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Upcoming talks


Tournus Magali (École Centrale de Marseille) Oskar-Morgenstern-Platz 1, Hörsaal 2, ground floor. Thu, 23. Nov 17, 14:15
Scalar conservation laws with heterogeneous flux in the BV framework
We consider a scalar conservation law with a flux containing spatial heterogeneities of bounded variation, where the number of discontinuities may be infinite. We address the question of existence of an adapted entropy solution in the BV framework. A sufficient key condition guaranteeing existence is identified and new BV estimates are given. This provides the most general BV theory available. Moreover, we show with a counter-example that if this hypothesis is violated, the problem may be ill-posed in the BV framework.
  • Thematic program: Models in Biology and Medicine (2016/2017)

Talks of the past month


Fellner Klemens (University of Graz) WPI, OMP 1, Seminar Room 08.135 Fri, 24. Mar 17, 15:10
Regularity and Equilibration for spatially inhomogeneous coagulation-fragmentation models
We consider results on discrete and continuous coagulation and coagulation-fragmentation models. For discrete models, we shall present some recent regularity results concerning smoothness of moments and absence of gelation. For the continuous Smoluchowski equation with constant rates, we shall prove exponential, resp. superlinear convergence to equlibrium. This are joint works with M. Breden, J.A. Canizo, J.A. Carrillo and L. Desvillettes.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Cańizo José A. (University of Granada, Spain) WPI, OMP 1, Seminar Room 08.135 Fri, 24. Mar 17, 14:30
Asymptotic behaviour of the Becker-Döring equations
We will present some recent results on the long behaviour of the Becker-Döring equations, mainly involving subcritical solutions: speed of convergence to equilibrium (sometimes exponential, sometimes algebraic) and some new uniform bounds on moments. We will also comment on a continuous model that serves as an analogy of the discrete equations, that seems to exhibit a similar long-time behaviour. This talk is based on collaborations with J. Conlon, A. Einav, B. Lods and A. Schlichting.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Salort Delphine (University Pierre & Marie Curie, Paris, France) WPI, OMP 1, Seminar Room 08.135 Fri, 24. Mar 17, 11:40
Fragmentation Equations and Fokker-Planck equations in neuroscience
In this talk, we present two types of linked partial differential equation models that describe the evolution of an interacting neural network and where neurons interact with one another through their common statistical distribution. We will show, according to the choice of EDP studied, what information can be obtained in terms of synchronization phenomena, qualitative and asymptotic properties of these solutions and what are the specific difficulties on each of these models.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Banasiak Jacek (University of Pretoria, South Africa) WPI, OMP 1, Seminar Room 08.135 Fri, 24. Mar 17, 11:10
Analytic fragmentation semigroups and discrete coagulation-fragmentation processes with growth
In the talk we shall describe how the substochastic semigroup theory can be used to prove analyticity of a class of fragmentation semigroup. This result is applied to discrete fragmentation processes with growth to analyze their long time behaviour and to prove the existence of classical solutions to equations describing such processes combined with coagulation.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Laurençot Philippe (Institut de Mathématiques de Toulouse, France) WPI, OMP 1, Seminar Room 08.135 Fri, 24. Mar 17, 10:10
Self-similar solutions to coagulation-fragmentation equations
When the coagulation kernel and the overall fragmentation rate are homogeneous of degree ë and ă > 0, respectively, there is a critical value ëc := ă + 1 which separates two different behaviours: all solutions are expected to be mass-conserving when ë < ëc while gelation is expected to take place when ë > ëc, provided the mass of the initial condition is large enough. The focus of this talk is the case ë = ëc for which we establish the existence of mass-conserving self-similar solutions. This is partly a joint work with Henry van Roessel (Edmonton).
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Niethammer Barbara (Institut for applied mathematics, Bonn, Germany) WPI, OMP 1, Seminar Room 08.135 Fri, 24. Mar 17, 9:30
The coagulation equation: kernels with homogeneity one
The question whether the long-time behaviour of solutions to Smoluchowski's coagulation equation is characterized by self-similar solutions has received a lot of interest within the last two decades. While this issue is by now well-understood for the three solvable cases, the theory for non-solvable kernels is much less developed. For kernels with homogeneity smaller than one existence results for self-similar solutions and some partial uniqueness results are available. In this talk I will report on some recent results on the borderline case of kernels with homogeneity of degree one. For so-called class II kernels we can prove the existence of a family of self-similar solutions. For class I, or diagonally dominant, kernels, it is known that self-similar solutions cannot exist. Formal arguments suggest that the long-time behaviour of solutions is, in suitable variables, to leading order the same as for the Burgers equation. However, in contrast to diffusive regularizations, we obtain phenomena such as instability of the constant solution or oscillatory traveling waves. (Joint work with Marco Bonacini, Michael Herrmann and Juan Velazquez)
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Gwiazda Piotr (Polish academy of sciences, Poland) WPI, OMP 1, Seminar Room 08.135 Thu, 23. Mar 17, 16:40
Relative entropy method for measure solutions in mathematical biology
In the last years there has appeared several applications of relative entropy method for strong measure-valued uniqueness of solutions in physical models (see: e.g. incompressible Euler equation [1], polyconvex elastodynamics [2], compressible Euler equation [3], compressible Navier-Stokes equation [4]). The topic of the talk will be application of similar techniques to structured population models. Preliminary result in this direction was obtain in [5]. The talk is based on the joint result with Marie Doumic-Jauffret and Emil Wiedemann. [1] Y. Brenier, C. De Lellis, and L. Sz´ekelyhidi, Jr. Weak-strong uniqueness for measure-valued solutions. Comm. Math. Phys., 305(2):351--361, 2011. [2] S. Demoulini, D.M.A. Stuart, and A.E. Tzavaras. Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics. Arch. Ration. Mech. Anal., 205(3):927--961, 2012. [3] P. Gwiazda, A. Œwierczewska-Gwiazda, and E. Wiedemann. Weak-strong uniqueness for measure-valued solutions of some compressible fluid models. Nonlinearity, 28(11):3873--3890, 2015. [4] E. Feireisl, P. Gwiazda, A. Œwierczewska-Gwiazda and E. Wiedemann Dissipative measure-valued solutions to the compressible Navier-Stokes system, Calc. Var. Partial Differential Equations 55 (2016), no. 6, 55--141 [5] P. Gwiazda, E. Wiedemann, Generalized Entropy Method for the Renewal Equation with Measure Data, to appear in Commun. Math. Sci., arXiv:1604.07657
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Van Brunt Bruce (Massey university, New Zealand) WPI, OMP 1, Seminar Room 08.135 Thu, 23. Mar 17, 16:00
Analytic solutions to certain equations from a cell division equation
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  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Haas Bénédicte (University of Paris XIII, France) WPI, OMP 1, Seminar Room 08.135 Thu, 23. Mar 17, 14:40
The fragmentation equation with shattering
We consider fragmentation equations with non-conservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under assumptions of regular variation on the fragmentation rate, we describe the large time behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equations are constructed via non-increasing self-similar Markov processes that continuously reach 0 in finite time. We describe the asymptotic behavior of these processes conditioned on non-extinction and then deduced the asymptotics of solutions to the equation.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Bertoin Jean (University of Zürich, Switzerland) WPI, OMP 1, Seminar Room 08.135 Thu, 23. Mar 17, 14:00
A probabilistic approach to spectral analysis of growth-fragmentation equations (based on a joint work with Alex Watson, Manchester University)
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach to the study of this asymptotic behaviour. We use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the spectral radius and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. In special cases, we obtain exponential convergence.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Gabriel Pierre (University of Versailles-Saint-Quentin, France) WPI, OMP 1, Seminar Room 08.135 Thu, 23. Mar 17, 11:10
Long time behaviour of growth-fragmentation equations
Growth-fragmentation equations can exhibit various asymptotic behaviours. In this talk we illustrate this diversity by working in suitable weighted L^p spaces which are associated to entropy functionals. We prove that, depending on the choice of the coefficients, the following behaviours can happen: uniform exponential convergence to the equilibrium, non-uniform convergence to the equilibrium, or convergence to periodic solutions. This is a joint work with Etienne Bernard and Marie Doumic.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Mischler Stéphane (University Paris-Dauphine, France) WPI, OMP 1, Seminar Room 08.135 Thu, 23. Mar 17, 10:30
Long time asymptotic of the solutions to the growth-fragmentation equation
I will discuss the long time asymptotic of the solutions to the growthfragmentation equation, presenting several results and approaches. I will then focus on the spectral analysis and semigroup approach for which I will give some more details about the proof.
  • Thematic program: Models in Biology and Medicine (2016/2017)
  • Event: Workshop on: "Coagulation and Fragmentation Equations" (2017)

Buszkowski Wojciech (Adam Mickiewicz University) WPI, OMP 1, Seminar Room 08.135 Wed, 15. Mar 17, 10:00
Some open problems in substructural logics
I will focus on several substructural logics, mainly conservative extensions of the Lambek calculus (associative and nonassociative, with and without constants) and point out some basic open problems. Examples: the lower bound of the complexity of the full nonassociative Lambek calculus, the decidability of Pratt's action logic, the decidability of the consequence relation for the nonassociative Lambek calculus with involutive negations, the decidability of the equational theory of lattice-ordered pregroups. I will briefly discuss what is known in these areas.
  • Event: Kick-off Meeting for Project TICAMORE (2017)

Brotherston James (University College London) WPI, OMP 1, Seminar Room 08.135 Tue, 14. Mar 17, 10:00
Biabduction (and Related Problems) in Array Separation Logic
I describe array separation logic (ASL), a variant of separation logic in which the data structures are either pointers or arrays. This logic can be used, e.g., to give memory safety proofs of imperative array programs. The key to automatically inferring specifications is the so-called "biabduction" problem, given formulas A and B, find formulas X and Y such that A + X |= B + Y (and such that A + X is also satisfiable), where + is the well-known "separating conjunction" of separation logic. We give an NP decision procedure for this problem that produces solutions of reasonable quality, and we also show that the problem of finding a consistent solution is NP-hard. Along the way, we study satisfiability and entailment in our logic, giving decision procedures and complexity bounds for both problems. This is joint work with Nikos Gorogiannis (Middlesex) and Max Kanovich (UCL).
  • Event: Kick-off Meeting for Project TICAMORE (2017)

Zhang Yong (WPI c/o Courant & NJIT) WPI, OMP 1, Seminar Room 08.135 Wed, 8. Mar 17, 13:45
Analysis-based fast algorithms for convolution-type nonlocal potential in Nonlinear Schrödinger equation
Convolution-type potential are common and important in many science and engineering fields. Efficient and accurate evaluation of such nonlocal potentials are essential in practical simulations.In this talk, I will focus on those arising from quantum physics/chemistry and lightning-shield protection, including Coulomb, dipolar and Yukawa potentials that are generated by isotropic and anisotropic smooth and fast-decaying density. The convolution kernel is usually singular or discontinuous at the origin and/or at the far field, and density might be anisotropic, which together present great challenges for numerics in both accuracy and efficiency. The state-of-art fast algorithms include Wavelet based Method(WavM), kernel truncation method(KTM), NonUniform-FFT based method(NUFFT) and Gaussian-Sumbased method(GSM). Gaussian-sum/exponential-sum approximation and kernel truncation technique, combined with finite Fourier series and Taylor expansion, finally lead to a O(NlogN) fast algorithm achieving spectral accuracy. Applications to NLSE are reviewed.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Working group "Efficient numerical methods for quantum systems" (2017)

Blanes Sergio (U. Politčcnica de Valčncia) WPI, OMP 1, Seminar Room 08.135 Tue, 7. Mar 17, 17:15
Time average on the numerical integration of non-autonomous differential equations
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  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Working group "Efficient numerical methods for quantum systems" (2017)

Casas Fernando (U. Jaume I Castellón) WPI, OMP 1, Seminar Room 08.135 Tue, 7. Mar 17, 16:15
Time dependent perturbation theory in matrix mechanics and time averaging
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  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Working group "Efficient numerical methods for quantum systems" (2017)
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