Related papers: Eyring equation ans the second order kinetic law
The prospect of a time-dependent Higgs vacuum expectation value is examined within the standard model of electroweak interactions. It is shown that the classical equation of motion for the Higgs field admits a solution that is a…
Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by…
We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models,…
Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called…
For a detailed understanding of chemical processes in nature and industry, we need accurate models of chemical reactions in complex environments. While Eyring transition state theory is commonly used for modeling chemical reactions, it is…
We propose a new kinetic BGK-type model for a mixture of four monatomic gases, undergoing a bimolecular and reversible chemical reaction. The elastic and reactive interactions are described separately by distinct relaxation terms and the…
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We investigate a class of parametric elliptic semilinear partial differential equations of second order with homogeneous essential boundary conditions, where the coefficients and the right-hand side (and hence the solution) may depend on a…
Recently, Gorban (2021) analysed some kinetic paradoxes of the transition state theory and proposed its revision that gave the "entangled mass action law", in which new reactions were generated as an addition to the reaction mechanism under…
The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard…
A recently proposed quantum mechanical criterion `concavity of energy' for the second law of thermodynamics is studied also for classical particle systems confined in a bounded region by a potential with a time-dependent coupling constant.…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
This paper extends the foundational concept to second-order quantum correlation tensors, representing intensity-intensity correlations.As their application in diverse optical field experiments gaining importance, we investigate conserved…
The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the…
We investigate the kinetics of $A+B \to 0$ reaction with the local attractive interaction between opposite species in one spatial dimension. The attractive interaction leads to isotropic diffusions inside segregated single species domains,…
We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of action principle…
The calculation of molecular excited states is critically important to decipher a plethora of molecular properties. In this manuscript, we develop an equation of motion formalism on top of a bi-exponentially parametrized ground state…
Transformation equations for the kinetic energy of a tardyon are derived in the limits of classical and of special relativity theory. Two formulas are presented. In the first one the energy of the particle in one of the involved reference…
Relativistically covariant form of equation of motion for real particle (neutral in charge) under the action of electromagnetic radiation is derived. Various formulations of the equation of motion in the proper frame of reference of the…