We study the asymptotic regime for the relativistic Vlasov-Maxwell-FokkerPlanck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in...

A simple analytical approach to estimate thermodynamic properties of model Yukawa systems is presented. The approach extends the traditional Debye-Hückel theory into the regime of moderate coupling and is able to qualitatively reproduce thermodynamics of Yukawa systems up to the fluid-solid phase transition. The simplistic equation of state (pressure equation) is derived and applied to the hydr...

The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson-Nerst-Planck (PNP) system, consists of a diffusion equation for each species augmented by transport due to a self consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important probl...

In this note, we analyze the classical magneto-static approach to theory of type I superconductors, and a Debye source representation that can be used numerically solve resultant equations. We also prove one fields, J−, found within superconductor via London equations, is physical current in outgoing part magnetic field given as Biot-Savart integral J−. Finally, compute static currents for mode...

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Maxwell’s equations in a bounded Debye medium are formulated in terms of the standard partial differential equations of electromagnetism with a Volterra-type history dependence of the polarization on the electric field intensity. This leads to Maxwell’s equations with memory. We make a correspondence between this type of constitutive law and the hereditary integral constitutive laws from linear...

We aim to derive a phenomenological approach link the theories of anomalous transport governed by fractional calculus and stochastic theory with conductivity behavior semi-empirical formalism involving Debye, Cole-Cole, Cole-Davidson, Havriliak-Negami type equations. want determine processes in amorphous semiconductors insulators developing theoretical over some mathematical instruments methods...

background beta-lactam resistance in gram-negative bacteria, especially escherichia coli, is a main clinical problem. it is often caused by the co-production of β-lactamases, particularly extended-spectrum β-lactamases (esbls) and ampc enzymes. it may lead to a problem for diagnosis via recommended phenotypic tests by the clinical and laboratory standards institute (clsi). conversely, β-lactama...

This research report related to nano-sized particles of tetragonal rutile phase TiO2. We havesuccessfully synthesized TiO2 nanoparticles, by chemical method non-toxic and bio-safe, at lower than 100°C. This method is simple, economic and friendly for environmentally and suitable for large scale grains. Using of choline chloride, to decrease the size of commercial TiO2 by chemical method. ...