BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cintia Pacchiano (Aalto University Helsinki) DTSTART;VALUE=DATE-TIME:20200702T101500Z DTEND;VALUE=DATE-TIME:20200702T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/1 DESCRIPTION:Title: Var iational solutions to the total variation ﬂow on metric measure spaces\nby Cintia Pacchiano (Aalto University Helsinki) as part of EDDy weekly seminar\n\n\nAbstract\nIn this talk I will discuss some aspects of the po tential theory\, ﬁne properties and boundary behaviour of the solutions to the Total Variation Flow. Instead of the classical Euclidean setting\, we intend to work mostly in the general setting of metric measure spaces. During the past two decades\, a theory of Sobolev functions and BV functio ns has been developed in this abstract setting. A central motivation for d eveloping such a theory has been the desire to unify the assumptions and m ethods employed in various speciﬁc spaces\, such as weighted Euclidean s paces\, Riemannian manifolds\, Heisenberg groups\, graphs\, etc. The total variation ﬂow can be understood as a process diminishing the total vari ation using the gradient descent method. This idea can be reformulated usi ng parabolic minimizers\, and it gives rise to a deﬁnition of variationa l solutions. The advantages of the approach using a minimization formulati on include much better convergence and stability properties. This is a ver y essential advantage as the solutions naturally lie only in the space of BV functions. Our main goal is to give a necessary and suﬃcient conditio n for continuity at a given point for proper solutions to the total variat ion ﬂow in metric spaces. \n\nThis is joint work with Vito Buﬀa and Ju ha Kinnunen.\n LOCATION:https://researchseminars.org/talk/EDDy/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Philipp Reiter (Martin-Luther-University Halle-Wittenberg) DTSTART;VALUE=DATE-TIME:20200707T081500Z DTEND;VALUE=DATE-TIME:20200707T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/2 DESCRIPTION:Title: A b ending‐twist model for elastic rods\nby Philipp Reiter (Martin-Luthe r-University Halle-Wittenberg) as part of EDDy weekly seminar\n\n\nAbstrac t\nFocussing on models of springy wires\, we study framed curves whose evo lution is driven both by the bending energy and the twisting energy. The l atter tracks the rotation of the frame about the centerline of the curve. In order to prevent topology changes during the evolution\, we add a self ‐avoiding term\, namely the tangent‐point energy. We discuss the discr etization of this model and present some numerical simulations. \n\nThis i s joint work with Sören Bartels.\n LOCATION:https://researchseminars.org/talk/EDDy/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Amina Mecherbet (Sorbonne Université Paris) DTSTART;VALUE=DATE-TIME:20200716T101500Z DTEND;VALUE=DATE-TIME:20200716T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/4 DESCRIPTION:Title: On the correction to Einstein's formula for the effective viscosity\nby A mina Mecherbet (Sorbonne Université Paris) as part of EDDy weekly seminar \n\n\nAbstract\nWe consider the problem of the derivation of an effective model for viscous dilute suspensions. A previous work by D. Gérard-Varet and M. Hillairet showed that\, if a second order Stokes effective approxim ation exists then the mean value of the second order correction for the ef fective viscosity is given by a mean-field limit that can be studied and c omputed under further assumptions on the particle configurations. We exten d this result by identifying the second order correction in the general ca se and show the convergence to the limit effective model as soon as the me an field limit exists. In particular we recover the mean-field analysis co nsidered by D. Gérard-Varet and M. Hillairet in their paper for the homog eneous case of periodic and random stationary particle configurations. \n\ nThis is a joint work with D. Gérard-Varet.\n LOCATION:https://researchseminars.org/talk/EDDy/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Sattig (University of Leipzig) DTSTART;VALUE=DATE-TIME:20200618T101500Z DTEND;VALUE=DATE-TIME:20200618T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/5 DESCRIPTION:Title: Non -Uniqueness for the Transport equation and ODEs with rough Coefficients\nby Gabriel Sattig (University of Leipzig) as part of EDDy weekly semina r\n\n\nAbstract\nIn this talk I will recall the classic theory of transpor t equations due to DiPerna\, P.-L. Lions and Ambrosio and then show to rec ent result on ill-posedness in the case that the DiPerna-Lions integrabili ty condition fails. Using the classic theory and recent extensions of it I will show how this result implies the failure of almost-everywhere-unique ness for ODEs with Sobolev coefficients. \n\nJoint work with S. Modena and L. Székelyhidi.\n LOCATION:https://researchseminars.org/talk/EDDy/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sascha Knüttel (Technische Universität Dortmund) DTSTART;VALUE=DATE-TIME:20200625T101500Z DTEND;VALUE=DATE-TIME:20200625T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/6 DESCRIPTION:Title: New diffuse Approximations of the Willmore Energy\nby Sascha Knüttel (Te chnische Universität Dortmund) as part of EDDy weekly seminar\n\n\nAbstra ct\nI will talk about a new phase ﬁeld approximation of the Willmore ene rgy. I start from a diﬀuse perimeter approximation considered by Amstutz -van Goethem and motivate from this an approximation of the Willmore energ y. I show a $\\Gamma$-$\\limsup$ estimate for the approximation and justif y by a formal asymptotic expansion that a corresponding $L^2$-Gradient Flo w converges to the Willmore Flow. I will also consider another model propo sed by Karali-Katsoulakis and motivate an approximation of the Willmore en ergy based on it. I will outline the similarities between the models conce rning the formal asymptotics of the $L^2$-Gradient Flow. \n\nJoint work wi th M. Röger\, TU Dortmund.\n LOCATION:https://researchseminars.org/talk/EDDy/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Klingenberg (University of Wuerzburg) DTSTART;VALUE=DATE-TIME:20201015T080000Z DTEND;VALUE=DATE-TIME:20201015T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/7 DESCRIPTION:Title: Fin ding solutions of the multi-dimensional compressible Euler equations\n by Christian Klingenberg (University of Wuerzburg) as part of EDDy weekly seminar\n\n\nAbstract\nThis talk will survey some results for the two- or three-space dimensional compressible Euler equations\, results both in the ory and numerics. We shall present $\\\\$\n - non-uniqueness results of weak entropy solutions for special initial data using convex integration $\\\\$\n - introducing solution concepts beyond weak solutions that all ows to show convergence to the incompressible limit of the compressible Eu ler equations with gravity $\\\\$\n - the relationship between stationa ry preservation\, maintaining vorticity\, and asymptotic preserving numeri cal methods $\\\\$\n - introduce a high order numerical method that hol ds promise to achieve this. $\\\\$\n\nThis is joint work among others with Simon Markfelder\, Wasilij Barsukow\, Eduard Feireisl and Phil Roe.\nRefe rences\n\n W. Barsukow\, J. Hohm\, C. Klingenberg\, and P. L. Roe. The active flux scheme on Cartesian grids and its low Mach number limit. Journ al of Scientific Computing 81\, pp. 594–622 (2019)\n\n E. Feireisl\, C. Klingenberg\, O. Kreml\, and S. Markfelder. On oscillatory solutions to the complete Euler equations. Journal of Differential Equations 296 (2)\, pp. 1521-1543 (2020)\n LOCATION:https://researchseminars.org/talk/EDDy/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Mária Lukácová-Medvidová (Johannes Gutenberg University Mainz) DTSTART;VALUE=DATE-TIME:20201105T091500Z DTEND;VALUE=DATE-TIME:20201105T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/8 DESCRIPTION:Title: K-c onvergence of numerical solutions of the Euler equations\nby Mária Lu kácová-Medvidová (Johannes Gutenberg University Mainz) as part of EDDy weekly seminar\n\n\nAbstract\nI present our recent results on the converge nce analysis of suitable finite volume methods for multidimensional Euler equations. We have shown that a sequence of numerical solutions converges weakly to a weak dissipative solution. The analysis requires only the cons istency and stability of a numerical method and can be seen as a generaliz ation of the famous Lax-equivalence theorem for nonlinear problems. The we ak-strong uniqueness principle implies the strong convergence of numerical solutions to the classical solution as long as it exists.\n\nOn the other hand\, if the classical solution does not exist we apply the so-called K- convergence and show how to compute effectively the observable quantities of a space-time parametrized measure generated by numerical solutions. Con sequently\, we derive the strong convergence of the empirical averages of numerical solutions to a weak dissipative solution. If time permits I will illustrate a connection to the concept of statistical convergence.\n LOCATION:https://researchseminars.org/talk/EDDy/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Umberto Hryniewicz (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20201112T091500Z DTEND;VALUE=DATE-TIME:20201112T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/9 DESCRIPTION:Title: Sym plectic Field Theory and topological entropy in Hamiltonian systems\nb y Umberto Hryniewicz (RWTH Aachen University) as part of EDDy weekly semin ar\n\n\nAbstract\nThe concept of topological entropy plays a central role in the modern theory of Dynamical Systems. Originally introduced by Adler\ , Konheim and McAndrew in 1960’s\, it was later reformulated and clarifi ed by work of Rufus Bowen. It has roots in the work of Kolmogorov and Sina i. Positive topological entropy is usually taken as the mathematical defin ition of (topological) chaos\, in fact fundamental results of Katok imply that\, in low dimensions\, positive topological entropy forces the presenc e of horseshoes.\n\nAfter discussing this circle of ideas\, the goal of th is talk will be to understand how variational methods can be used to detec t positive topological entropy in Hamiltonian systems. The prototypical ex ample is that of a geodesic flow on a negatively curved surface. In a seco nd step we will discuss how sophisticated variational methods - which go u nder the umbrella of Symplectic Field Theory and are based on elliptic PDE s - can be used to generalise the same kind of results to larger classes o f Hamiltonian systems.\n LOCATION:https://researchseminars.org/talk/EDDy/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Wolfgang Maurer (Universität Konstanz) DTSTART;VALUE=DATE-TIME:20200730T101500Z DTEND;VALUE=DATE-TIME:20200730T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/10 DESCRIPTION:Title: Cu rvature Bounds for Mean Curvature Flow of Complete Graphical Hypersurfaces \nby Wolfgang Maurer (Universität Konstanz) as part of EDDy weekly se minar\n\n\nAbstract\nWe investigate mean curvature flow of complete graphi cal hypersurfaces. These are complete hypersurfaces that can be written as graphs of functions defined on (bounded) domains and going to infinity at the boundary for completeness. We discuss two different curvature bounds for these flows\, one that works below some arbitrary height and one that works above a certain height and is dependent on the enveloping cylinder. We demonstrate what makes a uniform curvature bound difficult. Moreover\, we give an example that behaves quite badly\, illustrating issues that ari se in this context. Lastly\, we touch upon how one can obtain curvature bo unds beyond singularities in the mean convex case.\n LOCATION:https://researchseminars.org/talk/EDDy/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Albert Wood (University College London) DTSTART;VALUE=DATE-TIME:20200917T111500Z DTEND;VALUE=DATE-TIME:20200917T123000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/11 DESCRIPTION:Title: Si ngularities of Lagrangian Mean Curvature Flow\nby Albert Wood (Univers ity College London) as part of EDDy weekly seminar\n\n\nAbstract\nAfter Ri cci flow\, the mean curvature flow of submanifolds in a Riemannian manifol d is perhaps the most natural and famous geometric flow\, describing the g radient descent for the volume functional. It was therefore an exciting di scovery when Knut Smoczyk demonstrated that in an ambient Ricci-flat Kähl er manifold\, the class of Lagrangian submanifolds is preserved under the flow. This phenomenon is now referred to as Lagrangian mean curvature flow .\n\nLagrangian mean curvature flow has since been shown to have propertie s and behaviour distinct from that of mean curvature flow in general. In t his talk I will focus on the singular behaviour of the flow\, highlight th e differences and similarities to the general case\, and bring attention t o some open conjectures in the field.\n LOCATION:https://researchseminars.org/talk/EDDy/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Creutz (University of Cologne) DTSTART;VALUE=DATE-TIME:20201001T101500Z DTEND;VALUE=DATE-TIME:20201001T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/12 DESCRIPTION:Title: Ar ea minimizing surfaces for singular boundary values\nby Paul Creutz (U niversity of Cologne) as part of EDDy weekly seminar\n\n\nAbstract\nBy a c lassical result of Douglas\, for any given $p\\geq 0$ and configuration $\ \Gamma\\subset \\mathbb{R}^n$ of disjoint Jordan curves there exists an ar ea minimizer among all compact surfaces of genus at most $p$ which span $\ \Gamma$. In the talk we will discuss a generalization of this theorem to s ingular configurations $\\Gamma$ of possibly non-disjoint or self-intersec ting curves. Furthermore\, the talk will contain new existence results for regular configurations $\\Gamma$ in more general ambient spaces such as R iemannian manifolds.\n\nThis is joint work with M. Fitzi.\n LOCATION:https://researchseminars.org/talk/EDDy/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Sascha Eichmann (University Tübingen) DTSTART;VALUE=DATE-TIME:20200806T101500Z DTEND;VALUE=DATE-TIME:20200806T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/13 DESCRIPTION:Title: Ca nham-Helfrich energy and geometric measure theory\nby Sascha Eichmann (University Tübingen) as part of EDDy weekly seminar\n\n\nAbstract\nHelfr ich (1973) and Canham (1970) introduced the following geometric curvature energy to model the shape of human red blood cells. The idea is that the t wo dimensional boundary layer $\\Sigma\\subset\\mathbb{R}^3$ of such a cel l minimises\n$$\n \\int_\\Sigma |H-H_0|^2\\\, dA\n$$\nunder suitable const raints on e.g. the enclosed volume and surface area. Here $H$ is the scala r mean curvature of $\\Sigma$ and $H_0\\in\\mathbb{R}$ is a parameter call ed the spontaneous curvature\, which represents an asymmetry in the bounda ry layer of the cell. This induces a prefered curvature of the cell.\nIf t his asymmetry is not desired\, i.e. $H_0=0$\, this Canham-Helfrich energy becomes a variant of the famous Willmore energy.\nTo show existence of suc h a minimiser\, we will implement the direct method of the calculus of var iations. Compactness for a minimising sequence under varifold convergence can be easily obtained. Unfortunately lower-semicontinuity of the Helfrich energy under this varifold convergence is in general not correct by a cou nterexample of Große-Brauckmann (1993). Nevertheless we can actually show a lower-semicontinuity estimate for the minimising sequence itself.\nThro ughout the talk we will highlight the main tools used from geometric measu re theory. We explain these in some detail and how they are applied to our problem.\nIn the last part of the talk we will discuss some directions fo r future research in this area\, i.e. some open problems and some modifica tions to the Canham-Helfrich energy itself.\n LOCATION:https://researchseminars.org/talk/EDDy/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Reza Pakzad (University of Pittsburgh) DTSTART;VALUE=DATE-TIME:20201126T091500Z DTEND;VALUE=DATE-TIME:20201126T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/14 DESCRIPTION:Title: Th e geometry of weakly regular isometric immersions\nby Reza Pakzad (Uni versity of Pittsburgh) as part of EDDy weekly seminar\n\n\nAbstract\nWe co nsider isometric immersions of 3-dimensional domains into $\\mathbb{R}^3$ at low regularity regimes\, in particular in the case of a flat domain. A notion of second fundamental form can be defined when only $1/2$-fractiona l derivatives of the Gauss map are well-controlled. Through an Analysis of the Codazzi system which - in a sense - survives at $2/3$-fractional diff erentiability\, we can pass to a degenerate Monge-Ampère equation and ext ract valuable geometric information about the rigidity of these isometric immersions. Time permitting\, we will discuss a conjecture of Gromov in th is regard and some connected problems in nonlinear analysis and geometric function theory.\n LOCATION:https://researchseminars.org/talk/EDDy/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Samaey (Katholieke Universiteit Leuven) DTSTART;VALUE=DATE-TIME:20201217T091500Z DTEND;VALUE=DATE-TIME:20201217T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/15 DESCRIPTION:Title: Co upled finite-volume/Monte-Carlo methods for plasma edge simulation in fusi on reactors\nby Giovanni Samaey (Katholieke Universiteit Leuven) as pa rt of EDDy weekly seminar\n\n\nAbstract\nNuclear fusion reactor design cru cially depends on numerical simulation. The plasma can usually be modeled using fluid equations (for mass\, momentum and energy). However\, the reac tor also contains neutral (non-charged) particles (which are important in its operation)\, of which both the position and velocity distribution is i mportant. This leads to a Boltzmann-type transport equation that needs to be discretised with a Monte Carlo method. One then obtains a coupled finit e-volume/Monte-Carlo simulation\, of which the results possess both a bias and a variance. In this talk\, I introduce the problems associated with t he simulation of the plasma edge region in a fusion reactor. I discuss how to couple a finite volume discretisation of the plasma equations with a M onte Carlo simulation of the neutral particles\, and show how the Monte Ca rlo errors affect convergence of steady state computations and reliability of gradient computations (necessary during optimization).\n LOCATION:https://researchseminars.org/talk/EDDy/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolay A. Gusev (Steklov Mathematical Institute) DTSTART;VALUE=DATE-TIME:20201119T091500Z DTEND;VALUE=DATE-TIME:20201119T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/16 DESCRIPTION:Title: On the structure of divergence-free vector measures on the plane\nby Nik olay A. Gusev (Steklov Mathematical Institute) as part of EDDy weekly semi nar\n\n\nAbstract\nThe talk will be devoted to the problem of decomposing a divergence-free vector measure into a family of measures induced by clos ed simple curves. We will discuss applications of such decompositions to r igidity properties of vector measures. Moreover\, we will demonstrate that in the two-dimensional case such decomposition is possible for any diverg ence-free vector measure. Ultimately we will discuss some connections betw een such decompositions and uniqueness of solutions of Cauchy problem for continuity equation. \n\nThe talk will be based on a recent joint work wit h P. Bonicatto.\n LOCATION:https://researchseminars.org/talk/EDDy/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Gladbach (University of Bonn) DTSTART;VALUE=DATE-TIME:20201203T091500Z DTEND;VALUE=DATE-TIME:20201203T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/17 DESCRIPTION:Title: Ho mogenization of continuous and discrete dynamic transport costs\nby Pe ter Gladbach (University of Bonn) as part of EDDy weekly seminar\n\n\nAbst ract\nWe consider the space of solutions to the continuity equation $\\fra c{\\mathrm{d}}{\\mathrm{d}t} u(t\,x)+\\mathrm{div} j(t\,x)=0$ equipped wit h convex action functionals $A(u\,j)$\, which encode microstructure in e.g . porous media or road networks. In the limit over long distances\, we com pute the effective transport cost in terms of Gamma-convergence\, with app lications to the porous media equation.\n LOCATION:https://researchseminars.org/talk/EDDy/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Siegfried Müller (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20210114T091500Z DTEND;VALUE=DATE-TIME:20210114T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/18 DESCRIPTION:Title: Ad aptive multiresolution discontinuous Galerkin schemes for conservation law s\nby Siegfried Müller (RWTH Aachen University) as part of EDDy weekl y seminar\n\n\nAbstract\nSince the solution of hyperbolic conservation law s typically exhibits discontinuities\, efficient numerical schemes will em ploy locally refined discretizations that dynamically adapt to the solutio n. To trigger grid refinement and coarsening an appropriate indicator is n eeded. Due to the lack of a stable variational formulation for the problem at hand\, we apply a multiresolution analysis (MRA) based on multiwavelet s to perform data compression. The MRA is combined with a standard discont inuous Galerkin (DG) scheme to end up with an adaptive DG scheme. The fram ework of both the MRA and the DG scheme will be presented in some detail. The performance of the resulting scheme will be discussed by means of nume rous testcases in 1D and 2D for scalar as well as systems of conservation laws. We conclude with a brief outlook how to employ the adaptive framewor k for the investigation of stochastic conservation laws.\n LOCATION:https://researchseminars.org/talk/EDDy/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Herty (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20210121T091500Z DTEND;VALUE=DATE-TIME:20210121T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/19 DESCRIPTION:Title: Un certainty Quantification of Hyperbolic Problems and its Relation to Entrop y\nby Michael Herty (RWTH Aachen University) as part of EDDy weekly se minar\n\n\nAbstract\nWe will discuss recent results on intrusive stochasti c Galerkin expansion for hyperbolic transport problems with a focus on the role of entropy. Recent results on hyperbolicity and well-posedness of th e expanded hyperbolic systems will be presented and numerical results will be discussed. A focus is on $2\\times2$ nonlinear hyperbolic systems as a ppearing in shallow water or gas flow problems.\n LOCATION:https://researchseminars.org/talk/EDDy/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Samaey (Katholieke Universiteit Leuven) DTSTART;VALUE=DATE-TIME:20210408T081500Z DTEND;VALUE=DATE-TIME:20210408T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/20 DESCRIPTION:Title: Co upled finite-volume/Monte-Carlo methods for plasma edge simulation in fusi on reactors\nby Giovanni Samaey (Katholieke Universiteit Leuven) as pa rt of EDDy weekly seminar\n\n\nAbstract\nNuclear fusion reactor design cru cially depends on numerical simulation. The plasma can usually be modeled using fluid equations (for mass\, momentum and energy). However\, the reac tor also contains neutral (non-charged) particles (which are important in its operation)\, of which both the position and velocity distribution is i mportant. This leads to a Boltzmann-type transport equation that needs to be discretised with a Monte Carlo method. One then obtains a coupled finit e-volume/Monte-Carlo simulation\, of which the results possess both a bias and a variance. In this talk\, I introduce the problems associated with t he simulation of the plasma edge region in a fusion reactor. I discuss how to couple a finite volume discretisation of the plasma equations with a M onte Carlo simulation of the neutral particles\, and show how the Monte Ca rlo errors affect convergence of steady state computations and reliability of gradient computations (necessary during optimization).\n LOCATION:https://researchseminars.org/talk/EDDy/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Espath (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20210422T081500Z DTEND;VALUE=DATE-TIME:20210422T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/21 DESCRIPTION:Title: Ph ase-Field Gradient Theory: the geometry of gradient flows and its configur ation mechanics\nby Luis Espath (RWTH Aachen University) as part of ED Dy weekly seminar\n\n\nAbstract\nIn this talk\, I present a phase-field th eory for enriched continua\, exposing the geometry of gradient flows. We b egin the theory with a set of postulate balances on nonsmooth open surface s to characterize the fundamental fields. By considering nontrivial intera ctions inside the body\, we characterize the existence of a hypermicrotrac tion field\, a central aspect of this theory. Subject to thermodynamic con straints\, we develop a general set of constitutive relations for a phase- field model where its free-energy density depends on second gradients of t he phase field. To exemplify the usefulness of our theory\, we generalize two commonly used phase-field equations. We propose a generalized Swift– Hohenberg equation-a second-grade phase-field equation-and its conserved v ersion\, the generalized phase-field crystal equation-a conserved second-g rade phase-field equation. Furthermore\, we derive the configurational fie lds arising in this theory. Configurational forces are a generalization of Newtonian forces to describe the kinetics and kinematics of manifolds. We conclude with the presentation of a comprehensive and thermodynamically c onsistent set of boundary conditions.\n\nBased on: Espath & Calo\, Phase-f ield gradient theory. 2021\, ZAMP. DOI: 10.1007/s00033-020-01441-2.\n LOCATION:https://researchseminars.org/talk/EDDy/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Flavien Léger (ENS Paris) DTSTART;VALUE=DATE-TIME:20210506T081500Z DTEND;VALUE=DATE-TIME:20210506T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/22 DESCRIPTION:Title: Fa st computations of Wasserstein gradient flows\nby Flavien Léger (ENS Paris) as part of EDDy weekly seminar\n\n\nAbstract\nWe will present a met hod to efficiently compute Wasserstein gradient flows. The approach is bas ed on a generalization of the back-and-forth method that we developed with Matt Jacobs to solve optimal transport problems. The gradient flow is evo lved by solving the dual problem to the JKO scheme: in general\, this dual problem is much better behaved than the primal problem. This allows to ef ficiently run large scale gradient flows simulations for a large class of internal energies including singular and non-convex energies. \n\nThis is joint work with Matt Jacobs and Wonjun Lee.\n LOCATION:https://researchseminars.org/talk/EDDy/22/ END:VEVENT BEGIN:VEVENT SUMMARY:François Bouchut (Université Gustave Eiffel\, Marne-la-Vallée) DTSTART;VALUE=DATE-TIME:20210520T081500Z DTEND;VALUE=DATE-TIME:20210520T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/23 DESCRIPTION:Title: En tropy satisfying multi well-balanced schemes for shallow water type system s\nby François Bouchut (Université Gustave Eiffel\, Marne-la-Vallée ) as part of EDDy weekly seminar\n\n\nAbstract\nMany systems of shallow wa ter type arise in the modeling of thin layer flows. The sources can take s everal forms\, and for each of them the question of building a well-balanc ed scheme comes out. We are interested here in the case when it is require d to build a numerical scheme that preserves two nontrivial families of st eady states at rest. Such a scheme can be called multi well-balanced. In o rder to apply the reconstruction method one has to manage with the two fam ilies at the same time. I will show how it can be possible while at the sa me time verifying a semi-discrete entropy inequality. Two examples of entr opy satisfying multi well-balanced schemes will be given: the shallow wate r MHD system with topography\, and a shallow water system with internal va riable and topography.\n LOCATION:https://researchseminars.org/talk/EDDy/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Daneri (Gran Sasso Science Institute\, l'Aquila) DTSTART;VALUE=DATE-TIME:20210610T081500Z DTEND;VALUE=DATE-TIME:20210610T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/24 DESCRIPTION:Title: On the sticky particle solutions to the pressureless Euler system in general dimension\nby Sara Daneri (Gran Sasso Science Institute\, l'Aquila) a s part of EDDy weekly seminar\n\n\nAbstract\nIn this talk we consider the pressureless Euler system in dimension greater than or equal to two. Sever al works have been devoted to the search of solutions which satisfy the fo llowing adhesion or sticky particle principle: if two particles of the flu id do not interact\, then they move freely keeping constant velocity\, oth erwise they join with velocity given by the balance of momentum. For initi al data given by a finite number of particles pointing each in a given dir ection\, in general dimension\, it is easy to show that a global sticky pa rticle solution always exists and is unique. In dimension one\, sticky par ticle solutions have been proved to exist and be unique. In dimension grea ter or equal than two\, it was shown that as soon as the initial data is n ot concentrated on a finite number of particles\, it might lead to non-exi stence or non-uniqueness of sticky particle solutions.\n\nIn collaboration with S. Bianchini\, we show that even though the sticky particle solution s are not well-posed for every measure-type initial data\, there exists a comeager set of initial data in the weak topology giving rise to a unique sticky particle solution. Moreover\, for any of these initial data the sti cky particle solution is unique also in the larger class of dissipative so lutions (where trajectories are allowed to cross) and is given by a trivia l free flow concentrated on trajectories which do not intersect. In partic ular for such initial data there is only one dissipative solution and its dissipation is equal to zero. Thus\, for a comeager set of initial data th e problem of finding sticky particle solutions is well-posed\, but the dyn amics that one sees is trivial. Our notion of dissipative solution is lagr angian and therefore general enough to include weak and measure-valued sol utions.\n LOCATION:https://researchseminars.org/talk/EDDy/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Walter Schachermayer (University of Vienna) DTSTART;VALUE=DATE-TIME:20210701T081500Z DTEND;VALUE=DATE-TIME:20210701T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/25 DESCRIPTION:Title: Tr ajectorial Otto calculus\nby Walter Schachermayer (University of Vienn a) as part of EDDy weekly seminar\n\n\nAbstract\nWe revisit the variationa l characterization of diffusion as entropic gradient flux\, established by Jordan\, Kinderlehrer\, and Otto in \, and provide for it a probabilis tic interpretation based on stochastic calculus. It was shown in  that\ , for diffusions of Langevin-Smoluchowski type\, the Fokker-Planck probabi lity density flow minimizes the rate of relative entropy dissipation\, as measured by the distance traveled in the ambient space of probability meas ures with finite second moments\, in terms of the quadratic Wasserstein me tric. We obtain novel\, stochastic-process versions of these features\, va lid along almost every trajectory of the diffusive motion in both the forw ard and\, most transparently\, the backward\, directions of time\, using a very direct perturbation analysis. By averaging our trajectorial results with respect to the underlying measure on path space\, we establish the mi nimum rate of entropy dissipation along the Fokker-Planck flow and measure exactly the deviation from this minimum that corresponds to any given per turbation. As a bonus of the perturbation analysis\, we derive the so-call ed HWI inequality relating relative entropy (H)\, Wasserstein distance (W) and relative Fisher information (I).\n\nJoint work with I. Karatzas and B . Tschiderer.\n LOCATION:https://researchseminars.org/talk/EDDy/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Otto (MPI-MIS\, Leipzig) DTSTART;VALUE=DATE-TIME:20210819T083000Z DTEND;VALUE=DATE-TIME:20210819T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/26 DESCRIPTION:Title: Re gularity for optimal transportation and application to the matching proble m\nby Felix Otto (MPI-MIS\, Leipzig) as part of EDDy weekly seminar\n\ nLecture held in Aachen\, Templergraben 55\, lecture hall 2 (max. 33 perso ns\, so please announce participation by mail).\n\nAbstract\nThe optimal t ransportation of one measure into another\, leading to the notion of their Wasserstein distance\, is a problem in the calculus of variations with a wide range of applications. The regularity theory for the optimal map is s ubtle and was revolutionized by Caffarelli. This approach relies on the fa ct that the Euler-Lagrange equation of this variational problem is given b y the Monge-Ampère equation. The latter is a prime example of a fully non linear (degenerate) elliptic equation\, amenable to comparison principle a rguments.\n\nWe present a purely variational approach to the regularity th eory for optimal transportation\, introduced with M. Goldman and refined w ith M. Huesmann. Following De Giorgi’s philosophy for the regularity the ory of minimal surfaces\, it is based on the approximation of the displace ment by a harmonic gradient\, through the construction of a variational co mpetitor. This leads to a “one-step improvement lemma”\, and feeds int o a Campanato iteration on the $C^{1\,\\alpha}$-level for the optimal map\ , capitalizing on affine invariance.\n\nOn the one hand\, this allows to r e-prove the $\\varepsilon$-regularity result (Figalli-Kim\, De Philippis-F igalli) bypassing Caffarelli’s celebrated theory. This also extends to g eneral cost functions\, which is joint work with M. Prodhomme and T. Ried. \n\nOn the other hand\, due to its robustness and low-regularity approach\ , it can be used to study the popular problem of matching two independent Poisson point processes. For example\, it can be used to prove non-existen ce of a stationary cyclically monotone coupling\, which is joint work with M. Huesmann and F. Mattesini.\n LOCATION:https://researchseminars.org/talk/EDDy/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim Laux (University of Bonn) DTSTART;VALUE=DATE-TIME:20210419T080000Z DTEND;VALUE=DATE-TIME:20210419T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/27 DESCRIPTION:Title: Di stributional solutions to mean curvature flow (1/3)\nby Tim Laux (Univ ersity of Bonn) as part of EDDy weekly seminar\n\n\nAbstract\nThis course aims at presenting some of the ideas behind the (conditional) existence an d (weak-strong) uniqueness theory for distributional solutions to mean cur vature flow. Focusing on the simple two-phase case\, i.e.\, the evolution of a closed hypersurface\, allows for a self-contained and concise present ation\, which is accessible for graduate students with some background in PDEs and basic measure theory.\n\nThe first lecture provides an overview\, basic examples\, exercises\, and some computational tools. In the second lecture\, distributional solutions and a (conditional) closure theorem are presented. If time permits\, a relation to the viscosity solution in the two-phase case will be explained. The last lecture is devoted to the weak- strong uniqueness principle in the class of distributional solutions.\n LOCATION:https://researchseminars.org/talk/EDDy/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim Laux (University of Bonn) DTSTART;VALUE=DATE-TIME:20210420T080000Z DTEND;VALUE=DATE-TIME:20210420T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/28 DESCRIPTION:Title: Di stributional solutions to mean curvature flow (2/3)\nby Tim Laux (Univ ersity of Bonn) as part of EDDy weekly seminar\n\n\nAbstract\nThis course aims at presenting some of the ideas behind the (conditional) existence an d (weak-strong) uniqueness theory for distributional solutions to mean cur vature flow. Focusing on the simple two-phase case\, i.e.\, the evolution of a closed hypersurface\, allows for a self-contained and concise present ation\, which is accessible for graduate students with some background in PDEs and basic measure theory.\n\nThe first lecture provides an overview\, basic examples\, exercises\, and some computational tools. In the second lecture\, distributional solutions and a (conditional) closure theorem are presented. If time permits\, a relation to the viscosity solution in the two-phase case will be explained. The last lecture is devoted to the weak- strong uniqueness principle in the class of distributional solutions.\n LOCATION:https://researchseminars.org/talk/EDDy/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim Laux (University of Bonn) DTSTART;VALUE=DATE-TIME:20210421T080000Z DTEND;VALUE=DATE-TIME:20210421T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/29 DESCRIPTION:Title: Di stributional solutions to mean curvature flow (3/3)\nby Tim Laux (Univ ersity of Bonn) as part of EDDy weekly seminar\n\n\nAbstract\nThis course aims at presenting some of the ideas behind the (conditional) existence an d (weak-strong) uniqueness theory for distributional solutions to mean cur vature flow. Focusing on the simple two-phase case\, i.e.\, the evolution of a closed hypersurface\, allows for a self-contained and concise present ation\, which is accessible for graduate students with some background in PDEs and basic measure theory.\n\nThe first lecture provides an overview\, basic examples\, exercises\, and some computational tools. In the second lecture\, distributional solutions and a (conditional) closure theorem are presented. If time permits\, a relation to the viscosity solution in the two-phase case will be explained. The last lecture is devoted to the weak- strong uniqueness principle in the class of distributional solutions.\n LOCATION:https://researchseminars.org/talk/EDDy/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Röger (TU Dortmund) DTSTART;VALUE=DATE-TIME:20220217T091500Z DTEND;VALUE=DATE-TIME:20220217T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/30 DESCRIPTION:Title: A free boundary problem arising in a model of cell polarization\nby Matt hias Röger (TU Dortmund) as part of EDDy weekly seminar\n\n\nAbstract\nWe consider the polarization of a cell in response to an outer signal. The m athematical model consists of a diffusion equation in the inner volume cou pled to a reaction diffusion system on the cell membrane. In a certain asy mptotic limit we rigorously prove the convergence towards a generalized ob stacle problem. In term of this limit system we derive conditions for the onset of polarization.\n\n(This is joint work with Anna Logioti\, Barbara Niethammer and Juan Velazquez)\n LOCATION:https://researchseminars.org/talk/EDDy/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Kolb (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20210923T081500Z DTEND;VALUE=DATE-TIME:20210923T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/31 DESCRIPTION:Title: Hi gher–dimensional deterministic formulation of hyperbolic conservation la ws with uncertain initial data\nby Adrian Kolb (RWTH Aachen University ) as part of EDDy weekly seminar\n\nLecture held in Templergraben 55\, lec ture hall I (max. 33 persons --> please announce participation via email t o inf.\n\nAbstract\nWe discuss random hyperbolic conservation laws and int roduce a novel formulation interpreting the stochastic variables as additi onal spatial dimensions with zero flux. The approach is compared with esta blished non–intrusive approaches to random conservation laws. In the sca lar case\, an entropy solution is proven to exist if and only if a random entropy solution for the original problem exists. Furthermore\, existence and numerical convergence of stochastic moments is established. Along with this\, the boundedness of the $L^1$-error of the stochastic moments by th e $L^1$-error of the approximation is proven. For the numerical approximat ion a Runge–Kutta discontinuous Galerkin method is employed and a multi –element stochastic collocation is used for the approximation of the sto chastic moments. By means of grid adaptation the computational effort is r educed in the spatial as well as in the stochastic directions\, simultaneo usly. Results on Burger’s and Euler equation are validated by several nu merical examples and compared to Monte Carlo simulations.\n LOCATION:https://researchseminars.org/talk/EDDy/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Kidger (Oxford University) DTSTART;VALUE=DATE-TIME:20211014T081500Z DTEND;VALUE=DATE-TIME:20211014T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/32 DESCRIPTION:Title: On Neural Differential Equations\nby Patrick Kidger (Oxford University) as part of EDDy weekly seminar\n\n\nAbstract\nNeural Differential Equation s (NDEs) demonstrate that neural networks and differential equations are t wo sides of the same coin. Traditional parameterised differential equation s are a special case. Many popular neural network architectures (e.g. resi dual networks\, recurrent networks\, StyleGAN2\, coupling layers) are disc retisations. By treating differential equations as a learnt component of a differentiable computation graph\, then NDEs extend current physical mode lling techniques whilst integrating tightly with current deep learning pra ctice.\n\nNDEs offer high-capacity function approximation\, strong priors on model space\, the ability to handle irregular data\, memory efficiency\ , and a wealth of available theory on both sides. They are particularly su itable for tackling dynamical systems\, time series problems\, and generat ive problems.\n\nThis talk will offer a dedicated introduction to the topi c\, with examples including neural ordinary differential equations (e.g. t o model unknown physics)\, neural controlled differential equations (“co ntinuous recurrent networks”\; e.g. to model functions of time series)\, and neural stochastic differential equations (e.g. to model time series t hemselves). If time allows I will discuss other recent work\, such as nove l numerical neural differential equation solvers. This talk includes joint work with Ricky T. Q. Chen\, Xuechen Li\, James Foster\, and James Morril l.\n LOCATION:https://researchseminars.org/talk/EDDy/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Gugat (FAU Erlangen-Nürnberg) DTSTART;VALUE=DATE-TIME:20211104T091500Z DTEND;VALUE=DATE-TIME:20211104T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/33 DESCRIPTION:Title: Op timal control problems and the turnpike property\nby Martin Gugat (FAU Erlangen-Nürnberg) as part of EDDy weekly seminar\n\n\nAbstract\nOften i n dynamic optimal control problems with a long time horizon\, in a large n eighburhood of the middle of the time interval the optimal control and the optimal state are very close to the solution of a static control problem that is derived from the dynamic optimal control problems by omitting the information about the initial state and possibly a desired terminal state. \n\nThis can be shown in different situations\, for example under exact co ntrollability assumptions or with the assumption of nodal profile exact co ntrollability\, as studied by Tatsien Li and his group. In this situation\ , we obtain the turnpike property with interior decay\, that has been disc ussed in the paper Mathematics of Control\, Signals\, and Systems volume 3 3\, pages 237–258 (2021).\n LOCATION:https://researchseminars.org/talk/EDDy/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Reich (Universität Potsdam) DTSTART;VALUE=DATE-TIME:20210120T091500Z DTEND;VALUE=DATE-TIME:20210120T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/34 DESCRIPTION:Title: St atistical inverse problems and affine-invariant gradient flow structures i n the space of probability measures\nby Sebastian Reich (Universität Potsdam) as part of EDDy weekly seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EDDy/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Van Schaftingen (UCLouvain) DTSTART;VALUE=DATE-TIME:20210127T091500Z DTEND;VALUE=DATE-TIME:20210127T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/35 DESCRIPTION:Title: Si ngular harmonic maps from planar domains into manifolds through Ginzburg –Landau and p–harmonic relaxations\nby Jean Van Schaftingen (UCLou vain) as part of EDDy weekly seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EDDy/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Westdickenberg (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20211028T081500Z DTEND;VALUE=DATE-TIME:20211028T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/38 DESCRIPTION:Title: Lo cal mins\, saddle points\, and Gamma-convergence in a Cahn-Hilliard proble m: insights and challenges\nby Maria Westdickenberg (RWTH Aachen Unive rsity) as part of EDDy weekly seminar\n\nLecture held in Lecture Hall III\ , Main building.\nAbstract: TBA\n\nThis lecture is talking place in-person at lecture hall III in the main building of RWTH Aachen University\, Temp lergraben 55\, Aachen\, Germany.\nAccess is granted to vaccinated or teste d people.\n LOCATION:https://researchseminars.org/talk/EDDy/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Heiko von der Mosel (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20211209T091500Z DTEND;VALUE=DATE-TIME:20211209T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/41 DESCRIPTION:Title: Sy mmetric criticality\nby Heiko von der Mosel (RWTH Aachen University) a s part of EDDy weekly seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EDDy/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Torrilhon (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20220127T091500Z DTEND;VALUE=DATE-TIME:20220127T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/43 DESCRIPTION:Title: On the Structure of Moment Equations in Kinetic Theory\nby Manuel Torril hon (RWTH Aachen University) as part of EDDy weekly seminar\n\nAbstract: T BA\n LOCATION:https://researchseminars.org/talk/EDDy/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Umberto Hryniewicz (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20211216T091500Z DTEND;VALUE=DATE-TIME:20211216T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/44 DESCRIPTION:Title: Sy mplectic Field Theory\nby Umberto Hryniewicz (RWTH Aachen University) as part of EDDy weekly seminar\n\nLecture held in Lecture Hall III\, Main building.\nAbstract: TBA\n\nThis lecture is talking place in-person at lec ture hall III in the main building of RWTH Aachen University\, Templergrab en 55\, Aachen\, Germany. Access is granted to vaccinated\, recovered or t ested people.\n LOCATION:https://researchseminars.org/talk/EDDy/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Siegfried Müller (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20220714T081500Z DTEND;VALUE=DATE-TIME:20220714T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/45 DESCRIPTION:Title: On non-conservative products in nonlinear hyperbolic equations\nby Siegf ried Müller (RWTH Aachen University) as part of EDDy weekly seminar\n\nLe cture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nThere ex ist two-phase flow models such as Baer-Nunziato type models that exhibit n on-conservative products. Dal Maso\, Murat and LeFloch introduced a concep t of weak stability for non-conservative products. In the presentation the basics of their framework will be summarized and applied to hyperbolic eq uations with non-conservative-products.\n LOCATION:https://researchseminars.org/talk/EDDy/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Gianmichele Di Matteo (Karlsruhe Institute for Technology) DTSTART;VALUE=DATE-TIME:20220324T091500Z DTEND;VALUE=DATE-TIME:20220324T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/46 DESCRIPTION:Title: A Local Singularity Analysis for the Ricci flow\nby Gianmichele Di Matte o (Karlsruhe Institute for Technology) as part of EDDy weekly seminar\n\n\ nAbstract\nIn this talk\, I will describe a refined local singularity anal ysis for the Ricci flow developed jointly with R. Buzano. The key idea is to investigate blow-up rates of the curvature tensor locally\, near a sing ular point. Then I will show applications of this theory to Ricci flows wi th scalar curvature bounded up to the singular time.\n LOCATION:https://researchseminars.org/talk/EDDy/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Jennifer Crodelle (Middlebury College) DTSTART;VALUE=DATE-TIME:20220407T124500Z DTEND;VALUE=DATE-TIME:20220407T140000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/47 DESCRIPTION:Title: A mathematical model of the developing visual cortex of mice\nby Jennife r Crodelle (Middlebury College) as part of EDDy weekly seminar\n\nAbstract : TBA\n LOCATION:https://researchseminars.org/talk/EDDy/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Mattia Zanella (University of Pavia) DTSTART;VALUE=DATE-TIME:20220519T081500Z DTEND;VALUE=DATE-TIME:20220519T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/48 DESCRIPTION:Title: Un certainty quantification for kinetic equations of emergent phenomena\n by Mattia Zanella (University of Pavia) as part of EDDy weekly seminar\n\n Lecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nKineti c equations play a leading role in the modelling of large systems of inter acting particles/agents with a recognized effectiveness in describing real world phenomena ranging from plasma physics to multi-agent dynamics. The derivation of these models has often to deal with physical\, or even socia l\, forces that are deduced empirically and of which we have limited infor mation. Hence\, to produce realistic descriptions of the underlying system s it is of paramount importance to consider the effects of uncertain quant ities as a structural feature in the modelling process.\n\nIn this talk\, we focus on a class of numerical methods that guarantee the preservation o f main physical properties of kinetic models with uncertainties. In contra st to a direct application of classical uncertainty quantification methods \, typically leading to the loss of positivity of the numerical solution o f the problem\, we discuss the construction of novel schemes that are capa ble of achieving high accuracy in the random space without losing nonnegat ivity of the solution [1\,4]. Applications of the developed methods are pr esented in the classical RGD framework and in related models in life scien ces. In particular\, we concentrate on the interplay of this class of mode ls with mathematical epidemiology where the assessment of uncertainties in data assimilation is crucial to design efficient interventions\, see [2\, 3].\n\nBibliography:\n\n J. A. Carrillo\, L. Pareschi\, M. Zanella. Par ticle based gPC methods for mean-field models of swarming with uncertainty . Commun. Comput. Phys.\, 25(2): 508-531\, 2019.\n\n G. Dimarco\, B. Pe rthame\, G. Toscani\, M. Zanella. Kinetic models for epidemic dynamics wit h social heterogeneity. J. Math. Biol.\, 83\, 4\, 2021.\n\n A. Medaglia \, G. Colelli\, L. Farina\, A. Bacila\, P. Bini\, E. Marchioni\, S. Figini \, A. Pichiecchio\, M. Zanella. Uncertainty quantification and control of kinetic models of tumour growth under clinical uncertainties. Int. J. Non Linear Mech.\, 141: 103933\, 2022.\n\n L. Pareschi\, M. Zanella. Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertai nties: space-homogeneous case. J. Comput. Phys. 423:109822\, 2020.\n LOCATION:https://researchseminars.org/talk/EDDy/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Henning Struchtrup (University of Victoria) DTSTART;VALUE=DATE-TIME:20220317T091500Z DTEND;VALUE=DATE-TIME:20220317T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/49 DESCRIPTION:Title: Th ermodynamically admissible 13-moment equations\nby Henning Struchtrup (University of Victoria) as part of EDDy weekly seminar\n\nLecture held in Lecture Hall III\, Main building.\n\nAbstract\nGrad’s 13-moment equatio ns describe transport in mildly rarefied gases well\, but are not properly embedded into nonequilibrium thermodynamics since they are not accompanie d by a formulation of the second law. In this work\, the Grad-13 equations are embedded into the framework of GENERIC (general equation for the none quilibrium reversible–irreversible coupling)\, which demands additional contributions in the equations to guarantee thermodynamic structure. As GE NERIC building blocks\, we use a Poisson matrix for the basic convection b ehavior and antisymmetric friction matrices to correct for additional conv ective transport terms. The ensuing GENERIC-13 equations completely match the Grad-13 equations up to second-order terms in the Knudsen number and f ulfill all thermodynamic requirements.\n\nJoint work with H.C. Öttinger\, Zürich. Appeared in Phys. Fluids 34\, 017105 (2022)\n LOCATION:https://researchseminars.org/talk/EDDy/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Metsch (University of Freiburg) DTSTART;VALUE=DATE-TIME:20220505T081500Z DTEND;VALUE=DATE-TIME:20220505T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/50 DESCRIPTION:Title: On the area preserving Willmore flow of small bubbles sliding on a domain's boundary\nby Jan Metsch (University of Freiburg) as part of EDDy weekl y seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbs tract\nWe consider the area preserving Willmore evolution of surfaces $\\p hi$\, that are close to a half sphere with small radius\, sliding on the b oundary $S$ of a domain $\\Omega$ while meeting it orthogonally. We prove that the flow exists for all times and keeps a "half spherish" shape. Addi tionally we investigate the asymptotic behaviour of the flow and prove tha t for large times the barycenter of the surfaces approximately follows an explicit ordinary differential equation. If time allows we conclude by inv estigating the convergence of the flow.\n LOCATION:https://researchseminars.org/talk/EDDy/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Schiffer (University of Bonn) DTSTART;VALUE=DATE-TIME:20220512T081500Z DTEND;VALUE=DATE-TIME:20220512T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/51 DESCRIPTION:Title: A variational approach to data-driven problems in fluid mechanics\nby St efan Schiffer (University of Bonn) as part of EDDy weekly seminar\n\nLectu re held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nIn this tal k\, I introduce a data-driven approach to viscous fluid mechanics\, in par ticular to the stationary Navier-Stokes equation. The essential idea is to replace the constitutive law by experimental data. More precisely\, usual ly one takes experimental data and then extrapolates a relation (the visco sity) between the deviatoric stress $\\sigma$ and the strain $\\epsilon$\, for example $\\sigma(\\epsilon) = \\mu_{0}\\epsilon$ (Newtonian fluid) o r \n$\\sigma(\\epsilon) = \\mu_{0}\\vert\\epsilon\\vert^{\\alpha-1}\\epsil on$ (power-law fluid).\nThis relation is then used to obtain the Navier-St okes equation.\n\nInstead of using a constitutive relation\, we introduce a data-driven formulation that has previously been examined in the context of solid mechanics. The idea is to find a solution that satisfies the dif ferential constraints\, derived from first principles\, and is as close as possible to the experimental data. We obtain a variational formulation wh ich we analyse under the aspects of weak lower-semicontinuity\, coercivity and relaxation/$\\Gamma$-convergence.\n\nThis talk is based on joint work with Christina Lienstromberg (Stuttgart) and Richard Schubert (Bonn).\n LOCATION:https://researchseminars.org/talk/EDDy/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Tabea Tscherpel (University of Bielefeld) DTSTART;VALUE=DATE-TIME:20220309T091500Z DTEND;VALUE=DATE-TIME:20220309T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/52 DESCRIPTION:Title: Pr ojection methods for incompressible fluid flow (1/3)\nby Tabea Tscherp el (University of Bielefeld) as part of EDDy weekly seminar\n\nLecture hel d in Lecture Hall III\, Main building.\n\nAbstract\nIn this course we cons ider projection methods for the numerical approximation of time-dependent incompressible fluid equations. Such schemes are based on the projection s tructure of the equations due to the incompressibility constraint. An oper ator splitting leads to a prediction and a correction step in each time st ep both of which are simpler problems. For this reason (high order) projec tion methods are of particular interest for large scale simulations. But o n the other hand the splitting introduces additional challenges e.g. regar ding the boundary conditions.\n\nWe start by reviewing projection methods for viscous flows (Navier-Stokes and Stokes equations) dating back to Chor in and Temam and compare them to mixed methods. Then we take a look at wha t has been done for inviscous equations (Euler). Finally we present the Gr een-Naghdi model that is derived from the incompressible free surface Eule r equations. We discuss how its projection structure helps to pose meaning ful boundary conditions.\n LOCATION:https://researchseminars.org/talk/EDDy/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Tabea Tscherpel (University of Bielefeld) DTSTART;VALUE=DATE-TIME:20220310T091500Z DTEND;VALUE=DATE-TIME:20220310T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/53 DESCRIPTION:Title: Pr ojection methods for incompressible fluid flow (2/3)\nby Tabea Tscherp el (University of Bielefeld) as part of EDDy weekly seminar\n\nLecture hel d in Lecture Hall III\, Main building.\n\nAbstract\nIn this course we cons ider projection methods for the numerical approximation of time-dependent incompressible fluid equations. Such schemes are based on the projection s tructure of the equations due to the incompressibility constraint. An oper ator splitting leads to a prediction and a correction step in each time st ep both of which are simpler problems. For this reason (high order) projec tion methods are of particular interest for large scale simulations. But o n the other hand the splitting introduces additional challenges e.g. regar ding the boundary conditions.\n\nWe start by reviewing projection methods for viscous flows (Navier-Stokes and Stokes equations) dating back to Chor in and Temam and compare them to mixed methods. Then we take a look at wha t has been done for inviscous equations (Euler). Finally we present the Gr een-Naghdi model that is derived from the incompressible free surface Eule r equations. We discuss how its projection structure helps to pose meaning ful boundary conditions.\n LOCATION:https://researchseminars.org/talk/EDDy/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Tabea Tscherpel (University of Bielefeld) DTSTART;VALUE=DATE-TIME:20220311T091500Z DTEND;VALUE=DATE-TIME:20220311T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/54 DESCRIPTION:Title: Pr ojection methods for incompressible fluid flow (3/3)\nby Tabea Tscherp el (University of Bielefeld) as part of EDDy weekly seminar\n\nLecture hel d in Lecture Hall III\, Main building.\n\nAbstract\nIn this course we cons ider projection methods for the numerical approximation of time-dependent incompressible fluid equations. Such schemes are based on the projection s tructure of the equations due to the incompressibility constraint. An oper ator splitting leads to a prediction and a correction step in each time st ep both of which are simpler problems. For this reason (high order) projec tion methods are of particular interest for large scale simulations. But o n the other hand the splitting introduces additional challenges e.g. regar ding the boundary conditions.\n\nWe start by reviewing projection methods for viscous flows (Navier-Stokes and Stokes equations) dating back to Chor in and Temam and compare them to mixed methods. Then we take a look at wha t has been done for inviscous equations (Euler). Finally we present the Gr een-Naghdi model that is derived from the incompressible free surface Eule r equations. We discuss how its projection structure helps to pose meaning ful boundary conditions.\n LOCATION:https://researchseminars.org/talk/EDDy/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Likhit Ganedi (Carnegie-Mellon-University) DTSTART;VALUE=DATE-TIME:20220523T103000Z DTEND;VALUE=DATE-TIME:20220523T113000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/55 DESCRIPTION:Title: Ph ase Separation within Composite Structures\nby Likhit Ganedi (Carnegie -Mellon-University) as part of EDDy weekly seminar\n\nLecture held in Temp lergraben 55\, lecture hall III.\n\nAbstract\nA variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than t he former\, and when the wells of the double well potential are allowed to move and to have discontinuities. The zeroth and first order Γ\\GammaΓ- limits are identified. The topology considered for the latter is that of t wo-scale\, since it encodes more information on the asymptotic local micro structure. As a corollary\, the minimum of the mass constrained minimizati on problem is characterized in terms of discontinuities of the wells.\n LOCATION:https://researchseminars.org/talk/EDDy/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Bachmayr (University of Mainz) DTSTART;VALUE=DATE-TIME:20220707T081500Z DTEND;VALUE=DATE-TIME:20220707T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/56 DESCRIPTION:Title: No nlinear transient flows in porous media: porosity waves and channel format ion\nby Markus Bachmayr (University of Mainz) as part of EDDy weekly s eminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstra ct\nIn models of porous media flows\, for instance in hydrogeology\, the p orosity of the solid matrix is typically treated as a static quantity. How ever\, under certain circumstances\, such as in soft sedimentary rocks or in magma flows\, the porosity of the solid material can evolve under the i nfluence of fluid pressure. In particular\, this can lead to the formation of solitary porosity waves and of higher-porosity channels. We consider a system of nonlinear PDEs for porosity and effective pressure\, based on a poroviscoelastic model\, which describes such phenomena. The focus of thi s talk is on the well-posedness of this PDE problem\, which has been estab lished in the literature only for initial porosities of high Sobolev smoot hness. We discuss several preliminary results for porosities of low regula rity\, including cases with jump discontinuities that are of particular in terest in geological applications. We then turn to some first results on a space-time adaptive numerical method based on a discontinuous Petrov-Gale rkin approach for efficiently approximating the evolution of porosity chan nels. Finally\, we discuss available measurement data and associated inver se problems.\n\nThis is joint work in progress with Simon Boisserée (Main z)\, Lisa Maria Kreusser (Bath)\, and Evangelos Moulas (Mainz).\n LOCATION:https://researchseminars.org/talk/EDDy/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Ulmer (University of Edinburgh) DTSTART;VALUE=DATE-TIME:20220818T083000Z DTEND;VALUE=DATE-TIME:20220818T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/58 DESCRIPTION:Title: Pe rturbation theory and the Carleson condition for the $L^p$ Dirichlet bound ary value problem\nby Martin Ulmer (University of Edinburgh) as part o f EDDy weekly seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeM ath).\n\nAbstract\nIn this talk I am going to introduce the Dirichlet boun dary value problem with $L^p$ boundary data for elliptic linear second ord er PDEs and discuss the Carleson condition as sufficient condition for sol vability of this problem. In the last few years\, the theory involving Car leson type conditions is continuously making progress\, for example in rel ated different problems like the real or complex valued Neumann or Regular ity problem.\n\nTo start with we will motivate the Carleson condition and explain why it arises “naturally” as condition for solvability of the Dirichlet boundary value problem. Motivated by the Carleson condition we w ill discuss perturbation theory of operators without drift term. This pert urbation theory allows us to extent the class of operators which a Carleso n type condition can be applied to\, and hence we get a wider class of ope rators for whom the $L^p$ Dirichlet boundary value problem is solvable. Th e perturbation theory and its application is joint work Martin Dindoš and Erik Sätterqvist.\n LOCATION:https://researchseminars.org/talk/EDDy/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Kurganov (Southern University of Science and Technology) DTSTART;VALUE=DATE-TIME:20220712T083000Z DTEND;VALUE=DATE-TIME:20220712T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/59 DESCRIPTION:Title: We ll-Balanced Path-Conservative Central-Upwind Schemes Based on Flux Globali zation\nby Alexander Kurganov (Southern University of Science and Tech nology) as part of EDDy weekly seminar\n\nLecture held in Templergraben 55 \, seminar room 114 (1st floor).\n\nAbstract\nI will introduce a new appro ach for constructing robust well-balanced (WB) finite-volume methods for n onconservative onedimensional hyperbolic systems of nonlinear PDEs. The WB property\, namely\, the ability of the scheme to exactly preserve physica lly relevant steady-state solutions is enforced using a flux globalization approach according to which a studied system is rewritten in an equivalen t quasi-conservative form with global fluxes. To this end\, one needs to i ncorporate nonconservative product terms into the global fluxes. The resul ting system can then be solved using a Riemann-problem-solver-free central -upwind (CU) scheme. However\, a straightforward integration of the noncon servative terms would result in a scheme capable of exactly preserving ver y simple smooth steady states only and failing to preserve discontinuous s teady states naturally arising in the nonconservative models.\n\nIn order to ameliorate the flux globalization based CU scheme\, we evaluate the int egrals of the nonconservative product terms using a path-conservative tech nique. This results in a new WB flux globalization based path-conservative central-upwind scheme (PCCU) scheme\, which is much more accurate and rob ust than its predecessors. This is illustrated on the nonconservative syst em describing fluid flows in nozzles with variable cross-sections and a va riety of shallow water models including the two-layer thermal rotating sha llow water equations.\n LOCATION:https://researchseminars.org/talk/EDDy/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Hailiang Liu (Iowa State University) DTSTART;VALUE=DATE-TIME:20220705T083000Z DTEND;VALUE=DATE-TIME:20220705T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/60 DESCRIPTION:Title: Gr adient methods with Energy for large-scale optimization problems\nby H ailiang Liu (Iowa State University) as part of EDDy weekly seminar\n\nLect ure held in Templergraben 55\, lecture hall II (2nd floor).\n\nAbstract\nW e propose AEGD\, a new algorithm for gradient-based optimization of stocha stic objective functions\, based on adaptive updates of quadratic energy. The method is shown to be unconditionally energy stable\, irrespective of the step size. In addition\, AEGD enjoys tight convergence rates\, yet all ows a large step size. The method is straightforward to implement and requ ires little tuning of hyper-parameters. Experimental results demonstrate t hat AEGD works well for various optimization problems: it is robust with r espect to initial data\, capable of making rapid initial progress\, shows comparable and most times better generalization performance than SGD with momentum for deep neural networks.\n LOCATION:https://researchseminars.org/talk/EDDy/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Denis Brazke (University of Heidelberg) DTSTART;VALUE=DATE-TIME:20220804T083000Z DTEND;VALUE=DATE-TIME:20220804T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/61 DESCRIPTION:Title: Ga mma-limit for a sharp interface model related to pattern formation on biom embranes\nby Denis Brazke (University of Heidelberg) as part of EDDy w eekly seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\ nAbstract\nWe derive a macroscopic limit for a sharp interface version of a model proposed by Komura\, Shimokawa and Andelman to investigate pattern formation in biomembranes due to competition of chemical and mechanical f orces. We identify sub- and supercrital parameter regimes and show with th e introduction of the autocorrelation function that the ground state energ y leads to the isoperimetric problem in the subcritical regime\, which is interpreted to not form fine scale patterns.\n\nThis is joint work with Ha ns Knüpfer and Anna Marciniak–Czochra.\n\n10:00 monthly tea time\n LOCATION:https://researchseminars.org/talk/EDDy/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Röger (TU Dortmund) DTSTART;VALUE=DATE-TIME:20220623T083000Z DTEND;VALUE=DATE-TIME:20220623T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/62 DESCRIPTION:Title: A nonlocal free boundary problem arising in a model for cell polarization\nby Matthias Röger (TU Dortmund) as part of EDDy weekly seminar\n\nLect ure held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nWe conside r a model for cell polarization given by a nonlocal reaction-diffusion sys tem on a two-dimensional surface. We prove the convergence to a free bound ary problem in a fast reaction limit and derive conditions for the onset o f polarization. Furthermore we study regularity properties of the nonlocal parabolic obstacle problem that represents the asymptotic reduction.\n\n( This is joint work with Anna Logioti\, Barbara Niethammer and Juan Velazqu ez.)\n LOCATION:https://researchseminars.org/talk/EDDy/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Van Schaftingen (Université catholique de Louvain) DTSTART;VALUE=DATE-TIME:20220609T083000Z DTEND;VALUE=DATE-TIME:20220609T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/63 DESCRIPTION:Title: Gi nzburg-Landau functionals on planar domains for a general compact vacuum m anifold\nby Jean Van Schaftingen (Université catholique de Louvain) a s part of EDDy weekly seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nGinzburg-Landau type functionals provide a rela xation scheme to construct harmonic maps in the presence of topological ob structions. They arise in superconductivity models\, in liquid crystal mod els (Landau-de Gennes functional) and in the generation of cross-fields in meshing. For a general compact manifold target space we describe the asym ptotic number\, type and location of singularities that arise in minimizer s. We cover in particular the case where the fundamental group of the vacu um manifold is nonabelian and hence the singularities cannot be characteri zed univocally as elements of the fundamental group. We obtain similar res ults for ppp-harmonic maps with ppp going to 222. The results unify the ex isting theory and cover new situations and problems.\n\nThis is a joint wo rk with Antonin Monteil (Paris-Est Créteil\, France)\, Rémy Rodiac (Pari s–Saclay\, France) and Benoît Van Vaerenbergh (UCLouvain).\n LOCATION:https://researchseminars.org/talk/EDDy/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonie Langer (University of Ulm) DTSTART;VALUE=DATE-TIME:20221110T093000Z DTEND;VALUE=DATE-TIME:20221110T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/64 DESCRIPTION:Title: A dynamic approach to heterogeneous elastic wires\nby Leonie Langer (Uni versity of Ulm) as part of EDDy weekly seminar\n\nLecture held in Pontdrie sch 14-16\, Room 008 (SeMath).\n\nAbstract\nWe model heterogeneous elastic wires by closed planar curves with density. The associated elastic energy depends on a density-modulated stiffness. Working with the inclination an gle function\, the $L^2$-gradient flow corresponding to this energy is a n onlocal quasilinear coupled parabolic system of second order. We show loca l well-posedness and global existence of solutions and study properties of the flow.\n\nThis talk is based on a joint work with Anna Dall’Acqua\, Gaspard Jankowiak and Fabian Rupp.\n LOCATION:https://researchseminars.org/talk/EDDy/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Ferdinand Thein (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20221124T093000Z DTEND;VALUE=DATE-TIME:20221124T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/65 DESCRIPTION:Title: St abilization of a Multi-Dimensional System of Hyperbolic Balance Laws\n by Ferdinand Thein (RWTH Aachen University) as part of EDDy weekly seminar \n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nWe are interested in the feedback stabilization of a quantity which evolutio n can be described using a Hamilton-Jacobi equation in $R^n$. The mathemat ical treatment then leads to a system of $n$ hyperbolic transport PDEs for the perturbation of a desired state which should be stabilized. There exi sts a rich literature for the one dimensional case including different Lya punov functions leading to exponential decay of the $L^2$-norm when suitab le feedback controls are applied. Here we want to extend these results to the multi-dimensional case leading to a novel Lyapunov function with space dependent weight functions taking accounting for the multidimensional geo metry. We show the exponential decay of the Lyapunov function provided tha t the weights and controls are chosen appropriately. The design feedback c ontrol is closely related to the precise choice of the Lyapunov function a nd its weights. We further present numerical experiments.\n LOCATION:https://researchseminars.org/talk/EDDy/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Kunlun Qi (University of Minnesota) DTSTART;VALUE=DATE-TIME:20230223T093000Z DTEND;VALUE=DATE-TIME:20230223T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/66 DESCRIPTION:Title: St ability and Convergence Analysis of the Fourier-Galerkin Spectral Method f or the Boltzmann Equation\nby Kunlun Qi (University of Minnesota) as p art of EDDy weekly seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nNumerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional\, nonlocal\, and nonl inear collision integral. Over the past decade\, the Fourier-Galerkin spec tral method has become a popular deterministic method for solving the Bolt zmann equation\, manifested by its high accuracy and potential of being fu rther accelerated by the fast Fourier transform. Albeit its practical succ ess\, the stability of the method is only recently proved by utilizing the “spreading” property of the collision operator. In this talk\, we int roduce a new proof based on a careful $L^2$ estimate of the negative part of the solution. We also discuss the applicability of the result to variou s initial data\, including both continuous and discontinuous functions. Th is talk is based on some joint works with Tong Yang (PolyU Hong Kong) and Jingwei Hu (University of Washington).\n LOCATION:https://researchseminars.org/talk/EDDy/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Tommaso Ruggeri (University of Bologna) DTSTART;VALUE=DATE-TIME:20230126T093000Z DTEND;VALUE=DATE-TIME:20230126T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/67 DESCRIPTION:Title: Su b-Shocks formation in the Shock Structure of Hyperbolic Systems with a Con vex Extension with an application to a Binary Mixture of Gases\nby Tom maso Ruggeri (University of Bologna) as part of EDDy weekly seminar\n\nLec ture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nSince the system of field equations is hyperbolic\, the shock-structure solution is not always regular\, and discontinuous parts (sub-shocks) can be formed w hen the shock velocity meets a characteristic velocity . In particular\ , in the case of a hyperbolic system with a convex entropy (symmetric syst ems)\, a theorem by Boillat and Ruggeri  proved that a sub-shock surely arises when the shock’s velocity becomes greater than the maximum chara cteristic velocity in the unperturbed state. The question if there are sub -shocks also for shock velocities less than the maximum characteristic is still an open problem. An interesting case of the existence of sub-shocks for shock velocity smaller than the maximum velocity is offered by a binar y mixture of polyatomic Eulerian gases with different degrees of freedom o f a molecule based on the multi-temperature model of Rational Extended The rmodynamics . For given values of the mass ratio and the specific heats of the constituents\, we identify the possible sub-shocks as the Mach num ber of the shock wave and the concentration of the constituents change  . Namely\, the regions with no sub-shocks\, a sub-shock for only one compo nent\, or sub-shocks for both constituents are comprehensively classified. The most interesting case is that the lighter molecule has more degrees o f freedom than the heavier one. In this situation\, the topology of the va rious regions becomes different. We also numerically solve the system of t he field equations using the parameters in the various regions and confirm whether the sub-shocks emerge. Finally\, the relationship between an acce leration wave in one constituent and the sub-shock in the other is explici tly derived.\n\nReferences:\n\n T. Ruggeri\, “Breakdown of shock-wave -structure solutions\,” Phys. Rev. E 47\, 4135 (1993).\n\n G. Boillat and T. Ruggeri\, “On the shock structure problem for hyperbolic system of balance laws and convex entropy\,” Cont. Mech. Thermodyn. 10 285–29 2 (1998).\n\n T. Ruggeri and M. Sugiyama\, Classical and Relativistic R ational Extended Thermodynamics of Gases (Springer\, Cham\, 2021).\n\n T. Ruggeri and S. Taniguchi\, “A Complete Classification of Sub-Shocks i n the Shock Structure of a Binary Mixture of Eulerian Gases with Different Degrees of Freedom\,” Phys. Fluids 34\, 066116 (2022).\n LOCATION:https://researchseminars.org/talk/EDDy/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Niklas Kolbe (RWTH Aachen University) DTSTART;VALUE=DATE-TIME:20221215T093000Z DTEND;VALUE=DATE-TIME:20221215T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/68 DESCRIPTION:Title: Nu merical and data-based methods for networked scalar conservation laws\ nby Niklas Kolbe (RWTH Aachen University) as part of EDDy weekly seminar\n \nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nTwo new ways to couple scalar conservation laws on networks are presented. We first discuss a numerically motivated approach\, in which a new scheme is derived using a relaxation system and taking the relaxation limit also at the nodes of the network. The scheme is mass conservative\, allows for a s econd order extension and yields well defined and easy-to-compute coupling conditions for general networks. The second approach focuses on the traff ic flow model by Lighthill\, Witham and Richards in a network setting. The choice of coupling condition at the junction has been a major modeling ch allenge. Using car trajectory data obtained from drone photography over a German motorway we develop new data-driven coupling conditions\, which we compare to classical approaches from literature.\n LOCATION:https://researchseminars.org/talk/EDDy/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Modena (University of L'Aquila) DTSTART;VALUE=DATE-TIME:20221020T083000Z DTEND;VALUE=DATE-TIME:20221020T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/69 DESCRIPTION:Title: No n-uniqueness for the transport equation with Sobolev vector fields\nby Stefano Modena (University of L'Aquila) as part of EDDy weekly seminar\n\ nLecture held in Templergraben 55\, lecture hall II (2nd floor).\n\nAbstra ct\nOne of the main questions in the theory of the linear transport equati on is whether uniqueness of weak solutions to the Cauchy problem holds in the case the given vector field is not smooth. In the talk I will provide an overview on some results obtained in the last few years\, showing that even for incompressible\, Sobolev (thus quite “well-behaved”) vector f ields\, uniqueness of solutions can drastically fail. This result can be s een as a counterpart to DiPerna and Lions’ well-posedness theorem.\n LOCATION:https://researchseminars.org/talk/EDDy/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Ed Gallagher (University of Bath) DTSTART;VALUE=DATE-TIME:20230202T093000Z DTEND;VALUE=DATE-TIME:20230202T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/70 DESCRIPTION:Title: Th e infinity-elastica problem on a Riemannian manifold\nby Ed Gallagher (University of Bath) as part of EDDy weekly seminar\n\nLecture held in Pon tdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nWe consider the following question: among all curves lying on a given Riemannian manifold with pres cribed length and boundary data\, which ones minimise the $L^\\infty$ norm of the curvature? This extends a paper of Moser considering the same ques tion in Euclidean space. Using the method of $L^p$ approximation we show t hat minimisers of our problem and also a wider class of “pseudominimiser ” curves must satisfy an ODE system obtained as the limit as $p \\righta rrow \\infty$ of the $L^p$ Euler-Lagrange equations. This system gives us some geometric information about our (pseudo)minimisers. In particular we find that their curvature takes on at most two values: a positive constant $K$\, and possibly zero in some places.\nThis talk is based on joint work with Roger Moser which can be found at https://arxiv.org/abs/2202.07407.\ n LOCATION:https://researchseminars.org/talk/EDDy/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Cristoferi (Radboud University) DTSTART;VALUE=DATE-TIME:20230406T083000Z DTEND;VALUE=DATE-TIME:20230406T093000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/71 DESCRIPTION:by Riccardo Cristoferi (Radboud University) as part of EDDy we ekly seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/EDDy/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliette Dubois (Inria Paris) DTSTART;VALUE=DATE-TIME:20230216T093000Z DTEND;VALUE=DATE-TIME:20230216T103000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/72 DESCRIPTION:Title: Ac oustic and gravity waves in the ocean: modelling towards early-warning sys tems\nby Juliette Dubois (Inria Paris) as part of EDDy weekly seminar\ n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nIn this talk we present a new linear model for the propagation of acoustic wa ves and gravity waves in a simplified ocean. The use of acoustic waves mea surements in the ocean is currently seen as a good candidate for the impro vement of tsunami early-warning systems. The new model is obtained in the following way: the compressible Euler equation are written in Lagrangian c oordinates and linearized around a state at equilibrium corresponding to t he ocean at rest. A wave-like equation containing acoustic terms and gravi ty terms is then derived. The obtained model is compared with the literatu re by using some simplifications\, namely the barotropic assumption\, and the limits in the incompressible and in the acoustic regime.\n\nWe present then some numerical results. By using a finite element discretization in space and a finite difference scheme in time\, we are able to reproduce th e simulations available in the literature for the case without topography and with a constant temperature. Finally we show some aspects of the mathe matical analysis for the continuous problem\, and focus on the functional space needed to prove existence and uniqueness of the solution.\n\nThis is a joint work with Jacques Sainte-Maris (Inria Paris\, ANGE) and Sébastie n Imperiale (Inria Saclay\, M3DISIM).\n LOCATION:https://researchseminars.org/talk/EDDy/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuela Gussetti (University of Bielefeld) DTSTART;VALUE=DATE-TIME:20230131T110000Z DTEND;VALUE=DATE-TIME:20230131T120000Z DTSTAMP;VALUE=DATE-TIME:20230205T212228Z UID:EDDy/73 DESCRIPTION:Title: An application of rough paths theory to the study of the stochastic Landau-L ifschitz-Gilbert equation\nby Emanuela Gussetti (University of Bielefe ld) as part of EDDy weekly seminar\n\nLecture held in Pontdriesch 14-16\, Room 008 (SeMath).\n\nAbstract\nAbstract: The Landau-Lifschitz-Gilbert equ ation is a model describing the magnetisation of a ferromagnetic material. The stochastic model is studied to observe the role of thermal fluctuatio ns. We interpret the linear multiplicative noise appearing by means of rou gh paths theory and we study existence and uniqueness of the solution to t he equation on a one dimensional domain DD. We show that the map that to t he noise associates the unique solution to the equation is locally Lipschi tz continuous in the strong norm $L^\\infty([0\,T]\;H^1(D))\\cap L^2([0\,T ]\;H^2(D))$\, with initial condition in $H^1(D)$. This implies a Wong-Zaka i convergence result\, a large deviation principle\, a support theorem and the Feller property for the associated semigroup.\n\nThe talk is based on a joint work with A. Hocquet https://arxiv.org/abs/2103.00926 and on http s://arxiv.org/abs/2208.02136.\n LOCATION:https://researchseminars.org/talk/EDDy/73/ END:VEVENT END:VCALENDAR