Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus
Abstract We study the McKean–Vlasov equation ∂ _t ϱ= β^-1 Δ ϱ+ κ\, ∇ ⋅\,(ϱ ∇ (W ⋆
ϱ)),∂ t ϱ= β-1 Δ ϱ+ κ∇·(ϱ∇(W⋆ ϱ)), with periodic boundary conditions on the torus. We …
ϱ)),∂ t ϱ= β-1 Δ ϱ+ κ∇·(ϱ∇(W⋆ ϱ)), with periodic boundary conditions on the torus. We …
Jump processes as generalized gradient flows
We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …
state space is a space of nonnegative measures, and the class of systems includes the …
[HTML][HTML] Cosh gradient systems and tilting
MA Peletier, A Schlichting - Nonlinear Analysis, 2023 - Elsevier
We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …
We show how such dissipation potentials emerge in large deviations of jump processes …
Variational convergence of the Scharfetter–Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit
A Hraivoronska, A Schlichting, O Tse - Numerische Mathematik, 2024 - Springer
In this paper, we explore the convergence of the semi-discrete Scharfetter–Gummel scheme
for the aggregation-diffusion equation using a variational approach. Our investigation …
for the aggregation-diffusion equation using a variational approach. Our investigation …
On the difference between entropic cost and the optimal transport cost
S Pal - arXiv preprint arXiv:1905.12206, 2019 - arxiv.org
Consider the Monge-Kantorovich problem of transporting densities $\rho_0 $ to $\rho_1 $
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …
Entropy dissipation of Fokker-Planck equations on graphs
We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the
space of probability measures supported on the nodes with respect to the discrete …
space of probability measures supported on the nodes with respect to the discrete …
Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
A Esposito, FS Patacchini, A Schlichting… - Archive for Rational …, 2021 - Springer
We consider dynamics driven by interaction energies on graphs. We introduce graph
analogues of the continuum nonlocal-interaction equation and interpret them as gradient …
analogues of the continuum nonlocal-interaction equation and interpret them as gradient …
Modeling of chemical reaction systems with detailed balance using gradient structures
We consider various modeling levels for spatially homogeneous chemical reaction systems,
namely the chemical master equation, the chemical Langevin dynamics, and the reaction …
namely the chemical master equation, the chemical Langevin dynamics, and the reaction …
A noncommutative transport metric and symmetric quantum Markov semigroups as gradient flows of the entropy
M Wirth - arXiv preprint arXiv:1808.05419, 2018 - arxiv.org
We study quantum Dirichlet forms and the associated symmetric quantum Markov
semigroups on noncommutative $ L^ 2$ spaces. It is known from the work of Cipriani and …
semigroups on noncommutative $ L^ 2$ spaces. It is known from the work of Cipriani and …
The Scharfetter–Gummel scheme for aggregation–diffusion equations
A Schlichting, C Seis - IMA Journal of Numerical Analysis, 2022 - academic.oup.com
In this paper we propose a finite-volume scheme for aggregation–diffusion equations based
on a Scharfetter–Gummel approximation of the quadratic, nonlocal flux term. This scheme is …
on a Scharfetter–Gummel approximation of the quadratic, nonlocal flux term. This scheme is …