The Langevin equation approach to the evolution of the velocity distribution for the Brownian particle might leave you uncomfortable. A more formal treatment of this type of problem is given by the Fokker-Planck equation. We can either formulate the question in terms of the evolution of a nonstationary probability distribution from a defined initial condition, or in terms of the evolution of th...

The drift-diffusion (Poisson-Nernst-Planck) model is applied to the potassium channel in a biological membrane plus surrounding solution baths. Two-dimensional cylindrically symmetric simulations of the K channel in KCl solutions are presented which show significant boundary layers at the ends of the channel and display the spreading of charge into the bath regions. The computed current-voltage...

Abstract Traditional derivations of the Planck mass ignore the role of charge and spin in general relativity. From the Kerr-Newman null surface and horizon radii, quantized charge and spin dependence are introduced in an extended Planck scale of mass. Spectra emerge with selection rules dependent upon the choice of Kerr-Newman radius to link with the Compton wavelength. The appearance of the fi...

The transport of ions in nanofluidic systems, specifically the rectified ion or ionic diode phenomenon occurring presence asymmetrical geometry and/or charge distribution, has drawn considerable attention due to its relevance energy conversion and biosensing applications. However, previous numerical research frequently overlooked concurrent liquid flow within these even though multiple experime...

The Poisson-Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new PoissonBoltzmann type (PB n) equation with a small dielectric parameter 2 and nonlocal nonlinearity which takes into consideration of the preservation of the total amount of each individual ion. This equation can be derived from ...

We propose an edge averaged finite element (EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of computed charged density functions and temperature function. Also thermodynamic consistent discrete energy estimate which resembles second law system is prescribed. Numerical examples are provided.

The solution-diffusion-electromigration approximation model (SDE-A) was formulated to describe the salt permeability of effectively uncharged, weakly charged and strongly reverse osmosis (RO) membranes. uses three fewer parameters, depending on type charge behavior that a particular membrane exhibits under allowable experimental conditions regarding feedwater salinity acidity. resulting algebra...

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the...