Related papers: Gelfand type problem for two phase porous media
The classical Prats' problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This…
The Classical Nucleation Theory allegedly fails to describe the temperature dependence of the homogeneous crystal nucleation rates below the temperature of maximum nucleation, $T_{\mathrm{max}}$. Possible explanations for this suspected…
The deep problems caused from the limitations of theoretical framework itself can only be clarified by extending and reconstructing of the theoretical framework, we extend classical theoretical framework of thermodynamics, break through the…
No bootstrap assumption is needed to derive the exponential growth of the Hagedorn hadron mass spectrum: It is a consequence of the second law applied to a relativistic gas, and the relativistic equivalence between inertial mass and its…
In this paper we study the interaction between natural convection and heat explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction…
It is argued that two-particle collisions of relativistic particles "at a distance", irrespective of their position in the configuration space, generate uniform distribution of particles in Lorentz invariant phase space.
Segregation by thermal diffusion of an intruder immersed in a sheared granular gas is analyzed from the (inelastic) Boltzmann equation. Segregation is induced by the presence of a temperature gradient orthogonal to the shear flow plane and…
A bidisperse porous medium is one with two porosity scales. There are the usual pores known as macro pores but also cracks or fissures in the skeleton which give rise to micro pores. In this article we develop and analyse a model for…
Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics [10,11,12,16] is extended to the case of temperature-dependent surface tension. We prove well-posedness in an Lp-setting,…
There are several models for the effective thermal conductivity of two-phase composite materials in terms of the conductivity of the solid and the disperse material. In this paper, we generalise three models of Maxwell type (namely, the…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
The celebrated exchange fluctuation theorem -- proposed by Jarzynski and W\'ozcik, (Phys Rev. Lett. 92, 230602 (2004)) for heat exchange between two systems in thermal equilibrium at different temperatures -- is explored here for quantum…
The thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle temperature in natural units of information per second. The rate is calculated using a Gaussian process with a variance…
A general theory for the melting of two dimensional solids explaining the universal and non-universal properties is an open problem up to date. Although the celebrated KTHNY theory have been able to predict the critical properties of the…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
Pole-skipping offers compelling evidence for the hydrodynamic origin of chaotic behavior in strongly coupled quantum systems. We demonstrate that the cumulative effect of higher-order corrections to the hydrodynamic diffusive mode, captured…
We address two issues in the thermodynamic model for nuclear disassembly. Surprisingly large differences in results for specific heat were seen in predictions from the canonical and grand canonical ensembles when the nuclear system passes…
The thermal conductivity is calculated with the Helfand-moment method in the Lennard-Jones fluid near the triple point. The Helfand moment of thermal conductivity is here derived for molecular dynamics with periodic boundary conditions.…
Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively.…
We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and phase parameter. The system is a…