A field-theoretic approach to the Wiener Sausage

The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a single loop renormalised perturbation theory of a stochastic process closely related to the Wiener Sausage, which, however, proves to be exact for the exponents and some amplitudes. The field-theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem. While we recover a number of known, classical results, the field-theoretic techniques deployed provide a particularly versatile framework, which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions. At the same time, we provide a highly instructive, non-trivial example for some of the technical particularities of the field-theoretic description of stochastic processes, such as excluded volume, lack of translational invariance and immobile particles. The aim of the present work is not to improve upon the well-established results for the Wiener Sausage, but to provide a field-theoretic approach to it, in order to gain a better understanding of the field-theoretic obstacles to overcome.Comment: 45 pages, 3 Figures, Springer styl

Driven diffusion in a periodically compartmentalized tube: homogeneity versus intermittency of particle motion

We study the effect of a driving force F on drift and diffusion of a point Brownian particle in a tube formed by identical ylindrical compartments, which create periodic entropy barriers for the particle motion along the tube axis. The particle transport exhibits striking features: the effective mobility monotonically decreases with increasing F, and the effective diffusivity diverges as F → ∞, which indicates that the entropic effects in diffusive transport are enhanced by the driving force. Our consideration is based on two different scenarios of the particle motion at small and large F, homogeneous and intermittent, respectively. The scenarios are deduced from the careful analysis of statistics of the particle transition times between neighboring openings. From this qualitative picture, the limiting small-F and large-F behaviors of the effective mobility and diffusivity are derived analytically. Brownian dynamics simulations are used to find these quantities at intermediate values of the driving force for various compartment lengths and opening radii. This work shows that the driving force may lead to qualitatively different anomalous transport features, depending on the geometry design

Hysteresis in Pressure-Driven DNA Denaturation

In the past, a great deal of attention has been drawn to thermal driven denaturation processes. In recent years, however, the discovery of stress-induced denaturation, observed at the one-molecule level, has revealed new insights into the complex phenomena involved in the thermo-mechanics of DNA function. Understanding the effect of local pressure variations in DNA stability is thus an appealing topic. Such processes as cellular stress, dehydration, and changes in the ionic strength of the medium could explain local pressure changes that will affect the molecular mechanics of DNA and hence its stability. In this work, a theory that accounts for hysteresis in pressure-driven DNA denaturation is proposed. We here combine an irreversible thermodynamic approach with an equation of state based on the Poisson-Boltzmann cell model. The latter one provides a good description of the osmotic pressure over a wide range of DNA concentrations. The resulting theoretical framework predicts, in general, the process of denaturation and, in particular, hysteresis curves for a DNA sequence in terms of system parameters such as salt concentration, density of DNA molecules and temperature in addition to structural and configurational states of DNA. Furthermore, this formalism can be naturally extended to more complex situations, for example, in cases where the host medium is made up of asymmetric salts or in the description of the (helical-like) charge distribution along the DNA molecule. Moreover, since this study incorporates the effect of pressure through a thermodynamic analysis, much of what is known from temperature-driven experiments will shed light on the pressure-induced melting issue

The kinetic theory of a dilute ionized plasma

This book results from recent studies aimed at answering questions raised by astrophycists who use values of transport coefficients that are old and often unsatisfactory. The few books dealing with the rigorous kinetic theory of a ionized plasma are based on the so called Landau (Fokker-Planck) equation and they seldom relate the microscopic results with their macroscopic counterpart provided by classical non-equilibrium thermodynamics. In this book both issues are thoroughly covered. Starting from the full Boltzmann equation for inert dilute plasmas and using the Hilbert-Chapman-Enskog method to solve the first two approximations in Knudsen´s parameter, we construct all the transport properties of the system within the framework of linear irreversible thermodynamics. This includes a systematic study of all possible cross effects (which, except for a few cases, were never treated in the literature) as well as the famous H-theorem. The equations of magneto-hydrodynamics for dilute plasmas, including the rather surprising results obtained for the viscomagnetic effects, may be now fully assessed. This book will be of immediate interest to the plasma physics community, as well as to astrophysicists. It is also likely to make an impact in the field of cold plasmas, involving laser cooled Rydberg atoms

Relaxation phenomena in the glass transition

A review work on some of the most important aspects on relaxation phenomena that occur both in fragile and strong glass-formers is presented. In particular, different empirical forms for the logarithmic shift factor and its relation with the specific heat that have been studied in the literature are discussed. The application of the generalized stochastic matrix method in strong glasses and the behavior of the relaxation times are indicated. Special attention is given to the alpha and beta relaxation processes and the crossover between the different dynamical regimes that may be recognized in the vicinity of the glass transition

Contribution of floppy modes to configurational and excess entropy in chalcogenide glasses

In this work, following Naumis' ideas [G.G. Naumis, Phys. Rev. B 61 (2000) R9205], we include the floppy modes as a free energy in order to obtain the configurational and excess entropy as well as the jump of the heat capacity of the chalcogenide glasses as function of the coordination number . Theoretically, we find that S-ex/S-c ranges from 1.5 for strong liquids ( = 2) to 2 for fragile ones ( = 2.4). These results are consistent with the values reported by Angell and Borick [C.A. Angell, S. Borick, J. Non-Cryst. Solids 307&310 (2002) 393], who find experimentally for selenium, = 2, S-ex/S-c = 1.47. The proportionality between the configurational and total excess entropies supports the non-existence of the Adam-Gibbs equation paradox. Finally, using S, in the Adam-Gibbs equation we obtain a VFT-like equation as function of , predicting that when increases, D decreases as well, as it has been seen in previous work. (c) 2006 Elsevier B.V. All rights reserved

Diffusion coefficients for two-dimensional narrow asymmetric channels embedded on flat and curved surfaces

This paper focuses on the derivation of a general position-dependent diffusion coefficient to describe the two-dimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying cross section and non-straight midline embedded in a flat or on a curved surface. We consider the diffusion of non-interacting point-like Brownian particles under no external field. In order to project the 2D diffusion equation into an effective one-dimensional generalized Fick-Jacobs equation in both, flat and curved manifolds using the generalization of the mapping procedure introduced by Kalinay and Percus. The expression obtained is the more general position-dependent diffusion coefficient for 2D narrow channels that lies in a plane, which contains all the well-known previous results both symmetric and asymmetric channels as special cases. In a straightforward manner, previously defining the corresponding Fick-Jacobs equation on a curved surface, this result can be generalized to the case of a narrow 2D channel embedded on a no-flat smooth surface where the full position-dependent diffusion coefficient is modified according to the metric elements that accounts for the curvature of the surface. In addition, the equations for the mean first-passage time are obtained for asymmetrical channels on curved surfaces. As an example we shall solve this equation for the case of an asymmetric channel defined by straight walls embedded on a cylindrical surface having a reflecting wall at the origin and an absorbent one at distance θL