Related papers: Duality and Heat flow
We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold of probability measures with additional boundary parts. Yet…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
The paper considers the Ricci flow, coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analog of Perelman's differential…
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…
A shear flow of particles in a laser-driven two-dimensional (2D) dusty plasma are observed in a further study of viscous heating and thermal conduction. Video imaging and particle tracking yields particle velocity data, which we convert…
We develop a general comparison result for inf convolution operators related to rearrangement. As a consequence we derive comparison results under spherically symmetric rearrangement for Laplace and polar transforms. As a by product we…
We discuss in this paper phase-field approximations of the Willmore functional and the associated L2-flow. After recollecting known results on the approximation of the Willmore energy and its L1-relaxation, we derive the expression of the…
The possibility that the type of discontinuous flow changes as the conditions gradually (continuously) change is investigated in connection with the problems arising when the results of numerical simulations of magnetic reconnection in…
Using information theory we derive a thermodynamics for systems evolving under a collective motion, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex…
In previous publications [arXiv:1608.08430, arXiv:1704.06502], the authors have proposed Debye-H\"uckel-approximate free-energy functionals of the pair distribution functions for one-component fluid and two-component plasmas. These…
The paper is devoted to the study of natural convection and the formation of delamination in an incompressible liquid due to convective laminar flows in a closed region heated from the side. Weak, medium and intensive modes of stationary…
Steady-state advective accretion flows in the presence of thermal conduction are studied. All three components of velocity in a spherical coordinates are considered and the flow displays both inflowing and outflowing regions according to…
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a…
The Fluctuation Theorem (FT) gives an analytic expression for the probability, in a nonequilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the Second…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
The present investigation discusses the flow and heat transfer characteristics of a steady three dimensional Sisko fluid. The flow is induced due to bidirectional stretching sheet. The influence of power-law index and stretching ratio on…
Unlike solids, the heat transfer in fluids can be greatly enhanced due to the presence of convection. Under gravity, an unevenly distributed temperature field results in differences in buoyancy, driving fluid motion that is seen in…
This article is devoted to the study of the Hele-Shaw equation. We introduce an approach inspired by the water-wave theory. Starting from a reduction to the boundary, introducing the Dirichlet to Neumann operator and exploiting various…
We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…
We study a system describing the dynamics of a two-phase flow of incompressible viscous fluids influenced by the convective heat transfer of Caginalp-type. The separation of the fluids is expressed by the order parameter which is of diffuse…