Related papers: A variational principle for mass transport
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…
A study of the transport coefficients of a system of elastic hard disks, based on the use of Helfand-Einstein expressions is reported. The self-diffusion, the viscosity, and the heat conductivity are examined with averaging techniques…
In this work, we first prove a stability theorem for traveling waves in a class of non-cooperative reaction-diffusion systems with nonlocal dispersal of equal diffusivities. Our stability criterion is in the sense that the initial…
Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However,…
We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject…
This paper proposes a variational principle for the solutions of quantum field theories in which the ``trial functions'' are chosen from the algebra of asymptotic fields, and illustrates this variational principle in simple cases.
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…