background: malaria is a major cause of morbidity and mortality in nepal. the magnitude of malaria across the country is alarming and varies with location. therefore, the present study aimed to model malaria incidence rates during 1998 to 2009 in nepal. methods: data for the study were obtained from health management information system (hmis), ministry of public health. a negative binomial mode...

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluch...

In this note we study a fractional Poisson-Nernst-Planck equation modeling a semiconductor device. We prove several decay estimates for the Lebesgue and Sobolev norms in one, two and three dimensions. We also provide the first term of the asymptotic expansion as t → ∞.

We have previously developed a finite element simulator, ichannel, to simulate ion transport through three-dimensional ion channel systems via solving the Poisson–Nernst–Planck equations (PNP) and Sizemodified Poisson–Nernst–Planck equations (SMPNP), and succeeded in simulating some ion channel systems. However, the iterative solution between the coupled Poisson equation and the Nernst–Planck e...

A recently introduced real-space lattice methodology for solving the three-dimensional Poisson-Nernst-Planck equations is used to compute current-voltage relations for ion permeation through the gramicidin A ion channel embedded in membranes characterized by surface dipoles and/or surface charge. Comparisons to a variety of experimental results, presented herein, have proven largely successful....

The model reduction of a mesoscopic kinetic dynamics to macroscopic continuum has been one the fundamental questions in mathematical physics since Hilbert’s time. In this paper, we consider diagram diffusion limit from Vlasov–Poisson–Fokker–Planck (VPFP) system on bounded interval with specular reflection boundary condition Poisson–Nernst–Planck (PNP) no-flux condition. We provide Deep Learning...

A new numerical model is presented for analyzing the propagation of ionic concentrations and electrical potential in space and time in the liquid junction and in the solution/ion-exchanging membrane system. In this model, diffusion and migration according to the Nernst-Planck (NP) flux equation govern the transport of ions, and the electrical interaction of the species is described by the Poiss...

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and nonlinear dif...

High surface charges of polymer pore walls and applied electric fields can lead to the formation and subsequent dissolution of precipitates in nanopores. These precipitates block the pore, leading to current fluctuations. We present an extended Poisson-Nernst-Planck system which includes chemical reactions of precipitation and dissolution. We discuss the mathematical modeling and present 2D num...