Random Walks on a Fluctuating Lattice: A Renormalization Group Approach Applied in One Dimension

We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with dimensionality of the lattice.Comment: PostScript file including 2 figures, total 15 pages, 8 other figures obtainable by mail from D.L. Stei

Crossover from percolation to diffusion

A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is completely new. It describes the increase of the diffusion below percolation threshold. As an example, an exact solution of one dimensional lattice problem is given. In this case the new exponent $q=2$.Comment: 10 pages, 1 figur

Generalized model for dynamic percolation

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $\rho_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $\rho_s$ and the relaxation towards $\rho_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.Comment: Latex, 32 pages, 4 ps-figures, submitted to PR

University Physics Volume 2

University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.https://commons.erau.edu/oer-textbook/1002/thumbnail.jp

Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering.

The angular function for elements of the Mueller matrix for polarized light scattering from suspensions of microorganisms is known to be reproducible for different growths of a given bacterial strain in the log (or exponential) phase of growth. The reason for this, the stability of the size and shape distribution for cells, is briefly discussed. Experiments were performed using suspensions of two different strains of Escherichia coli cells in log phase and measuring the angular dependence of the Mueller matrix ratio S34/S11. Calculations were then performed using the coupled dipole approximation to model electromagnetic scattering from particles where the shape of an individual cell was approximated by a cylinder capped with hemispheres of the same radius as the cylinder. Using previously measured values for the length distribution and index of refraction of the cells, the calculated scattering curve was found to fit the measured curve very well. The values obtained for the cell diameters were quite close to diameters previously measured by optical microscopy. Thus this method provides a rapid and convenient method for monitoring bacterial diameters in vivo even when there is an appreciable distribution of bacterial lengths in the population