Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFouriers Law from Closure Equations
134
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We give a rigorous derivation of Fouriers law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.
rate research
Read More
In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter asymptotic expansion based on two small parameters characterizing nonlinear and dispersive effects and strictly following the arguments in the asymptotic derivation of the classical CH equation. The resulting equations generalize the CH equation in two different ways. The first generalization replaces the quadratic nonlinearity of the CH equation with a general power-type nonlinearity while the second one replaces the dispersive terms of the CH equation with fractional-type dispersive terms. In the absence of both higher-order nonlinearities and fractional-type dispersive effects, the generalized equations derived reduce to the classical CH equation that describes unidirectional propagation of shallow water waves. The generalized equations obtained are compared to similar equations available in the literature, and this leads to the observation that the present equations have not appeared in the literature.
Newton viscosity law for the momentum flux and Fouriers law for the heat flux define Navier-Stokes hydrodynamics for a simple, one component fluid. There is ample evidence that a hydrodynamic description applies as well to a mesoscopic granular fluid with the same form for Newtons viscosity law. However, theory predicts a qualitative difference for Fouriers law with an additional contribution from density gradients even at uniform temperature. The reasons for the absence of such terms for normal fluids are indicated, and a related microscopic explanation for their existence in granular fluids is presented.
This paper contains a rigorous mathematical example of direct derivation of the system of Euler hydrodynamic equations from Hamiltonian equations for N point particle system as N tends to infinity. Direct means that the following standard tools are not used in the proof: stochastic dynamics, thermodynamics, Boltzmann kinetic equations, correlation functions approach by N. N. Bogolyubov.
In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities cite{Lowengrub1998}. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a $C^0$ finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with $C^0$ finite element. A Newtons method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.
In the present paper, we give a simple proof of the level density of fixed trace square ensemble.We derive the integral equation of the level density of fixed trace square ensemble.Then we analyze the asymptotic behavior of the level density.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
