@article {JS21, title = {Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants}, journal = {Ann. Fenn. Math.}, volume = {46}, number = {2}, year = {2021}, pages = {1071{\textendash}1087}, doi = {10.5186/aasfm.2021.4666}, author = {Julin, V. and Saracco, G.} } @booklet {HunJexLan20-Potential, title = {Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; Critical Potentials and dimensionality}, howpublished = {arXiv:2107.14128}, year = {2021}, pages = {8}, author = {Dirk Hundertmark and Michal Jex and Markus Lange} } @booklet {HunJexLan-PhysRev, title = {Quantum Systems at The Brink: Properties of Atomic Bound States at The Ionization Threshold}, year = {2020}, author = {Dirk Hundertmark and Michal Jex and Markus Lange} } @article {2020, title = {Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation}, journal = {International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng}, volume = {n/a}, year = {2020}, month = {2020/05/27}, pages = {e3367}, abstract = {

Abstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

}, keywords = {coronary artery bypass grafts, data assimilation, flow control, Galerkin methods, hemodynamics modeling, Optimization, patient-specific simulations, Proper orthogonal decomposition, reduced order methods}, isbn = {2040-7939}, doi = {https://doi.org/10.1002/cnm.3367}, url = {https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R}, author = {Zakia Zainib and F. Ballarin and Stephen E. Fremes and Piero Triverio and Laura Jim{\'e}nez-Juan and Gianluigi Rozza} } @booklet {HunJexLan19-Helium, title = {Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; Helium}, howpublished = {arXiv:1908.04883}, year = {2019}, pages = {25}, author = {Dirk Hundertmark and Michal Jex and Markus Lange} } @booklet {HunJexLan19-NAtom, title = {Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; Atoms}, howpublished = {arXiv:1908.05016}, year = {2019}, pages = {14}, author = {Dirk Hundertmark and Michal Jex and Markus Lange} } @article {MR3478183, title = {Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes}, journal = {Appl. Numer. Math.}, volume = {104}, year = {2016}, pages = {3{\textendash}14}, issn = {0168-9274}, doi = {10.1016/j.apnum.2014.06.007}, url = {https://doi.org/10.1016/j.apnum.2014.06.007}, author = {Andrea Cangiani and E.H. Georgoulis and Jensen, Max} } @article {20.500.11767_11949, title = {Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation}, journal = {JOURNAL OF SCIENTIFIC COMPUTING}, volume = {69}, year = {2016}, pages = {430{\textendash}459}, doi = {10.1007/s10915-016-0201-1}, author = {Rotundo, N. and Kim, T. -Y. and Jiang, W. and Luca Heltai and Fried, E.} } @article {jevnikar_2016, title = {New existence results for the mean field equation on compact surfaces via degree theory}, journal = {Rend. Sem. Mat. Univ. Padova}, volume = {136}, year = {2016}, pages = {11{\textendash}17}, doi = {10.4171/RSMUP/136-2}, author = {Aleks Jevnikar} } @article {jevnikar2016note, title = {A note on a multiplicity result for the mean field equation on compact surfaces}, journal = {Advanced Nonlinear Studies}, volume = {16}, year = {2016}, pages = {221{\textendash}229}, publisher = {De Gruyter}, doi = {10.1515/ans-2015-5009}, author = {Aleks Jevnikar} } @article {doi:10.1137/130950793, title = {Complexity of Control-Affine Motion Planning}, journal = {SIAM Journal on Control and Optimization}, volume = {53}, number = {2}, year = {2015}, pages = {816-844}, abstract = {

In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

}, doi = {10.1137/130950793}, url = {https://doi.org/10.1137/130950793}, author = {Jean, F. and Dario Prandi} } @article {BATTAGLIA2015937, title = {A general existence result for the Toda system on compact surfaces}, journal = {Advances in Mathematics}, volume = {285}, year = {2015}, pages = {937 - 979}, abstract = {

In this paper we consider the following Toda system of equations on a compact surface:-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-Δu1=-4π∑j=1mα1,j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-Δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern{\textendash}Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation-Δu=ρ1(heu∫ΣheudVg-1)-ρ2(he-u∫Σhe-udVg-1), which arises in fluid dynamics."

}, keywords = {Geometric PDEs, Min{\textendash}max schemes, Variational methods}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2015.07.036}, url = {http://www.sciencedirect.com/science/article/pii/S0001870815003072}, author = {Luca Battaglia and Aleks Jevnikar and Andrea Malchiodi and David Ruiz} } @article {jevnikar2015topological, title = {A topological join construction and the Toda system on compact surfaces of arbitrary genus}, journal = {Analysis \& PDE}, volume = {8}, number = {8}, year = {2015}, pages = {1963{\textendash}2027}, publisher = {Mathematical Sciences Publishers}, doi = {10.2140/apde.2015.8.1963}, author = {Aleks Jevnikar and Kallel, Sadok and Andrea Malchiodi} } @mastersthesis {2015, title = {Variational aspects of Liouville equations and systems}, year = {2015}, note = {The PHD thesis is composed of 112 pages and is recorded in PDF format}, school = {SISSA}, keywords = {Toda system}, author = {Aleks Jevnikar} } @article {2014, title = {Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription}, number = {International Mathematics Research Notices;volume 2014; issue 9; pages 2356-2400;}, year = {2014}, publisher = {Oxford University Press}, abstract = {In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant{\textquoteright}s Nodal Domain Theorem. We also show that on any manifold of dimension n>=3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n>=3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.}, doi = {10.1093/imrn/rns295}, url = {http://urania.sissa.it/xmlui/handle/1963/35128}, author = {Rod R. Gover and Yaiza Canzani and Dmitry Jakobson and Rapha{\"e}l Ponge and Andrea Malchiodi} } @article {JaggliIapichinoRozza2014, title = {An improvement on geometrical parameterizations by transfinite maps}, journal = {Comptes Rendus Mathematique}, volume = {352}, number = {3}, year = {2014}, pages = {263{\textendash}268}, abstract = {We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.}, doi = {10.1016/j.crma.2013.12.017}, author = {J{\"a}ggli, C. and Laura Iapichino and Gianluigi Rozza} } @article {MR3218334, title = {On local super-penalization of interior penalty discontinuous Galerkin methods}, journal = {Int. J. Numer. Anal. Model.}, volume = {11}, number = {3}, year = {2014}, pages = {478{\textendash}495}, issn = {1705-5105}, author = {Andrea Cangiani and Chapman, John and E.H. Georgoulis and Jensen, Max} } @article {2014, title = {Semiclassical limit of focusing NLS for a family of square barrier initial data}, number = {Communications on Pure and Applied Mathematics;volume 67; issue 2; pages 246-320;}, year = {2014}, publisher = {Wiley Periodicals}, abstract = {The small dispersion limit of the focusing nonlinear Schr{\"o}dinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.}, doi = {10.1002/cpa.21494}, url = {http://urania.sissa.it/xmlui/handle/1963/35066}, author = {Robert Jenkins and Kenneth McLaughlin} } @article {MR3121762, title = {Discontinuous Galerkin methods for mass transfer through semipermeable membranes}, journal = {SIAM J. Numer. Anal.}, volume = {51}, number = {5}, year = {2013}, pages = {2911{\textendash}2934}, issn = {0036-1429}, doi = {10.1137/120890429}, url = {https://doi.org/10.1137/120890429}, author = {Andrea Cangiani and E.H. Georgoulis and Jensen, Max} } @article {jevnikar_2013, title = {An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime}, journal = {Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, volume = {143}, number = {5}, year = {2013}, pages = {1021{\textendash}1045}, publisher = {Royal Society of Edinburgh Scotland Foundation}, doi = {10.1017/S030821051200042X}, author = {Aleks Jevnikar} } @inbook {MR3307565, title = {Implementation of the continuous-discontinuous Galerkin finite element method}, booktitle = {Numerical mathematics and advanced applications 2011}, year = {2013}, pages = {315{\textendash}322}, publisher = {Springer, Heidelberg}, organization = {Springer, Heidelberg}, author = {Andrea Cangiani and Chapman, J. and E.H. Georgoulis and Jensen, M.} } @article {MR3108752, title = {On the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problems}, journal = {J. Sci. Comput.}, volume = {57}, number = {2}, year = {2013}, pages = {313{\textendash}330}, issn = {0885-7474}, doi = {10.1007/s10915-013-9707-y}, url = {https://doi.org/10.1007/s10915-013-9707-y}, author = {Andrea Cangiani and Chapman, John and E.H. Georgoulis and Jensen, Max} } @article {2012, title = {Vertices, vortices \& interacting surface operators}, journal = {JHEP 06(2012)178}, number = {SISSA;03/2011/FM-EP}, year = {2012}, note = {22 pages, 4 figures}, publisher = {SISSA}, abstract = {We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.}, doi = {10.1007/JHEP06(2012)178}, url = {http://hdl.handle.net/1963/4134}, author = {Giulio Bonelli and Alessandro Tanzini and Zhao Jian} } @article {2011, title = {The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry}, journal = {Journal of Dynamical and Control Systems }, volume = {17 }, number = {arXiv:1009.2612;}, year = {2011}, pages = {141-161}, publisher = {Springer}, abstract = {

We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

}, doi = {10.1007/s10883-011-9113-4}, url = {http://hdl.handle.net/1963/4914}, author = {Bernard Bonnard and Gr{\'e}goire Charlot and Roberta Ghezzi and Gabriel Janin} } @article {2009, title = {Decoupling A and B model in open string theory: topological adventures in the world of tadpoles}, journal = {JHEP 06 (2009) 046}, number = {SISSA;26/2009/FM-EP}, year = {2009}, abstract = {In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula.}, doi = {10.1088/1126-6708/2009/06/046}, url = {http://hdl.handle.net/1963/3632}, author = {Giulio Bonelli and Andrea Prudenziati and Alessandro Tanzini and Yang Jie} } @article {2007, title = {BV instability for the Lax-Friedrichs scheme}, number = {SISSA;100/2004/M}, year = {2007}, abstract = {It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.}, url = {http://hdl.handle.net/1963/2335}, author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen} } @article {2006, title = {An instability of the Godunov scheme}, journal = {Comm. Pure Appl. Math. 59 (2006) 1604-1638}, number = {arXiv.org;math/0502125v1}, year = {2006}, abstract = {We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.}, doi = {10.1002/cpa.20141}, url = {http://hdl.handle.net/1963/2183}, author = {Alberto Bressan and Helge Kristian Jenssen and Paolo Baiti} } @article {2001, title = {On the spreading of characteristics for non-convex conservation laws}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925}, year = {2001}, publisher = {Cambridge University Press}, abstract = {We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an H{\"o}lder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution.}, doi = {10.1017/S0308210500001189}, url = {http://hdl.handle.net/1963/3265}, author = {Helge Kristian Jenssen and Carlo Sinestrari} } @article {2000, title = {On the convergence of Godunov scheme for nonlinear hyperbolic systems}, journal = {Chinese Ann. Math. B, 2000, 21, 269}, number = {SISSA;15/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1473}, author = {Alberto Bressan and Helge Kristian Jenssen} } @article {1999, title = {Blowup asymptotics for scalar conservation laws with a source}, journal = {Comm. in Partial Differential Equations 24 (1999) 2237-2261}, number = {SISSA;91/97/M}, year = {1999}, publisher = {Taylor and Francis}, doi = {10.1080/03605309908821500}, url = {http://hdl.handle.net/1963/3482}, author = {Helge Kristian Jenssen and Carlo Sinestrari} }