Related papers: Balance Laws and Transport Theorems for Flows with…
We review recent results on the anomalous transport in one-dimensional and quasi-one-dimensional systems with bulk and surface disorder. Main attention is paid to the role of long-range correlations in random potentials for the bulk…
This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical…
We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity…
Water, a subject of human fascination for millennia, is likely the most studied substance on Earth, with an entire scientific field -- hydrodynamics -- dedicated to understanding water in motion. However, when water flows through…
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…
In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on…
The fluid in global equilibrium must fulfill some constraints. These constraints can be derived from quantum statistical theory or kinetic theory. In this paper we will show that how these constraints can be applied to determine the…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
In the realm of Continuum Physics, material bodies are realized as continous media and so-called extensive quantities, such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Instabilities at interface of two stream granular flows have been reported in recent experiment [1] that breaking waves can form at the interface between two streams of identical grains flowing on an inclined plane downstream of a splitter…
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations.…
This paper presents results of a theoretical investigation of transport in a numerical model of a two-dimensional Kolmogorov flow. We investigate the changes in its mixing properties associated with transition from laminar regime to…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
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…
We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a…
The linear laws of transport phenomena are central in our description of irreversible processes in systems across the physical sciences. Linear irreversible thermodynamics allows for the identification of the underlying forces driving…
The breaking of detailed balance, the symmetry between forward and backward probability transition between two states, is crucial to understand irreversible systems. In hydrodynamic turbulence, a far-from equilibrium system, we observe a…