Jaroslaw Piasecki | PubMed Health

PubMed2004

Kinetic models of ion transport through a nanopore.

Kinetic equations for the stationary state distribution function of ions moving through narrow pores are solved for a number of 1D models of single ion transport. Ions move through pores of length L, under the action of a constant external field and of a concentration gradient. The interaction of single ions with the confining pore surface and with water molecules inside the pore are modeled by a Fokker-Planck term in the kinetic equation, or by uncorrelated collisions with thermalizing centers distributed along the pore. The temporary binding of ions to polar residues lining the pore is modeled by stopping traps or energy barriers. Analytic expressions for the stationary ion current through the pore are derived for several versions of the model, as functions of key physical parameters. In all cases, saturation of the current at high fields is predicted. Such simple models, for which results are analytic, may prove useful in the study of the current/voltage relations of ion channels through membranes.

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PubMed2003

Self-consistent equation for an interacting Bose gas.

We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential V(r) such that 0< integral dr V(r)=a< infinity. Expressing the partition function by the Feynman-Kac functional integral yields a classicallike polymer representation of the quantum gas. With the Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation rho(mu)=F(mu-(a)rho(mu)) between the density rho and the chemical potential mu, valid in the range of convergence of Mayer series. The function F is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling V(gamma)(r)=gamma3V(gamma(r)), we prove that in the mean-field limit gamma-->0, only the tree diagrams contribute and function F reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of the Mayer series (vicinity of Bose-Einstein condensation), and study the dominant corrections to the mean field. At the lowest order, the form of function F is shown to depend on a single polymer partition function for which we derive the lower and the upper bounds and on the resummation of ring diagrams which can be analytically performed.

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