Related papers: Limits of density-constrained optimal transport
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
A fundamental dynamical constraint -- that fluctuation induced charge-weighted particle flux must vanish -- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density…
An ideal compressible fluid is considered, with an equilibrium density being a given function of coordinates due to presence of some static external forces. The slow flows in such system, which do not disturb the density, are investigated…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…
We describe a new model for image propagation through open air in the presence of changes in the index of refraction (e.g. due to turbulence) using the theory of optimal transport. We describe the relationship between photon density, or…
We consider a given region $\Omega$ where the traffic flows according to two regimes: in a region $C$ we have a low congestion, where in the remaining part $\Omega\setminus C$ the congestion is higher. The two congestion functions $H_1$ and…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…
Microorganisms often encounter strong confinement and complex hydrodynamic flows while navigating their habitats. Combining finite-element methods and stochastic simulations, we study the interplay of active transport and heterogeneous…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through…
We examine the optimal mass transport problem in $\mathbb{R}^{n}$ between densities having independent compact support by considering the geometry of a continuous interpolating support boundary in space-time within which the mass density…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the…
In this paper, we investigate optimal (partial) transport problems for which the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transport problem, we prove that the singular set is locally a smooth…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or $L^{p}$ regularization, general transport costs and…