Related papers: Balance Laws and Transport Theorems for Flows with…
An extension of the H-theorem for dissipative particle dynamics (DPD) to the case of a multi-component fluid is made. Detailed balance and an additional H-theorem are proved for an energy-conserving version of the DPD algorithm. The…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
We consider waves travelling in two different mediums each endowed with a different constant speed of propagation. At the interface between the two mediums, the refraction of the rays of the optic geometry is described by the…
This technical report presents a direct proof of Theorem~1 in [1] and some consequences that also account for (20) in [1]. This direct proof exploits a state space change of basis which replaces the coupled difference equations (10) in [1]…
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of…
Using the techniques developed in arxiv: 1203.3544 we compute the universal part of the equilibrium partition function characteristic of a theory with multiple abelian U(1) anomalies in arbitrary even spacetime dimensions. This contribution…
The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
We examine classical, transient fluctuation theorems within the unifying framework of Langevin dynamics. We explicitly distinguish between the effects of non-conservative forces that violate detailed balance, and non-autonomous dynamics…
We consider the one-dimensional shallow water problem with capillary surfaces and moving contact {lines}. An energy-based model is derived from the two-dimensional water wave equations, where we explicitly discuss the case of a stationary…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
We study a system of two coupled transport equations with freezing. The solutions freeze in time when they are equal. We prove existence and uniqueness of continuous solutions if the initial conditions are continuous. We discuss several…
We derive a continuity equation to study transport properties in a $\mathcal{PT}$-symmetric tight-binding chain with gain and loss in symmetric configurations. This allows us to identify the density fluxes in the system, and to define a…
In this paper, we will critically discuss recent theoretical and experimental developments on the transport of one dimensional quantum systems. In particular, we will focus on open issues and controversial results related to the finite…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
In two space dimensions, we study a general double-free-boundary problem which models a stream flowing through a gravitaional potentiay. ntial-energy terrain. The existence theorem generalizes (by a different proof) a result of A. Beurling.…
We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely-suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from…
Control theory often takes the mathematical model of the to-be-control-led system for granted. In contrast, port-Hamiltonian systems theory bridges the gap between modelling and control for physical systems. It provides a unified framework…