Displaying similar documents to “A Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region and its Applications”

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Shixin Xu, Minxin Chen, Sheereen Majd, Xingye Yue, Chun Liu (2014)

Molecular Based Mathematical Biology

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Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence...

Analyzing nonlocal effects in the plasmon spectra of a metal slab by the Green’s function technique for hydrodynamic model

Naijing Kang, Z.L. Miškovic, Ying-Ying Zhang, Yuan-Hong Song, You-Nian Wang (2014)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We study the dynamic response of a metal slab containing electron gas described by the hydrodynamic model with dispersion. The resulting wave equation for the perturbed electron density is solved by means of the Green’s function that satisfies Neumann boundary conditions at the endpoints of the slab. This solution is coupled with the electrostatic potential, which is expressed in terms of the Green’s function for the Poisson equation for a layered structure consisting of three dielectric...

Transmission-line laser modeling of carrier diffusion in VCSEL

Vladimir Gerasik, Jacek Miloszewski, Marek S. Wartak (2014)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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The transmission-line laser model (TLLM) is an equivalent-circuit model which provides stable and explicit matrix routines for the solution of the laser rate equations. The application of TLLM method to the analysis of a vertical-cavity surface-emitting laser (VCSEL) requires certain modifications. The theoretical basis of the model is considered, including space discretization of the inhomogeneous VCSEL cavity so that it yields the synchronization condition. The main attention is paid...

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

Jaydeep P. Bardhan, Matthew G. Knepley, Peter Brune (2015)

Molecular Based Mathematical Biology

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In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundaryintegral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first...

Copula approach to residuals of regime-switching models

Anna Petričková, Magda Komorníková (2012)

Kybernetika

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The autocorrelation function describing the linear dependence is not suitable for description of residual dependence of the regime-switching models. In this contribution, inspired by Rakonczai ([20]), we will model the residual dependence of the regime-switching models (SETAR, LSTAR and ESTAR) with the autocopulas (Archimedean, EV and their convex combinations) and construct improved quality models for the original real time series.

Numerical simulation of the motion of a three-dimensional glacier

Marco Picasso, Jacques Rappaz, Adrian Reist (2008)

Annales mathématiques Blaise Pascal

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The motion of a three-dimensional glacier is considered. Ice is modeled as an incompressible non-Newtonian fluid. At each time step, given the shape of the glacier, a nonlinear elliptic system has to be solved in order to obtain the two components of the horizontal velocity field. Then, the shape of the glacier is updated by solving a transport equation. Finite element techniques are used to compute the velocity field and to solve the transport equation. Numerical results are compared...

Convergence model of interest rates of CKLS type

Zuzana Zíková, Beáta Stehlíková (2012)

Kybernetika

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This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities...