Related papers: Duality and Heat flow
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the…
Albeit laboratory experiments and numerical simulations have proven themselves successful in enhancing our understanding of long-living large-scale flow structures in horizontally extended Rayleigh-B\'enard convection, some discrepancies…
We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by…
The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the…
We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to define an evolution of metrics on non-smooth metric measure…
The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is well studied. Here we review results from the investigation of this system as well as a number of related…
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We…
The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid…
First, we provide an exposition of a theorem due to Slodkowski regarding the largest "eigenvalue" of a convex function. In his work on the Dirichlet problem, Slodkowski introduces a generalized second-order derivative which for $C^2$…
In this paper we present a mathematical analysis of thin film flow and heat transfer to a laminar liquid film from a horizontal stretching sheet. The flow of thin liquid film and subsequent heat transfer from the stretching surface is…
A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is introduced. Various characteristic…
This paper aims to investigate the evolution problem for planar curves with singularities. Motivated by the inverse curvature flow introduced by Li and Wang (Calc. Var. Partial Differ. Equ. 62 (2023), No. 135), we intend to consider the…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
We prove a certain relation between Legendre's conjecture and Bertrand's postulate in terms of a certain transformation of Legendre's function phi. We show a certain property of a prime.
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…
For every Banach space $(Y,\|\cdot\|_Y)$ that admits an equivalent uniformly convex norm we prove that there exists $c=c(Y)\in (0,\infty)$ with the following property. Suppose that $n\in \mathbb{N}$ and that $X$ is an $n$-dimensional normed…
We establish global existence of smooth solutions to heat flow for Yang-Mills-Higgs functional on Kahler fibrations. As an application, we give a new proof of the key inequality for Mundet's Hitchin-Kobayashi correspondence theorem using…
The Blaschke-Santal\'o Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and only by) ellipsoids. In this paper we give a Fourier analytic proof of this fact.