In this paper the quantum hyperbolic equation formulated in [1] is applied to the study of the propagation of the initial thermal state of the Universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced, VP = h̄/8tP = 1.25 10 GeV where tP is a Planck time. For the barrier height V < VP the master thermal equation is the modified Klein-Gordon ...

Abstract. Reactive transport processes in natural environments often involve many ionic species. The diffusivities of species vary. Since assigning different the advection–diffusion equation leads to charge imbalance, a single diffusivity is usually used for all In this work, we apply Nernst–Planck equation, which resolves unequal an electroneutral manner, model reactive transport. To demonstra...

The diffusiophoresis of a soft particle governed by an imposed ionic concentration gradient is studied based on modified ion transport equation. surface the rigid core considered to be hydrophobic, which coated with charged polyelectrolyte layer (PEL) whose dielectric constant different from dispersion medium. This step-change in PEL and medium creates partitioning effect. governing equations c...

Physical and chemical stochastic processes described by the master equation are investigated. The system-size expansion, called the Ω-expansion, trasnforms the master equation to the corresponding Fokker-Planck equation. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master equation, the exact expression of...

Physical and chemical stochastic processes described by the master equation are investigated. The system-size expansion, called the Ω-expansion, transforms the master equation to the corresponding Fokker-Planck equation. In this paper, we examine the entropy production for both the master equation and the corresponding Fokker-Planck equation. For the master equation, the exact expression of the...

recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. the spherical tours (st) fusion energy development path is complementary to the tokamak burning plasma experiment such as nstx and higher toroidal beta regimes and improves the design of a po...

Ehrenfest's urn model is modified by introducing nonlinear terms in the associated transition probabilities. It is shown that these modifications lead, in the continuous limit, to a Fokker-Planck equation characterized by two competing diffusion terms, namely, the usual linear one and a nonlinear diffusion term typical of anomalous diffusion. By considering a generalized H theorem, the associat...