Related papers: Lagrangian discretization of crowd motion and line…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
We describe the main ingredients needed to create, from the smooth lagrangian density, a variational principle for discrete motions of a discrete rod, with corresponding conserved Noether currents. We describe all geometrical objects in…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
The long time behavior of the dynamics of a fast-slow system of ordinary differential equations is examined. The system is derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow…
In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation…
A Bayesian approach is developed for the inference of an eddy-diffusivity field from Lagrangian trajectory data. The motion of Lagrangian particles is modelled by a stochastic differential equation associated with the advection-diffusion…
We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…
We prove the existence of weak solutions to a system of two diffusion equations that are coupled by a pointwise volume constraint. The time evolution is given by gradient dynamics for a free energy functional. Our primary example is a model…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
In cosmology, a basic explanation of the observed concentration of mass in singular structures is provided by the Zeldovich approximation, which takes the form of free-streaming flow for perturbations of a uniform Einstein-de Sitter…
The Lagrangian approach is natural to study issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model including velocity and acceleration as dynamical variables for inhomogeneous turbulent…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no…
We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multiple species. An approach inspired by augmented Lagrangian…
Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures that determine material…