Related papers: Boundary layer variational principles: A case stud…
Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
We study heat conduction in a one-dimensional {finite}, unpinned chain of atoms perturbed by stochastic momentum exchange and coupled to Langevin heat baths at {possibly} distinct temperatures placed at the endpoints of the chain. While…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…
Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's…
We introduce the idea of {\it collisional models} for Brownian particles, in which a particle is sequentially placed in contact with distinct thermal environments and external forces. Thermodynamic properties are exactly obtained,…
We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…
We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of…
In this paper, using the entropy production inequality of Green and Laws, the theory of thermopiezoelectricity is presented, in which the second gradient of displacement and the second gradient of electric potential are included in the set…
Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the…
We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative…
In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…
A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…
A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators.For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schr\"odinger equation, we find that the…
This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…
The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to…
We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the…
We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the dynamical map, referred to as the…
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state…
A thermodynamic model of a plasma boundary layer, characterized by enhanced temperature contrasts is proposed. The theory is constructed to determine the inner boundary temperature $T_1$ for a specified outer (colder) boundary temperature…