000245010100041210006900142260001000211520092400221100002201145700002401167700002201191700001701213700001901230700002201249856012401271 2013 en d00aCommon dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.0 aCommon dynamical features of sensory adaptation in photoreceptor bSISSA3 aSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

1 aDe Palo, Giovanna1 aFacchetti, Giuseppe1 aMazzolini, Monica1 aMenini, Anna1 aTorre, Vincent1 aAltafini, Claudio uhttps://www.math.sissa.it/publication/common-dynamical-features-sensory-adaptation-photoreceptors-and-olfactory-sensory00809nas a2200157 4500008004100000245003700041210003700078260002300115520037700138653001900515100002000534700002000554700002200574700001900596856003600615 2013 en d00aExpanded degenerations and pairs0 aExpanded degenerations and pairs bTaylor and Francis3 aSince Jun Li's original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.10aExpanded pairs1 aAbramovich, Dan1 aCadman, Charles1 aFantechi, Barbara1 aWise, Jonathan uhttp://hdl.handle.net/1963/738301258nas a2200145 4500008004100000245010200041210006900143260008500212300001400297490000700311520069200318100002201010700002301032856005701055 2013 eng d00aGeneralized Sturm-Liouville boundary conditions for first order differential systems in the plane0 aGeneralized SturmLiouville boundary conditions for first order d bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a293–3250 v423 aWe study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://projecteuclid.org:443/euclid.tmna/146124898100625nas a2200157 4500008004100000245011600041210006900157260001700226300001400243490000700257100001500264700002300279700002200302700001800324856012500342 2013 eng d00aMacroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations0 aMacroscopic contact angle and liquid drops on rough solid surfac bEDP Sciences a837–8580 v471 aCacace, S.1 aChambolle, Antonin1 aDeSimone, Antonio1 aFedeli, Livio uhttps://www.math.sissa.it/publication/macroscopic-contact-angle-and-liquid-drops-rough-solid-surfaces-homogenization-and00784nas a2200109 4500008004100000245008400041210006900125520032000194100002500514700002300539856011200562 2013 eng d00aA note on non-homogeneous hyperbolic operators with low-regularity coefficients0 anote on nonhomogeneous hyperbolic operators with lowregularity c3 aIn this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

1 aColombini, Ferruccio1 aFanelli, Francesco uhttps://www.math.sissa.it/publication/note-non-homogeneous-hyperbolic-operators-low-regularity-coefficients00503nas a2200133 4500008004100000245006500041210006500106260003700171300001400208490000700222100002200229700001900251856009900270 2013 eng d00aPeriodic bouncing solutions for nonlinear impact oscillators0 aPeriodic bouncing solutions for nonlinear impact oscillators bAdvanced Nonlinear Studies, Inc. a179–1890 v131 aFonda, Alessandro1 aSfecci, Andrea uhttps://www.math.sissa.it/publication/periodic-bouncing-solutions-nonlinear-impact-oscillators00868nas a2200145 4500008004100000245004700041210004400088260004800132520037400180100002100554700002100575700002500596700002200621856007900643 2012 en d00aAsymptotics of the s-perimeter as s →0 0 aAsymptotics of the sperimeter as s →0 bAmerican Institute of Mathematical Sciences3 aWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

1 aDipierro, Serena1 aFigalli, Alessio1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/asymptotics-s-perimeter-s-%E2%86%92001031nas a2200133 4500008004100000245009200041210006900133260002100202300001400223490000700237520058100244100002300825856004900848 2012 eng d00aConservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids0 aConservation of Geometric Structures for NonHomogeneous Inviscid bTaylor & Francis a1553-15950 v373 aIn this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

1 aFanelli, Francesco uhttps://doi.org/10.1080/03605302.2012.69834301741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650401004nas a2200169 4500008004100000022001400041245009800055210006900153300001600222490000800238520043000246653002300676653002300699100002200722700001900744856007100763 2012 eng d a0022-039600aA general method for the existence of periodic solutions of differential systems in the plane0 ageneral method for the existence of periodic solutions of differ a1369 - 13910 v2523 aWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

10aNonlinear dynamics10aPeriodic solutions1 aFonda, Alessandro1 aSfecci, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002203961100319600826nas a2200133 4500008004300000245007200043210006900115260002100184520038600205100002000591700002500611700002000636856003600656 2012 en_Ud 00aNonlinear thin-walled beams with a rectangular cross-section-Part I0 aNonlinear thinwalled beams with a rectangular crosssectionPart I bWorld Scientific3 aOur aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/410400499nas a2200133 4500008004100000245010300041210006900144260003300213300001500246490000700261100002200268700001900290856005600309 2012 eng d00aPeriodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces0 aPeriodic solutions of a system of coupled oscillators with onesi bKhayyam Publishing, Inc.c11 a993–10100 v251 aFonda, Alessandro1 aSfecci, Andrea uhttps://projecteuclid.org:443/euclid.die/135601224802201nas a2200133 4500008004100000245010400041210006900145260001900214520173100233100002401964700002201988700002102010856003602031 2012 en d00aPredicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.0 aPredicting and characterizing selective multiple drug treatments bBioMed Central3 aBackground: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.1 aFacchetti, Giuseppe1 aAltafini, Claudio1 aZampieri, Mattia uhttp://hdl.handle.net/1963/651500946nas a2200145 4500008004100000245007300041210006900114260000900183520047100192653002200663100002900685700002500714700002500739856003600764 2012 en d00aQuasistatic evolution in non-associative plasticity - the cap models0 aQuasistatic evolution in nonassociative plasticity the cap model bSIAM3 aNon-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled.10aElasto-plasticity1 aBabadjian, Jean-Francois1 aFrancfort, Gilles A.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/413901607nas a2200157 4500008004100000245009600041210006900137260002100206520106500227100002201292700002901314700002001343700002901363700002101392856003601413 2012 en d00aStability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions0 aStability for a System of N Fermions Plus a Different Particle w bWorld Scientific3 aWe study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://hdl.handle.net/1963/606901286nas a2200145 4500008004100000245007900041210006900120260003300189520078400222653003101006100002401037700002101061700002201082856003601104 2011 en d00aComputing global structural balance in large-scale signed social networks.0 aComputing global structural balance in largescale signed social bNational Academy of Sciences3 aStructural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"10aCombinatorial optimization1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/642601344nas a2200181 4500008004100000022001400041245010900055210007100164300001600235490000800251520070400259653002100963653003300984653002901017100002201046700002301068856007101091 2011 eng d a0022-039600aDouble resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations0 aDouble resonance with Landesman–Lazer conditions for planar syst a1052 - 10820 v2503 aWe prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman–Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

10aDouble resonance10aLandesman–Lazer conditions10aNonlinear planar systems1 aFonda, Alessandro1 aGarrione, Maurizio uhttp://www.sciencedirect.com/science/article/pii/S002203961000290101329nas a2200169 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520081100240100001801051700002201069700002201091856004601113 2011 eng d a1432-095900aMetastable equilibria of capillary drops on solid surfaces: a phase field approach0 aMetastable equilibria of capillary drops on solid surfaces a pha cSep a453–4710 v233 aWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

1 aFedeli, Livio1 aTurco, Alessandro1 aDeSimone, Antonio uhttps://doi.org/10.1007/s00161-011-0189-600992nas a2200145 4500008004100000245009400041210006900135260003700204300001400241490000700255520041000262100002200672700002300694856012900717 2011 eng d00aNonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions0 aNonlinear resonance a comparison between LandesmanLazer and Ahma bAdvanced Nonlinear Studies, Inc. a391–4040 v113 aWe show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://www.math.sissa.it/publication/nonlinear-resonance-comparison-between-landesman-lazer-and-ahmad-lazer-paul-conditions00668nas a2200145 4500008004100000245007500041210006900116260001000185520019000195653003600385100002000421700002500441700002000466856003600486 2011 en d00aNonlinear thin-walled beams with a rectangular cross-section - Part II0 aNonlinear thinwalled beams with a rectangular crosssection Part bSISSA3 aIn this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..10aThin-walled cross-section beams1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/416902121nas a2200145 4500008004100000245007900041210006900120260001300189520164700202100002001849700002201869700002301891700002501914856003601939 2011 en d00aQuantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators0 aQuantum Geometry on Quantum Spacetime Distance Area and Volume O bSpringer3 aWe develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.1 aBahns, Dorothea1 aDoplicher, Sergio1 aFredenhagen, Klaus1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/520301135nas a2200145 4500008004300000245008100043210006900124260002300193520065600216100002100872700002100893700001900914700002000933856003600953 2011 en_Ud 00aSingular perturbation models in phase transitions for second order materials0 aSingular perturbation models in phase transitions for second ord bIndiana University3 aA variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.1 aChermisi, Milena1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/385802515nas a2200205 4500008004100000022001400041245009600055210006900151300001400220490000700234520182300241653002202064653002402086653003502110653001302145653003502158100002202193700002302215856007102238 2011 eng d a0021-782400aThe well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces0 awellposedness issue for the densitydependent Euler equations in a253 - 2780 v963 aThis work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

10aBlow-up criterion10aCritical regularity10aIncompressible Euler equations10aLifespan10aNonhomogeneous inviscid fluids1 aDanchin, Raphaël1 aFanelli, Francesco uhttp://www.sciencedirect.com/science/article/pii/S002178241100051100773nas a2200145 4500008004300000245007900043210006900122260001300191520030200204100001900506700002000525700002100545700002500566856003600591 2010 en_Ud 00aExact reconstruction of damaged color images using a total variation model0 aExact reconstruction of damaged color images using a total varia bElsevier3 aIn this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.1 aFonseca, Irene1 aLeoni, Giovanni1 aMaggi, Francesco1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/403900807nas a2200157 4500008004300000245008900043210006900132260002800201520027900229100002200508700002100530700002100551700002200572700001900594856003600613 2010 en_Ud 00aOn the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system0 ageometric origin of the biHamiltonian structure of the CalogeroM bOxford University Press3 aWe show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.1 aBartocci, Claudio1 aFalqui, Gregorio1 aMencattini, Igor1 aOrtenzi, Giovanni1 aPedroni, Marco uhttp://hdl.handle.net/1963/380001051nas a2200169 4500008004300000245007900043210006900122260003000191520049800221100001800719700002600737700002300763700001800786700002200804700001900826856003600845 2010 en_Ud 00aHomogeneous binary trees as ground states of quantum critical Hamiltonians0 aHomogeneous binary trees as ground states of quantum critical Ha bAmerican Physical Society3 aMany-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aMontangero, Simone1 aRizzi, Matteo1 aCirac, J. Ignacio1 aFazio, Rosario uhttp://hdl.handle.net/1963/390901188nas a2200157 4500008004300000245010800043210006900151260001900220520065100239100001800890700002300908700001800931700002600949700001900975856003600994 2010 en_Ud 00aHomogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems0 aHomogeneous multiscale entanglement renormalization ansatz tenso bIOP Publishing3 aIn this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

1 aRizzi, Matteo1 aMontangero, Simone1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/406700409nas a2200109 4500008004300000245009100043210006900134100002100203700001900224700002000243856003600263 2010 en_Ud 00aNonlocal character of the reduced theory of thin films with higher order perturbations0 aNonlocal character of the reduced theory of thin films with high1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/375400902nas a2200169 4500008004100000020002200041245007700063210006900140260003600209300001200245520028600257100002200543700001800565700002200583700001700605856011000622 2010 eng d a978-90-481-9195-600aA Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena0 aPhase Field Approach to Wetting and Contact Angle Hysteresis Phe aDordrechtbSpringer Netherlands a51–633 aWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

1 aDeSimone, Antonio1 aFedeli, Livio1 aTurco, Alessandro1 aHackl, Klaus uhttps://www.math.sissa.it/publication/phase-field-approach-wetting-and-contact-angle-hysteresis-phenomena01121nas a2200121 4500008004300000245007400043210006900117260003700186520069600223100002200919700002200941856003600963 2010 en_Ud 00aRiemann-Roch theorems and elliptic genus for virtually smooth schemes0 aRiemannRoch theorems and elliptic genus for virtually smooth sch bMathematical Sciences Publishers3 aFor a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.1 aFantechi, Barbara1 aGöttsche, Lothar uhttp://hdl.handle.net/1963/388800622nas a2200109 4500008004300000245010100043210006900144520021400213100002900427700002000456856003600476 2010 en_Ud 00aSharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials0 aSharp nonexistence results for a linear elliptic inequality invo3 aIn this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.1 aFall, Mouhamed Moustapha1 aMusina, Roberta uhttp://hdl.handle.net/1963/386901029nas a2200157 4500008004100000245008100041210006900122300001000191490000800201520055000209100001800759700001700777700001600794700001800810856004300828 2010 eng d00aA three-dimensional model for the dynamics and hydrodynamics of rowing boats0 athreedimensional model for the dynamics and hydrodynamics of row a51-610 v2243 aThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

1 aFormaggia, L.1 aMola, Andrea1 aParolini, N1 aPischiutta, M uhttps://doi.org/10.1243/17543371jset4601175nas a2200133 4500008004300000245008500043210006900128260001300197520072500210100002900935700002000964700002100984856003601005 2010 en_Ud 00aA time-dependent perturbative analysis for a quantum particle in a cloud chamber0 atimedependent perturbative analysis for a quantum particle in a bSpringer3 aWe consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/396908321nas a2200145 4500008004100000245008100041210006900122260001300191300001600204490000700220520785400227100003008081700001908111856004508130 2009 eng d00aFoliations of small tubes in Riemannian manifolds by capillary minimal discs0 aFoliations of small tubes in Riemannian manifolds by capillary m bElsevier a4422–44400 v703 aLetting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://doi.org/10.1016/j.na.2008.10.02400927nas a2200133 4500008004300000245007300043210006900116520048700185100002100672700001900693700002000712700002500732856003600757 2009 en_Ud 00aA higher order model for image restoration: the one dimensional case0 ahigher order model for image restoration the one dimensional cas3 aThe higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/317400903nas a2200145 4500008004100000245006400041210006300105260002900168300001600197490000700213520043600220100003000656700001900686856005200705 2009 eng d00aMinimal disc-type surfaces embedded in a perturbed cylinder0 aMinimal disctype surfaces embedded in a perturbed cylinder bKhayyam Publishing, Inc. a1115–11240 v223 aIn the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://projecteuclid.org/euclid.die/135601940700433nas a2200157 4500008004100000245004500041210004300086260001500129300001400144490000700158100001800165700001700183700001700200700002100217856003700238 2009 eng d00aA model for the dynamics of rowing boats0 amodel for the dynamics of rowing boats bWileycsep a119–1430 v611 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aMontano, Antonio uhttps://doi.org/10.1002/fld.194001344nas a2200145 4500008004300000245009700043210006900140260001900209520085100228100002001079700002101099700002001120700002201140856003601162 2009 en_Ud 00amRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle0 amRNA stability and the unfolding of gene expression in the longp bBioMed Central3 aBackground: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.1 aSoranzo, Nicola1 aZampieri, Mattia1 aFarina, Lorenzo1 aAltafini, Claudio uhttp://hdl.handle.net/1963/363000416nas a2200133 4500008004100000022001400041245005800055210005700113300001500170490000700185100001900192700001800211856005300229 2009 eng d a1751-811300aTopological expansion for the Cauchy two-matrix model0 aTopological expansion for the Cauchy twomatrix model a335201, 280 v421 aBertola, Marco1 aFerrer, Prats uhttp://dx.doi.org/10.1088/1751-8113/42/33/33520100501nas a2200157 4500008004100000245009500041210007100136260001000207300001400217490000700231100001800238700001700256700001700273700001600290856003700306 2008 eng d00aFluid–structure interaction problems in free surface flows: Application to boat dynamics0 aFluid–structure interaction problems in free surface flows Appli bWiley a965–9780 v561 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aParolini, N uhttps://doi.org/10.1002/fld.158301559nas a2200157 4500008004300000245008100043210006900124520105300193100001801246700001801264700002501282700002001307700001901327700001901346856003601365 2008 en_Ud 00aFulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices0 aFuldeFerrellLarkinOvchinnikov pairing in onedimensional optical 3 aSpin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

1 aRizzi, Matteo1 aPolini, Marco1 aCazalilla, Miguel A.1 aBakhtiari, M.R.1 aTosi, Mario P.1 aFazio, Rosario uhttp://hdl.handle.net/1963/269400434nas a2200121 4500008004100000022001400041245005200055210005100107300002300158100001900181700002500200856008700225 2008 eng d a1073-792800aHarish-Chandra integrals as nilpotent integrals0 aHarishChandra integrals as nilpotent integrals aArt. ID rnn062, 151 aBertola, Marco1 aFerrer, Aleix, Prats uhttps://www.math.sissa.it/publication/harish-chandra-integrals-nilpotent-integrals01518nas a2200109 4500008004300000245007900043210006900122520114200191100001701333700002201350856003601372 2008 en_Ud 00aSymmetric obstruction theories and Hilbert schemes of points on threefolds0 aSymmetric obstruction theories and Hilbert schemes of points on 3 aIn an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C∗-action and that admits a symmetric obstruction theory compatible with the C∗-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande.1 aBehrend, Kai1 aFantechi, Barbara uhttp://hdl.handle.net/1963/270901323nas a2200133 4500008004300000245010700043210006900150520085200219100001901071700001801090700002001108700002501128856003601153 2007 en_Ud 00aEquilibrium configurations of epitaxially strained crystalline films: existence and regularity results0 aEquilibrium configurations of epitaxially strained crystalline f3 aStrained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers.1 aFonseca, Irene1 aFusco, Nicola1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/235001450nas a2200169 4500008004300000245007300043210006900116520092200185100001801107700001801125700001801143700001901161700001901180700002601199700001901225856003601244 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 aThe Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600729nas a2200121 4500008004300000245002700043210002700070520041600097100002200513700001800535700001800553856003600571 2007 en_Ud 00aSmooth toric DM stacks0 aSmooth toric DM stacks3 aWe give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.1 aFantechi, Barbara1 aMann, Etienne1 aNironi, Fabio uhttp://hdl.handle.net/1963/212000907nas a2200121 4500008004300000245005500043210005300098520053100151100001900682700002500701700002300726856003600749 2007 en_Ud 00aSurfactants in Foam Stability: A Phase-Field Model0 aSurfactants in Foam Stability A PhaseField Model3 aThe role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.1 aFonseca, Irene1 aMorini, Massimiliano1 aSlastikov, Valeriy uhttp://hdl.handle.net/1963/203501031nas a2200121 4500008004300000245007500043210006900118520062400187100001800811700002500829700001900854856003600873 2006 en_Ud 00a4e-condensation in a fully frustrated Josephson junction diamond chain0 a4econdensation in a fully frustrated Josephson junction diamond 3 aFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

1 aRizzi, Matteo1 aCataudella, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/240001054nas a2200097 4500008004300000245006500043210005900108520073200167100002100899856003600920 2006 en_Ud 00aOn a Camassa-Holm type equation with two dependent variables0 aCamassaHolm type equation with two dependent variables3 aWe consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced in [16]. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures\\non (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and\\nprovide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/172100790nas a2200133 4500008004300000245005400043210005200097520038200149100002200531700002100553700002200574700002400596856003600620 2006 en_Ud 00aN=1 superpotentials from multi-instanton calculus0 aN1 superpotentials from multiinstanton calculus3 aIn this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.1 aFucito, Francesco1 aMorales, Jose F.1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/177300738nas a2200109 4500008004300000245003400043210003400077520044300111100002100554700001700575856003600592 2006 en_Ud 00aQuantisation of bending flows0 aQuantisation of bending flows3 aWe briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\\\\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we consider the quantisation problem of the set of Hamiltonians pertaining to the problem, quite naturally called Bending Hamiltonians, and prove that their commutativity is preserved at the quantum level.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/253700519nas a2200109 4500008004300000245006800043210006300111520016100174100002100335700001700356856003600373 2006 en_Ud 00aOn Separation of Variables for Homogeneous SL(r) Gaudin Systems0 aSeparation of Variables for Homogeneous SLr Gaudin Systems3 aBy means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/253800648nas a2200109 4500008004300000245006600043210005800109520029500167100002100462700001900483856003600502 2005 en_Ud 00aOn the Blow-up for a Discrete Boltzmann Equation in the Plane0 aBlowup for a Discrete Boltzmann Equation in the Plane3 aWe study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/224400711nas a2200109 4500008004300000245009600043210006900139520031700208100002100525700001900546856003600565 2005 en_Ud 00aGel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited0 aGelfandZakharevich Systems and Algebraic Integrability the Volte3 aIn this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/168900958nas a2200121 4500008004300000245009200043210006900135520053000204100002400734700002000758700002200778856003600800 2005 en_Ud 00aGround states of nonlinear Schroedinger equations with potentials vanishing at infinity0 aGround states of nonlinear Schroedinger equations with potential3 aWe deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.1 aAmbrosetti, Antonio1 aFelli, Veronica1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/235201006nas a2200133 4500008004300000245007100043210006900114520056200183100002200745700002900767700002000796700002000816856003600836 2005 en_Ud 00aIonization for Three Dimensional Time-dependent Point Interactions0 aIonization for Three Dimensional Timedependent Point Interaction3 aWe study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aMantile, Andrea uhttp://hdl.handle.net/1963/229700982nas a2200109 4500008004300000245008000043210006900123520060400192100002100796700001900817856003600836 2005 en_Ud 00aAn Optimal Transportation Metric for Solutions of the Camassa-Holm Equation0 aOptimal Transportation Metric for Solutions of the CamassaHolm E3 aIn this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/171900706nas a2200121 4500008004300000245005300043210005300096520033400149100002100483700002500504700001900529856003600548 2005 en_Ud 00aQuasistatic Crack Growth in Nonlinear Elasticity0 aQuasistatic Crack Growth in Nonlinear Elasticity3 aIn this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/229300908nas a2200145 4500008004300000245010400043210007000147260001300217520040600230100002000636700002900656700002000685700002100705856003600726 2004 en_Ud 00aBlow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity0 aBlowup solutions for the Schrödinger equation in dimension three bElsevier3 aWe present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions.1 aAdami, Riccardo1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/299800797nas a2200121 4500008004300000245007900043210006900122520038600191100002200577700002100599700001900620856003600639 2004 en_Ud 00aA geometric approach to the separability of the Neumann-Rosochatius system0 ageometric approach to the separability of the NeumannRosochatius3 aWe study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.1 aBartocci, Claudio1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/254101010nas a2200145 4500008004300000245005800043210005800101260001300159520057100172100002100743700001900764700002000783700002500803856003600828 2004 en_Ud 00aHigher order quasiconvexity reduces to quasiconvexity0 aHigher order quasiconvexity reduces to quasiconvexity bSpringer3 aIn this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/291100759nas a2200121 4500008004300000245007800043210006900121520034600190100002100536700002500557700001900582856003600601 2004 en_Ud 00aQuasi-static evolution in brittle fracture: the case of bounded solutions0 aQuasistatic evolution in brittle fracture the case of bounded so3 aThe main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/222900859nas a2200121 4500008004300000245007000043210006900113260001300182520046800195100001600663700002200679856003600701 2004 en_Ud 00aSuperlocalization formulas and supersymmetric Yang-Mills theories0 aSuperlocalization formulas and supersymmetric YangMills theories bElsevier3 aBy using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.1 aBruzzo, Ugo1 aFucito, Francesco uhttp://hdl.handle.net/1963/288600496nas a2200109 4500008004100000245017800041210006900219260001800288100002100306700002300327856003600350 2003 en d00aAutonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations0 aAutonomous integral functionals with discontinous nonconvex inte bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/162501156nas a2200121 4500008004300000245006500043210006400108260001900172520076900191100002100960700001700981856003600998 2003 en_Ud 00aGaudin models and bending flows: a geometrical point of view0 aGaudin models and bending flows a geometrical point of view bIOP Publishing3 aIn this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/288401197nas a2200121 4500008004300000245012700043210006900170260001300239520074500252100002200997700002001019856003601039 2003 en_Ud 00aMotion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group0 aMotion on submanifolds of noninvariant holonomic constraints for bElsevier3 aFor a control system on a matrix Lie group with one or more configuration constraints that are not left/right invariant, finding the combinations of (kinematic) control inputs satisfying the motion constraints is not a trivial problem. Two methods, one coordinate-dependent and the other coordinate-free are suggested. The first is based on the Wei-Norman formula; the second on the calculation of the annihilator of the coadjoint action of the constraint one-form at each point of the group manifold. The results are applied to a control system on SE(3) with a holonomic inertial constraint involving the noncommutative part in a nontrivial way. The difference in terms of compactness of the result between the two methods is considerable.1 aAltafini, Claudio1 aFrezza, Ruggero uhttp://hdl.handle.net/1963/301800423nas a2200133 4500008004100000245005600041210005500097260001800152100001600170700002100186700002200207700002400229856003600253 2003 en d00aMulti-instanton calculus and equivariant cohomology0 aMultiinstanton calculus and equivariant cohomology bSISSA Library1 aBruzzo, Ugo1 aMorales, Jose F.1 aFucito, Francesco1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/164500961nas a2200109 4500008004300000245006400043210006200107260001000169520061500179100002100794856003600815 2003 en_Ud 00aPoisson Pencils, Integrability, and Separation of Variables0 aPoisson Pencils Integrability and Separation of Variables bSISSA3 aIn this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \\\\bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/302600998nas a2200121 4500008004100000245005500041210005400096260001800150520063200168100002100800700001900821856003600840 2003 en d00aSeparation of variables for Bi-Hamiltonian systems0 aSeparation of variables for BiHamiltonian systems bSISSA Library3 aWe address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/159800365nas a2200109 4500008004100000245006500041210005500106260001800161100002100179700001900200856003600219 2002 en d00aOn a Poisson reduction for Gel\\\'fand-Zakharevich manifolds0 aPoisson reduction for GelfandZakharevich manifolds bSISSA Library1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/160200417nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700001900240856003600259 2001 en d00aBihamiltonian geometry and separation of variables for Toda lattices0 aBihamiltonian geometry and separation of variables for Toda latt bSISSA Library1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco uhttp://hdl.handle.net/1963/135400848nas a2200109 4500008004300000245006600043210006600109260001900175520048700194100002100681856003600702 2001 en_Ud 00aLax representation and Poisson geometry of the Kowalevski top0 aLax representation and Poisson geometry of the Kowalevski top bIOP Publishing3 aWe discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel\\\'fand-Zakharevich bi-Hamiltonian setting for integrable systems.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/324400437nas a2200133 4500008004100000245006500041210005600106260001800162100001600180700002200196700002400218700002500242856003600267 2001 en d00aOn the Multi-Instanton Measure for Super Yang-Mills Theories0 aMultiInstanton Measure for Super YangMills Theories bSISSA Library1 aBruzzo, Ugo1 aFucito, Francesco1 aTanzini, Alessandro1 aTravaglini, Gabriele uhttp://hdl.handle.net/1963/153100873nas a2200133 4500008004100000245003800041210003600079260001800115520050900133100002100642700001800663700002200681856003600703 2001 en d00aA note on the super Krichever map0 anote on the super Krichever map bSISSA Library3 aWe consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa`a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian.1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/149401109nas a2200121 4500008004100000245009500041210006900136260001800205520068400223100002100907700002300928856003600951 2001 en d00aUniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations0 aUniqueness of solutions to HamiltonJacobi equations arising in t bSISSA Library3 aWe prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians.1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/151500587nas a2200169 4500008004100000245010300041210006900144260001800213100001900231700001700250700002400267700001800291700002700309700002300336700002200359856003600381 2000 en d00a3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_30 a3D superconformal theories from Sasakian sevenmanifolds new nont bSISSA Library1 aFabbri, Davide1 aFré, Pietro1 aGualtieri, Leonardo1 aReina, Cesare1 aTomasiello, Alessandro1 aZaffaroni, Alberto1 aZampa, Alessandro uhttp://hdl.handle.net/1963/132700454nas a2200133 4500008004100000245007600041210006900117260001800186100002100204700001800225700001900243700002200262856003600284 2000 en d00aA bi-Hamiltonian theory for stationary KDV flows and their separability0 abiHamiltonian theory for stationary KDV flows and their separabi bSISSA Library1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco1 aZubelli, Jorge P. uhttp://hdl.handle.net/1963/135200863nas a2200145 4500008004300000245008500043210006900128260001300197520039100210100002100601700001800622700001900640700002200659856003600681 2000 en_Ud 00aAn elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy0 aelementary approach to the polynomial taufunctions of the KP Hie bSpringer3 aWe give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly.1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco1 aZubelli, Jorge P. uhttp://hdl.handle.net/1963/322300781nas a2200133 4500008004300000245011000043210006900153260001300222520032300235100002100558700001800579700001400597856003600611 2000 en_Ud 00aReduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy0 aReduction of biHamiltonian systems and separation of variables a bSpringer3 aWe discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel\\\'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.1 aFalqui, Gregorio1 aMagri, Franco1 aTondo, G. uhttp://hdl.handle.net/1963/321900914nas a2200133 4500008004300000245007500043210006900118260002100187520047300208100002200681700002200703700001900725856003600744 2000 en_Ud 00aA Remark on One-Dimensional Many-Body Problems with Point Interactions0 aRemark on OneDimensional ManyBody Problems with Point Interactio bWorld Scientific3 aThe integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\\\\delta$-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.1 aAlbeverio, Sergio1 aDabrowski, Ludwik1 aFei, Shao-Ming uhttp://hdl.handle.net/1963/321400454nas a2200121 4500008004100000245010700041210006900148260001800217100002100235700001800256700002200274856003600296 2000 en d00aSuper KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy0 aSuper KP equations and Darboux transformations another perspecti bSISSA Library1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/136700421nas a2200109 4500008004100000245010300041210006900144260001800213100002100231700002300252856003600275 2000 en d00aValue Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities0 aValue Functions for Bolza Problems with Discontinuous Lagrangian bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/151400585nas a2200133 4500008004300000245006900043210006700112260002100179520015700200100002100357700001800378700001900396856003600415 1999 en_Ud 00aA bihamiltonian approach to separation of variables in mechanics0 abihamiltonian approach to separation of variables in mechanics bWorld Scientific3 aThis paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry.1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco uhttp://hdl.handle.net/1963/322201398nas a2200133 4500008004100000245006400041210006000105260001300165520099200178100002101170700001801191700001901209856003601228 1999 en d00aThe method of Poisson pairs in the theory of nonlinear PDEs0 amethod of Poisson pairs in the theory of nonlinear PDEs bSpringer3 aThe aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation.\\nIn these lectures we touch the following subjects:\\ni) the birth and the role of the method of Poisson pairs inside the theory of the KdV equation;\\nii) the theoretical basis of the method of Poisson pairs;\\niii) the Gel\\\'fand-Zakharevich theory of integrable systems on bi-Hamiltonian manifolds;\\niv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold.\\nv) the reduction technique(s) and its use to construct classes of solutions;\\nvi) the role of the technique of separation of variables in the study of the reduced systems;\\nvii) some relations intertwining the method of Poisson pairs with the method of Lax pairs.1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco uhttp://hdl.handle.net/1963/135000417nas a2200121 4500008004100000245007300041210006900114260001800183100001800201700002100219700001900240856003600259 1999 en d00aA note on fractional KDV hierarchies. II. The bihamiltonian approach0 anote on fractional KDV hierarchies II The bihamiltonian approach bSISSA Library1 aCasati, Paolo1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/122000418nas a2200121 4500008004100000245006600041210006600107260001800173100002900191700002000220700002100240856003500261 1998 en d00aDiffusion of a particle in presence of N moving point sources0 aDiffusion of a particle in presence of N moving point sources bSISSA Library1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/13401059nas a2200133 4500008004300000245007500043210007000118260001300188520062700201100002100828700001800849700002200867856003600889 1997 en_Ud 00aKrichever maps, Faà di Bruno polynomials, and cohomology in KP theory0 aKrichever maps Faà di Bruno polynomials and cohomology in KP the bSpringer3 aWe study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/353901073nas a2200133 4500008004100000245003800041210003800079260001800117520069900135100002900834700002000863700002100883856003500904 1997 en d00aStatistics in space dimension two0 aStatistics in space dimension two bSISSA Library3 aWe construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect).1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/13001348nas a2200133 4500008004100000245006700041210006400108260001000172520093800182100002001120700002001140700001801160856003601178 1997 en d00aThree-Phase Solutions of the Kadomtsev - Petviashvili Equation0 aThreePhase Solutions of the Kadomtsev Petviashvili Equation bSISSA3 aThe Kadomtsev]Petviashvili KP. equation is known to admit explicit periodic\\r\\nand quasiperiodic solutions with N independent phases, for any integer\\r\\nN, based on a Riemann theta-function of N variables. For Ns1 and 2,\\r\\nthese solutions have been used successfully in physical applications. This\\r\\narticle addresses mathematical problems that arise in the computation of\\r\\ntheta-functions of three variables and with the corresponding solutions of\\r\\nthe KP equation. We identify a set of parameters and their corresponding\\r\\nranges, such that e¨ery real-valued, smooth KP solution associated with a\\r\\nRiemann theta-function of three variables corresponds to exactly one choice\\r\\nof these parameters in the proper range. Our results are embodied in a\\r\\nprogram that computes these solutions efficiently and that is available to the\\r\\nreader. We also discuss some properties of three-phase solutions.1 aDubrovin, Boris1 aFlickinger, Ron1 aSegur, Harvey uhttp://hdl.handle.net/1963/648400381nas a2200121 4500008004100000245005900041210005900100260001000159100002000169700001600189700001800205856003600223 1994 en d00aIntegrable functional equations and algebraic geometry0 aIntegrable functional equations and algebraic geometry bSISSA1 aDubrovin, Boris1 aFokas, A.S.1 aSantini, P.M. uhttp://hdl.handle.net/1963/648200706nas a2200121 4500008004300000245007200043210006200115260001300177520032100190100001900511700001800530856003600548 1993 en_Ud 00aA Borel-Weil-Bott approach to representations of {\rm sl}\sb q(2,C)0 aBorelWeilBott approach to representations of rm sl sb q2C bSpringer3 aWe use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

1 aFranco, Davide1 aReina, Cesare uhttp://hdl.handle.net/1963/353800404nas a2200121 4500008004100000245006200041210006000103260001800163100002100181700002000202700002500222856003500247 1991 en d00aA class of absolute retracts of dwarf spheroidal galaxies0 aclass of absolute retracts of dwarf spheroidal galaxies bSISSA Library1 aBressan, Alberto1 aCellina, Arrigo1 aFryszkowski, Andrzej uhttp://hdl.handle.net/1963/83700394nas a2200109 4500008004100000245008600041210006900127260001000196653002100206100002100227856003600248 1990 en d00aModuli Spaces and Geometrical Aspects of Two-Dimensional Conformal Field Theories0 aModuli Spaces and Geometrical Aspects of TwoDimensional Conforma bSISSA10aAlgebraic curves1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/555200855nas a2200121 4500008004100000245005400041210005300095260003400148520047700182100001800659700002100677856003500698 1990 en d00aN=2 super Riemann surfaces and algebraic geometry0 aN2 super Riemann surfaces and algebraic geometry bAmerican Institute of Physics3 aThe geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems.1 aReina, Cesare1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/80700355nas a2200109 4500008004100000245005700041210005500098260001800153100001800171700002100189856003500210 1990 en d00aA note on the global structure of supermoduli spaces0 anote on the global structure of supermoduli spaces bSISSA Library1 aReina, Cesare1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/80600306nas a2200109 4500008004100000245003200041210003100073260001800104100002100122700001800143856003500161 1988 en d00aSusy-curves and supermoduli0 aSusycurves and supermoduli bSISSA Library1 aFalqui, Gregorio1 aReina, Cesare uhttp://hdl.handle.net/1963/761