125 citations · 859 across the 68 of their papers we have counts for
38 papers · 1 filter
Nonlinear diffusion limit of non-local interactions on a sphere
Mark A. Peletier, Anna Shalova
We study an aggregation PDE with competing attractive and repulsive forces on a sphere of arbitrary dimension. In particular, we consider the limit of strongly localized repulsion…
Cosh gradient systems and tilting
Mark A. Peletier, André Schlichting
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, m…
Gamma-convergence of a gradient-flow structure to a non-gradient-flow structure
Mark A. Peletier, Mikola C. Schlottke
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffectiv…
EDP-convergence for nonlinear fast-slow reaction systems with detailed balance
Alexander Mielke, Mark A. Peletier, Artur Stephan
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with L…
Discrete-to-continuum convergence of charged particles in 1D with annihilation
Patrick van Meurs, Mark A. Peletier, Norbert Pozar
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite ti…
Jump processes as Generalized Gradient Flows
Mark A. Peletier, Riccarda Rossi, Giuseppe Savaré +1
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 Forward…
Atomistic origins of continuum dislocation dynamics
Thomas Hudson, Patrick van Meurs, Mark A. Peletier
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocati…
Convergence and non-convergence of many-particle evolutions with multiple signs
Adriana Garroni, Patrick van Meurs, Mark A. Peletier +1
We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive an…
Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation
Richard C. Kraaij, Alexandre Lazarescu, Christian Maes +1
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonst…
Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics
M. H. Duong, A. Lamacz, M. A. Peletier +2
In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quant…
On microscopic origins of generalized gradient structures
Matthias Liero, Alexander Mielke, Mark A. Peletier +1
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadra…
Variational approach to coarse-graining of generalized gradient flows
Manh Hong Duong, Agnes Lamacz, Mark A. Peletier +1
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is pr…
Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock
Adriana Garroni, Patrick van Meurs, Mark Peletier +1
In this paper we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a cont…
A moving boundary problem for the Stokes equations involving osmosis: variational modelling and short-time well-posedness
Friedrich Lippoth, Mark A. Peletier, Georg Prokert
Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by…
Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement
Maria Giovanna Mora, Mark Peletier, Lucia Scardia
We consider systems of parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We…
Coarse-graining and fluctuations: Two birds with one stone
Manh Hong Duong, Mark A. Peletier, Upanshu Sharma
We show how the mathematical structure of large-deviation principles matches well with the concept of coarse-graining. For those systems with a large-deviation principle, this may…
Variational analysis of a mesoscale model for bilayer membranes
Luca Lussardi, Mark A. Peletier, Matthias Röger
We present an asymptotic analysis of a mesoscale energy for bilayer membranes that has been introduced and analyzed in two space dimensions by the second and third author (Arch. Ra…
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
Giovanni A. Bonaschi, José A. Carrillo, Marco Di Francesco +1
We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and…
Hexagonal patterns in a simplified model for block copolymers
D. P. Bourne, M. A. Peletier, S. M. Roper
In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer melts with a dominant phase. The model is simple enough to be amenable not only to…
GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles
Manh Hong Duong, Mark A. Peletier, Johannes Zimmer
In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of…
Optimality of the triangular lattice for a particle system with Wasserstein interaction
D. P. Bourne, M. A. Peletier, F. Theil
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or…
Conservative-dissipative approximation schemes for a generalized Kramers equation
Manh Hong Duong, Mark A. Peletier, Johannes Zimmer
We propose three new discrete variational schemes that capture the conservative-dissipative structure of a generalized Kramers equation. The first two schemes are single-step minim…
Asymptotic behaviour of a pile-up of infinite walls of edge dislocations
Marc Geers, Ron Peerlings, Mark Peletier +1
We consider a system of parallel straight edge dislocations and we analyse its asymptotic behaviour in the limit of many dislocations. The dislocations are represented by points in…
Large deviations and gradient flows
Stefan Adams, Nicolas Dirr, Mark A. Peletier +1
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles descri…