相关论文: Two Series Formulae from the Solution of a System …
The study of Mayer's cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE non-physical behavior at condensed states of fluids. In particular, a general equation of state is derived…
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
In this note, we propose the first mathematical derivation of a macroscopic Baer-Nunziato type system for compressible two-phase flows allowing two pressure state laws depending on the different phases. By doing so, we extend the results…
In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the $(1+1)$-dimensional Dodson's…
Reaction cross diffusion systems are a two species generalization of the porous media equation. These systems play an important role in the mechanical modeling of living tissues and tumor growth. Due to their mixed parabolic-hyperbolic…
It has been found the exact solutions for nonstationary distribution of the temperature in the liquid ring with two viscosities and two free boundaries of the ring.
Reaction-diffusion equations on infinite graphs can have an infinite number of stationary solutions. These solutions are generally described as roots of a countable system of algebraic equations. As a generalization of periodic stationary…
We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence $\{g(k)\}$), to be reduced to an infinite $q$-product times a single basic…
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
The fluid flow across an unbounded horizontal plate embedded with uniform mass diffusion is studied in this article together with the impacts of the chemical reaction and parabolic motion, while the temperature and concentration of the…
Non-linear equations of radial motion of a gas bubble in a compressible viscous liquid have been modified considering effects of viscosity and compressibility more complete than all previous works. A new set of equations has been derived…
We prove an almoste representation formula for positive solutions of semilinear heat equations with power-type absorption the initial trace of which is the indicatrix function of a compact set. The representations involves a Wiener test via…
An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is…
The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
We propose a generalization of quantum mechanical equations in the hydrodynamic form by introducing, into the Lagrangian density, terms taking into account the diffusion velocity at zero and finite temperatures and the diffusion pressure…
Contents: 1. Introduction. 2. Sum rules prior to QCD. 3. Dispersion relations. 4. Types of two point function sum rules. 5. Non-perturbative power corrections. 6. Some examples of QCD sum rules.