Related papers: A transport theorem for nonconvecting open sets on…
This paper deals with collisionless transport equations in bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonally invariant velocity measure $\bm{m}(\d v)$ with support…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
In this paper we consider a scalar transport equation with constant coefficients on domains with discrete space and continuous, discrete or general time. We show that on all these underlying domains solutions of the transport equation can…
In this paper we analyze the problem of the geodesic connectedness of subsets of Riemannian manifolds. By using variational methods, the geodesic connectedness of open domains (whose boundaries can be not differentiable and not convex) of a…
The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…
This paper investigates the dynamics of time-periodic Euler flows in multi-connected, planar fluid regions which are ``stirred'' by the moving boundaries. The classical Helmholtz theorem on the transport of vorticity implies that if the…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…
Let $L=\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process…
A non-equilibrium theory of isothermal and diffusionless evolution of incoherent interfaces within a plastically deforming solid is developed. The irreversible dynamics of the interface are driven by its normal motion, incoherency (slip and…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
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 consider expressions of the form of an exponential of the sum of two non-commuting operators of a single variable inside a path integration. We show that it is possible to shift one of the non-commuting operators from the exponential to…
We present a higher-dimensional version of the Poincar\'e-Birkhoff theorem which applies to Poincar\'e time maps of Hamiltonian systems. The maps under consideration are neither required to be close to the identity nor to have a monotone…
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…