Related papers: Transport Theorem and Continuity Equations: a Stoc…
We study a free boundary problem which arises as the continuum version of a stochastic particles system in the context of Fourier law. Local existence and uniqueness of the classical solution are well known in the literature of free…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
For quantum transport through mesoscopic system, a quantum master equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of…
We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
We consider the problem of loss and propagation of regularity of transport equation with Osgood vector field. As an application, we obtain a quantitative stability estimate for 2D incompressible Euler equation with generalized Yudovich…
In the preceding paper, linear response methods have been applied to obtain formally exact expressions for the parameters of Navier-Stokes order hydrodynamics. The analysis there is general, applying to both normal and granular fluids with…
We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure $\rho$ under variations of the target measure $\mu$, when the cost function is the squared Riemannian distance on…
Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
We show that the steady and unsteady system of transport equations with a nonhomogeneous right hand side can be extended from its domain that possesses an impermeable $C^2$-boundary to the whole space.
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients and unbounded divergence. In the first result we assume the drift is $L^{2}([0,T] \times \R^{d})\cap…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the…
This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a…