Related papers: An energy method for averaging lemmas

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas,…

In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservative due to mutual interaction between species. In…

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with…

We establish improved hypoelliptic estimates on the solutions of kinetic transport equations, using a suitable decomposition of the phase space. Our main result shows that the relative compactness in all variables of a bounded family…

A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…

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…

This article develops a duality principle for non-linear elasticity. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation is concave. Moreover,…

We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…

We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown in [S.Flach, O.Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000)] that…

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of…

We apply the physics-learning duality to molecular systems by complementing the physical description of interacting particles with a dual learning description, where each particle is modeled as an agent minimizing a loss function. In the…

This work aims to provide standard formulations for direct minimization approaches on various types of static problems of continuum mechanics. Particularly, form-finding problems of tension structures are discussed in the first half and the…

A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype…

We use quantum graphs as a model to study various mathematical aspects of the vacuum energy, such as convergence of periodic path expansions, consistency among different methods (trace formulae versus method of images) and the possible…

We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to…

We analyze the statistical physics of self-propelled particles from a general theoretical framework that properly describes the most salient characteristic of active motion, $persistence$, in arbitrary spatial dimensions. Such a framework…

In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…

The nature of the BA function and its adjoint for KP-Toda is traced through the averaging method in generating the Whitham equations, differentials, and symplectic forms, with connections to EM duality.

The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of…