A poster session is planned on Monday at 18:00 and posters will remain posted throughout the week.
How to print your poster in Toulouse: Posters can be printed HERE -- the place is very close to the campus. We recommend using the A0 format.
TITLES & ABSTRACTS OF POSTER PRESENTATIONS
Idriss Adjaout (Institut Pascal, Clermont Ferrand)
Stochastic Representations of PDEs for Multiphysics Simulation
Hetranso Ahni (Université Jean-Monnet, Saint-Étienne)
Arrhenius’law and Kramers-type law for a kinetic interacting particle system
The Cucker–Smale model, introduced by Cucker and Smale (2007), is a kinetic interacting particle system that exhibits asymptotic emerging phenomena, where agents tend to align their velocities, leading to a flocking configuration. In the presence of small noise, friction, and a confining potential, excursions out of a positively invariant domain—which represents this emerging phenomenon—become possible, albeit extremely rare. We establish Arrhenius-type and Kramers-type laws to describe the asymptotics of the exit time from this domain, thereby extending the seminal work of Freidlin and Wentzell. This is joint work with Jean-Fran¸cois Jabir and Julian Tugaut.
Julian Amorim (University of São Paulo)
Scaling Limits of Smoluchowski's particles
We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equation, and the fluctuations around this limit are shown to be described by an Ornstein-Uhlenbeck process with drift term given by the linearization of the Smoluchowski operator.
Alexandre Bertolino (Sorbonne Université - LJLL)
Parabolic Lane–Emden Systems with Hardy–Leray Potentials
Pilar Branquinho (University of Coimbra, Center for Mathematics)
Regularity theory for free transmission problems with mixed singularities
Tomas Blore (University of Oxford)
Some insights from the probabilistic to the supercooled Stefan problem
Nicoleta Cazacu (CMAP, Ecole polytechnique)
A semigroup approach for quantitative uniform in time PoC for singular interaction kernels
Based on a semigroup approach, we provide quantitative uniform in time propagation of chaos results for a mollified system of interacting particles with singular interaction kernels of type Lk, k > d and a contractive Lipschitz confinement force field. The method relies on the regularity properties of the solution of the associated nonlinear Fokker-Planck equation combined with estimates of the Duhamel formulation of the mollified empirical measure.
Zhe Chen (MAP5, Université Paris Cité)
A Derivation of the Thick Spray Model
We present a formal derivation of a thick spray model from a binary Enskog–Boltzmann system describing gas–particle mixtures. Unlike classical thin spray models, the Enskog framework accounts for finite-size effects through spatially nonlocal collision operators. Considering a regime with a small mass ratio between gas and particle and a hydrodynamic limit for the gas phase, we show formally that the system converges to an Euler–Vlasov description coupling a compressible gas with a kinetic dispersed phase. The derivation naturally produces the volume-fraction function associated with particle excluded volume and yields finite-volume corrections of order (O(a^3)) in the momentum equations. These corrections include pressure gradient effects analogous to buoyancy forces and higher-order modifications of the friction force. The result provides a mesoscopic level justification of thick spray models commonly used in engineering applications and clarifies the mesoscopic origin of volume fracttion function in dense sprays.
Ruiqi Ding (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Branching Lévy processes with selection and its asymptotic velocity
Ruairi Garrett (Oxford)
Fluctuations of spatial population models with non-local density dependence
The ancestry of a uniform sample from a population of branching brownian particles on the torus, who compete through their total population size, is shown to converge to the brownian spatial coalescent.
Raphael Gastaldello (CNRS / Ecole des Ponts)
On the diffusive-mean field limit of kinetic interacting particle system
Nicholas Graham (University of Bath)
Blow-up and Well-posedness of 2D Keller-Segel PDE perturbed by rough Kraichnan noise
I will present an extension of the Blow-up result found in Mayorcas and Tomasevic's 2023 on the Keller-Segel PDE. I will also discuss the problem of well-posedness on the other side of the blow-up threshold and possible approaches to this question.
Jules Grass (Institut Camille Jordan)
Propagation of chaos in Fisher information
Marcel Hudiani (Umeå University)
Singular Diffusion Limit of Tagged Particle in Zero Range Process with Sinai-type Medium
Oihan Joyot (IRIT Toulouse)
Learning the dynamic of cellular condensates
Tamari Kldiashvili (De Vinci Higher Education; University of Graz)
Mean-field limit for Motsch-Tadmor model
Dowan Koo (University of Oxford, Yonsei University)
On kinetic porous medium equations
Adrienne Le Meur (École Polytechnique)
Quantitative propagation of chaos for particle systems with memory and their long-time behaviour
We study a class of interacting diffusion particle systems with memory and their mean-field limit using coupling methods. We first establish quantitative propagation of chaos estimates for this class of models. Our first main result is a uniform-in-time propagation of chaos estimate, under a suitable contraction condition. We also discuss conditions for existence of stationary solutions and show that long-time convergence to a non-stationary equilibrium may also hold. This requires an asymptotic behaviour for the memory interaction and a memory loss condition. As a consequence, our second main result is that the particle system converges asymptotically to the same equilibrium up to the propagation of chaos error, which shows that the large-particle limit and the large-time limit are exchangeable.
Andrew Nugent (University College London)
Opinion dynamics with continuous age structure
This work extends a model of opinion formation as an interacting particle system to explicitly include an age-structured population. A stochastic differential equation model is first introduced, incorporating ageing dynamics and birth/death processes within a bounded confidence framework. The corresponding mean-field partial differential equation is then derived and analysed, with numerical simulations used to compare the resulting dynamics at microscopic and macroscopic scales. The existence of stationary states in the mean-field model is rigorously established, and these states are shown to be non-unique in general.
Jules Olayé (IMT Toulouse)
Convergence of branching-coalescing brownian motions towards a Hamilton-Jacobi equation
Alexander Pilakoutas (Warwick University)
Steady States and Hypocoercivity for a Nonlinear Perturbation of an Inhomogeneous Nonlinear Boltzmann Equation
Sakari Pirnes (University of Helsinki)
Finite lattice kinetic equations for bosons, fermions, and discrete NLS
We introduce and study finite lattice kinetic equations for bosons, fermions, and discrete NLS. For each model this closed evolution equation provides an approximate description of the appropriate covariance function conjectured to characterize the system. To have such a reference solution should simplify rigorous derivation and control of applicability of kinetic theory. We consider the well-posedness of the resulting evolution equation up to finite kinetic times. We obtain decay of the solutions and upper bounds depending only on Sobolev type norms of the interaction potential and initial data. Joint work with Jani Lukkarinen and Aleksis Vuoksenmaa.
Vishnu Sanjay (Gran Sasso Science Institute)
On the weak coupling limit of the periodic quantum Lorentz gas
I will show that for the periodic quantum Lorentz gas, in the weak coupling limit, certain observables are freely transported, while for general observables, the existence of the limit depends on the regularity of a certain phase space object at resonant momenta.
Sihyun Song (Yonsei University)
Strong compactness phenomena arising in nonlinear and degenerate kinetic Fokker--Planck equations
We consider nonlinear Vlasov--Fokker--Planck equations in which the diffusion and drift depend on the hydrodynamic quantities of the solution. Working with only the most physically natural assumptions of finite mass, entropy, and energy, we prove that solutions to this equation enjoy strong compactness in $L^1$, despite the diffusion being degenerate and singular simultaneously. The proof is based upon a level set decomposition of the Fisher information, and exploiting averaging lemmas. As a consequence, we deduce the global-in-time existence of weak solutions to this equation in the Diperna--Lions framework.
Andrea Tedesco (Centre for Mathematics of the University of Coimbra (CMUC))
Second order regularity for supersolutions to fully nonlinear PDE and applications