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.

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087646515&doi=10.1002%2fcnm.3367&partnerID=40&md5=3713db6d2b8f9d079b5534445621decf ER - TY - JOUR T1 - Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation JF - JOURNAL OF SCIENTIFIC COMPUTING Y1 - 2016 A1 - Rotundo, N. A1 - Kim, T. -Y. A1 - Jiang, W. A1 - Luca Heltai A1 - Fried, E. VL - 69 ER - TY - JOUR T1 - New existence results for the mean field equation on compact surfaces via degree theory JF - Rend. Sem. Mat. Univ. Padova Y1 - 2016 A1 - Aleks Jevnikar VL - 136 ER - TY - JOUR T1 - A note on a multiplicity result for the mean field equation on compact surfaces JF - Advanced Nonlinear Studies Y1 - 2016 A1 - Aleks Jevnikar PB - De Gruyter VL - 16 ER - TY - JOUR T1 - Complexity of Control-Affine Motion Planning JF - SIAM Journal on Control and Optimization Y1 - 2015 A1 - Jean, F. A1 - Dario Prandi AB -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.

VL - 53 UR - https://doi.org/10.1137/130950793 ER - TY - JOUR T1 - A general existence result for the Toda system on compact surfaces JF - Advances in Mathematics Y1 - 2015 A1 - Luca Battaglia A1 - Aleks Jevnikar A1 - Andrea Malchiodi A1 - David Ruiz KW - Geometric PDEs KW - Min–max schemes KW - Variational methods AB -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–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."

VL - 285 UR - http://www.sciencedirect.com/science/article/pii/S0001870815003072 ER - TY - JOUR T1 - A topological join construction and the Toda system on compact surfaces of arbitrary genus JF - Analysis & PDE Y1 - 2015 A1 - Aleks Jevnikar A1 - Kallel, Sadok A1 - Andrea Malchiodi PB - Mathematical Sciences Publishers VL - 8 ER - TY - THES T1 - Variational aspects of Liouville equations and systems Y1 - 2015 A1 - Aleks Jevnikar KW - Toda system PB - SISSA N1 - The PHD thesis is composed of 112 pages and is recorded in PDF format U1 - 34676 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription Y1 - 2014 A1 - Rod R. Gover A1 - Yaiza Canzani A1 - Dmitry Jakobson A1 - Raphaël Ponge A1 - Andrea Malchiodi AB - 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'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. PB - Oxford University Press UR - http://urania.sissa.it/xmlui/handle/1963/35128 U1 - 35366 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - An improvement on geometrical parameterizations by transfinite maps JF - Comptes Rendus Mathematique Y1 - 2014 A1 - Jäggli, C. A1 - Laura Iapichino A1 - Gianluigi Rozza AB - 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. VL - 352 ER - TY - JOUR T1 - Semiclassical limit of focusing NLS for a family of square barrier initial data Y1 - 2014 A1 - Robert Jenkins A1 - Kenneth McLaughlin AB - The small dispersion limit of the focusing nonlinear Schrödinger 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. PB - Wiley Periodicals UR - http://urania.sissa.it/xmlui/handle/1963/35066 U1 - 35301 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics Y1 - 2013 A1 - Aleks Jevnikar PB - Royal Society of Edinburgh Scotland Foundation VL - 143 ER - TY - JOUR T1 - Vertices, vortices & interacting surface operators JF - JHEP 06(2012)178 Y1 - 2012 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Zhao Jian AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/4134 N1 - 22 pages, 4 figures U1 - 3874 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry JF - Journal of Dynamical and Control Systems Y1 - 2011 A1 - Bernard Bonnard A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Gabriel Janin AB -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.

PB - Springer VL - 17 UR - http://hdl.handle.net/1963/4914 U1 - 4692 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Decoupling A and B model in open string theory: topological adventures in the world of tadpoles JF - JHEP 06 (2009) 046 Y1 - 2009 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini A1 - Yang Jie AB - 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. UR - http://hdl.handle.net/1963/3632 U1 - 672 U2 - Physics U3 - Mathematical Physics ER - TY - RPRT T1 - BV instability for the Lax-Friedrichs scheme Y1 - 2007 A1 - Paolo Baiti A1 - Alberto Bressan A1 - Helge Kristian Jenssen AB - 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. UR - http://hdl.handle.net/1963/2335 U1 - 1681 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An instability of the Godunov scheme JF - Comm. Pure Appl. Math. 59 (2006) 1604-1638 Y1 - 2006 A1 - Alberto Bressan A1 - Helge Kristian Jenssen A1 - Paolo Baiti AB - 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. UR - http://hdl.handle.net/1963/2183 U1 - 2061 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the spreading of characteristics for non-convex conservation laws JF - Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 Y1 - 2001 A1 - Helge Kristian Jenssen A1 - Carlo Sinestrari AB - 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 Hölder 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. PB - Cambridge University Press UR - http://hdl.handle.net/1963/3265 U1 - 1436 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence of Godunov scheme for nonlinear hyperbolic systems JF - Chinese Ann. Math. B, 2000, 21, 269 Y1 - 2000 A1 - Alberto Bressan A1 - Helge Kristian Jenssen PB - SISSA Library UR - http://hdl.handle.net/1963/1473 U1 - 2690 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Blowup asymptotics for scalar conservation laws with a source JF - Comm. in Partial Differential Equations 24 (1999) 2237-2261 Y1 - 1999 A1 - Helge Kristian Jenssen A1 - Carlo Sinestrari PB - Taylor and Francis UR - http://hdl.handle.net/1963/3482 U1 - 782 U2 - Mathematics U3 - Functional Analysis and Applications ER -