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Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…
In the paper discusses the interaction between two charged balls in equilibrium state. It is shown that, depending of the sizes, charges and distance, the balls can move in the same or opposite direction. They can repulse and attract. It is…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical…
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully…
The scientific field of traffic engineering encompasses a rich set of mathematical techniques, as well as researchers with entirely different backgrounds. This paper provides an overview of what is currently the state-of-the-art with…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the…
We consider steady gravity-driven flow of a thin layer of viscous fluid over a curved substrate. The substrate has topographical variations (`bumps') on a large scale compared to the layer thickness. Using lubrication theory, we find the…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
Incompressible fluid equations are studied with UV cut-off and in periodic boundary conditions. Properties of the resulting ODEs holding uniformly in the cut-off are considered and, in particular, are conjectured to be equivalent to…
From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
Most transport theorems---that is, a formula for the rate of change of an integral in which both the integrand and domain of integration depend on time---involve domains that evolve according to a flow map. Such domains are said to be…
A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by…
We study the problem of the motion of substance in a channel of a network for the case of channel having two arms. Stationary regime of the flow of the substance is considered. Analytical relationships for the distribution of the substance…
The methods of abstract simplicial homology and cohomology are reviewed and applied to the topology of electrical networks. Kirchhoffs laws of electrical circuits are shown to be manifestly homological in their origins. Since they are based…
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…