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.

%B International Journal for Numerical Methods in Biomedical Engineering %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087646515&doi=10.1002%2fcnm.3367&partnerID=40&md5=3713db6d2b8f9d079b5534445621decf %R 10.1002/cnm.3367 %0 Journal Article %J JOURNAL OF SCIENTIFIC COMPUTING %D 2016 %T Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation %A Rotundo, N. %A Kim, T. -Y. %A Jiang, W. %A Luca Heltai %A Fried, E. %B JOURNAL OF SCIENTIFIC COMPUTING %V 69 %P 430–459 %G eng %R 10.1007/s10915-016-0201-1 %0 Journal Article %J Rend. Sem. Mat. Univ. Padova %D 2016 %T New existence results for the mean field equation on compact surfaces via degree theory %A Aleks Jevnikar %B Rend. Sem. Mat. Univ. Padova %V 136 %P 11–17 %G eng %R 10.4171/RSMUP/136-2 %0 Journal Article %J Advanced Nonlinear Studies %D 2016 %T A note on a multiplicity result for the mean field equation on compact surfaces %A Aleks Jevnikar %B Advanced Nonlinear Studies %I De Gruyter %V 16 %P 221–229 %G eng %R 10.1515/ans-2015-5009 %0 Journal Article %J SIAM Journal on Control and Optimization %D 2015 %T Complexity of Control-Affine Motion Planning %A Jean, F. %A Dario Prandi %XIn 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.

%B SIAM Journal on Control and Optimization %V 53 %P 816-844 %G eng %U https://doi.org/10.1137/130950793 %R 10.1137/130950793 %0 Journal Article %J Advances in Mathematics %D 2015 %T A general existence result for the Toda system on compact surfaces %A Luca Battaglia %A Aleks Jevnikar %A Andrea Malchiodi %A David Ruiz %K Geometric PDEs %K Min–max schemes %K Variational methods %XIn 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."

%B Advances in Mathematics %V 285 %P 937 - 979 %G eng %U http://www.sciencedirect.com/science/article/pii/S0001870815003072 %R https://doi.org/10.1016/j.aim.2015.07.036 %0 Journal Article %J Analysis & PDE %D 2015 %T A topological join construction and the Toda system on compact surfaces of arbitrary genus %A Aleks Jevnikar %A Kallel, Sadok %A Andrea Malchiodi %B Analysis & PDE %I Mathematical Sciences Publishers %V 8 %P 1963–2027 %G eng %R 10.2140/apde.2015.8.1963 %0 Thesis %D 2015 %T Variational aspects of Liouville equations and systems %A Aleks Jevnikar %K Toda system %I SISSA %G en %1 34676 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by ajevnika@sissa.it (ajevnika@sissa.it) on 2015-08-08T16:04:38Z No. of bitstreams: 1 tesi phd.pdf: 1034249 bytes, checksum: 6988a3a6220b4d1bbd38c3124f520655 (MD5) %0 Journal Article %D 2014 %T Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription %A Rod R. Gover %A Yaiza Canzani %A Dmitry Jakobson %A Raphaël Ponge %A Andrea Malchiodi %X 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. %I Oxford University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35128 %1 35366 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:09:57Z No. of bitstreams: 1 preprint2014.pdf: 356671 bytes, checksum: 20e817f9f20d9c72d717e04f94f86bd9 (MD5) %R 10.1093/imrn/rns295 %0 Journal Article %J Comptes Rendus Mathematique %D 2014 %T An improvement on geometrical parameterizations by transfinite maps %A Jäggli, C. %A Laura Iapichino %A Gianluigi Rozza %X 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. %B Comptes Rendus Mathematique %V 352 %P 263–268 %G eng %R 10.1016/j.crma.2013.12.017 %0 Journal Article %D 2014 %T Semiclassical limit of focusing NLS for a family of square barrier initial data %A Robert Jenkins %A Kenneth McLaughlin %X 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. %I Wiley Periodicals %G en %U http://urania.sissa.it/xmlui/handle/1963/35066 %1 35301 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-30T14:57:14Z No. of bitstreams: 1 preprint2014.pdf: 5320973 bytes, checksum: 457b6c96cf2335a7c55084d85eed3dbc (MD5) %R 10.1002/cpa.21494 %0 Journal Article %J Proceedings of the Royal Society of Edinburgh: Section A Mathematics %D 2013 %T An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime %A Aleks Jevnikar %B Proceedings of the Royal Society of Edinburgh: Section A Mathematics %I Royal Society of Edinburgh Scotland Foundation %V 143 %P 1021–1045 %G eng %R 10.1017/S030821051200042X %0 Journal Article %J JHEP 06(2012)178 %D 2012 %T Vertices, vortices & interacting surface operators %A Giulio Bonelli %A Alessandro Tanzini %A Zhao Jian %X 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. %B JHEP 06(2012)178 %I SISSA %G en %U http://hdl.handle.net/1963/4134 %1 3874 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T08:59:30Z\\r\\nNo. of bitstreams: 1\\r\\n1102.0184v1.pdf: 250685 bytes, checksum: b0209b95cc58d31e3cd28c41cd8b0f25 (MD5) %R 10.1007/JHEP06(2012)178 %0 Journal Article %J Journal of Dynamical and Control Systems %D 2011 %T The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry %A Bernard Bonnard %A Grégoire Charlot %A Roberta Ghezzi %A Gabriel Janin %XWe 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.

%B Journal of Dynamical and Control Systems %I Springer %V 17 %P 141-161 %G en %U http://hdl.handle.net/1963/4914 %1 4692 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T09:38:15Z\\nNo. of bitstreams: 1\\n1009.2612v1.pdf: 263401 bytes, checksum: 0ddf4bcfd9663ee3c0da870233d119bb (MD5) %R 10.1007/s10883-011-9113-4 %0 Journal Article %J JHEP 06 (2009) 046 %D 2009 %T Decoupling A and B model in open string theory: topological adventures in the world of tadpoles %A Giulio Bonelli %A Andrea Prudenziati %A Alessandro Tanzini %A Yang Jie %X 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. %B JHEP 06 (2009) 046 %G en_US %U http://hdl.handle.net/1963/3632 %1 672 %2 Physics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-14T12:10:45Z\\nNo. of bitstreams: 1\\n0905.1286v1.pdf: 335944 bytes, checksum: fe5d3723cd904f1c7123c5bc83356013 (MD5) %R 10.1088/1126-6708/2009/06/046 %0 Report %D 2007 %T BV instability for the Lax-Friedrichs scheme %A Paolo Baiti %A Alberto Bressan %A Helge Kristian Jenssen %X 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. %G en_US %U http://hdl.handle.net/1963/2335 %1 1681 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-05T09:55:21Z\\nNo. of bitstreams: 1\\n0502043v1.pdf: 257155 bytes, checksum: 5055aa260394ac1339fa775b656f3b15 (MD5) %0 Journal Article %J Comm. Pure Appl. Math. 59 (2006) 1604-1638 %D 2006 %T An instability of the Godunov scheme %A Alberto Bressan %A Helge Kristian Jenssen %A Paolo Baiti %X 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. %B Comm. Pure Appl. Math. 59 (2006) 1604-1638 %G en_US %U http://hdl.handle.net/1963/2183 %1 2061 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T07:52:50Z\\nNo. of bitstreams: 1\\n0502125v1.pdf: 337578 bytes, checksum: 41193faac363c00e9f80d6c05c0b098c (MD5) %R 10.1002/cpa.20141 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %D 2001 %T On the spreading of characteristics for non-convex conservation laws %A Helge Kristian Jenssen %A Carlo Sinestrari %X 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. %B Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %I Cambridge University Press %G en_US %U http://hdl.handle.net/1963/3265 %1 1436 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-10T13:53:07Z\\nNo. of bitstreams: 1\\nJS2.pdf: 302742 bytes, checksum: 563821a822c34aef0ca1b4c55065827c (MD5) %R 10.1017/S0308210500001189 %0 Journal Article %J Chinese Ann. Math. B, 2000, 21, 269 %D 2000 %T On the convergence of Godunov scheme for nonlinear hyperbolic systems %A Alberto Bressan %A Helge Kristian Jenssen %B Chinese Ann. Math. B, 2000, 21, 269 %I SISSA Library %G en %U http://hdl.handle.net/1963/1473 %1 2690 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:54Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Journal Article %J Comm. in Partial Differential Equations 24 (1999) 2237-2261 %D 1999 %T Blowup asymptotics for scalar conservation laws with a source %A Helge Kristian Jenssen %A Carlo Sinestrari %B Comm. in Partial Differential Equations 24 (1999) 2237-2261 %I Taylor and Francis %G en_US %U http://hdl.handle.net/1963/3482 %1 782 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-04T09:24:17Z\\nNo. of bitstreams: 1\\nJenssen_Sinestrari.pdf: 273573 bytes, checksum: 309317a9fa20bd7a5c05c98b059384b8 (MD5) %R 10.1080/03605309908821500