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Displaying similar documents to “Modification of Bikerman model with specific ion sizes”

Compound Compound Poisson Risk Model

Minkova, Leda D. (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 60K10, 62P05. The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular...

Compartmental Models of Migratory Dynamics

J. Knisley, T. Schmickl, I. Karsai (2011)

Mathematical Modelling of Natural Phenomena

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Compartmentalization is a general principle in biological systems which is observable on all size scales, ranging from organelles inside of cells, cells in histology, and up to the level of groups, herds, swarms, meta-populations, and populations. Compartmental models are often used to model such phenomena, but such models can be both highly nonlinear and difficult to work with. Fortunately, there are many significant biological systems that are amenable to linear compartmental...

Stationary solutions of the generalized Smoluchowski-Poisson equation

Robert Stańczy (2008)

Banach Center Publications

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The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.

Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

Jinn-Liang Liu, Dexuan Xie, Bob Eisenberg (2017)

Molecular Based Mathematical Biology

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We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation...

Relative dielectric constants and selectivity ratios in open ionic channels

Bob Eisenberg, Weishi Liu (2017)

Molecular Based Mathematical Biology

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We investigate the effects of the relative dielectric coefficient on ionic flows in open ion channels, using mathematical analysis of reasonably general Poisson-Nernst-Planck type models that can include the finite sizes of ions. The value of the relative dielectric coefficient is of course a crucial parameter for ionic behavior in general. Using the powerful theory of singularly perturbed problems in applied mathematics, we show that some properties of open channels are quite insensitive...

A continuous-time model for claims reserving

T. Rolski, A. Tomanek (2014)

Applicationes Mathematicae

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Prediction of outstanding liabilities is an important problem in non-life insurance. In the framework of the Solvency II Project, the best estimate must be derived by well defined probabilistic models properly calibrated on the relevant claims experience. A general model along these lines was proposed earlier by Norberg (1993, 1999), who suggested modelling claim arrivals and payment streams as a marked point process. In this paper we specify that claims occur in [0,1] according to a...

A Quantum Corrected Poisson-Nernst-Planck Model for Biological Ion Channels

Jinn-Liang Liu (2015)

Molecular Based Mathematical Biology

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A quantum corrected Poisson-Nernst-Planck (QCPNP) model is proposed for simulating ionic currents through biological ion channels by taking into account both classical and quantum mechanical effects. A generalized Gummel algorithm is also presented for solving the model system. Compared with the experimental results of X-ray crystallography, it is shown that the quantum PNP model is more accurate than the classical model in predicting the average number of ions in the channel pore. Moreover,...

Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials: Ion size effects on individual fluxes

Mingji Zhang, Jianbao Zhang, Daniel Acheampong (2017)

Molecular Based Mathematical Biology

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We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck model for ionic flows through membrane channels. Excess chemical potentials are included in this work to account for finite ion size effects. This is the main difference from the classical Poisson-Nernst-Planck models, which treat ion species as point charges and neglect ion-to-ion interactions. Due to the fact that most experiments (with some exceptions) can only measure the total current while individual fluxes contain...

Spatial bayesian models of tree density with zero inflation and autocorrelation

Frédéric Mortier, Olivier Flores, Sylvie Gourlet-Fleury (2007)

Journal de la société française de statistique

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Understanding the spatial and temporal dynamics of rain forests is a challenge for assessing the impact of disturbance on forest stands and tree populations. Still few studies address the modelling of spatial patterns of tree density. Here, we present Hierarchical bayesian (HB) models for the local density of juveniles trees in a tropical forest. These models are specifically designed to handle zero inflation and spatial autocorrelation in the data. Height types of models were built...

A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations

Weihua Geng (2015)

Molecular Based Mathematical Biology

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Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement...