V. M. Kenkre

Generalized master equations for continuous-time random walks

An equivalence is established between generalized master equations and continuous-time random walks by means of an explicit relationship betweenψ(t), which is the pausing time distribution in the theory of continuous-time random walks, andφ(t), which represents the memory in the kernel of a generalized master equation. The result of Bedeaux, Lakatos-Lindenburg, and Shuler concerning the equivalence of the Markovian master equation and a continuous-time random walk with an exponential distribution forψ(t) is recovered immediately. Some explicit examples ofφ(t) andψ(t) are also presented, including one which leads to the equation of telegraphy.

Theory of vibrational relaxation of polyatomic molecules in liquids

A simple tractable theory of vibrational relaxation of polyatomic molecules in polyatomic solvents, which is also applicable to solid solutions, is presented. The theory takes as its starting point Fermi’s golden rule, avoids additional assumptions such as the rotating wave or random phase approximations, and treats both the internal degrees of freedom of the relaxing molecule and the bath degrees of freedom in a fully quantum mechanical manner. The results yield intuitively understandable expressions for the relaxation rates. The treatment of the annihilation as well as the creation of all participating bosons allows the theory to go beyond earlier analyses which treated only cascade processes. New predicted features include temperature effects and asymmetry effects in the frequency dependence. The theory is constructed in a manner which facilitates the use of recent developments in the analysis of instantaneous normal modes of liquids.

Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.

Nonlocal Interaction Effects on Pattern Formation in Population Dynamics

We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is nonlocal, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.

Traveling waves of infection in the hantavirus epidemics.

Traveling waves are analyzed in a model of the hantavirus infection in deer mice. The existence of two kinds of wave phenomena is predicted. An environmental parameter governs a transition between two regimes of propagation. In one of them the front of infection lags behind at a constant rate. In the other, fronts of susceptible and infected mice travel at the same speed, separated by a constant delay. The dependence of the delay on system parameters is analyzed numerically and through a piecewise linearization.

Theory of depolarization of fluorescence in molecular pairs

Abstract Depolarization of fluorescence as a result of energy transfer is studied phenomenologically for a model pair of electronically coupled molecules. The usual rate equations are replaced by the Stochastic Liouville Equations and new radiative terms are included. An expression for the fluorescence polarization for all strengths of electronic coupling between the molecules is obtained. The inclusion of off-diagonal density matrix elements is essential for resolving a paradox arising in the Forster theory of depolarization. The calculation points the way toward using a previously untapped source of information on coherence in complex systems.

Analytic solutions for nonlinear waves in coupled reacting systems

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the piecewise linearized system, showing how the linearization affects the amplitude and frequency of the solutions.

Applicability of the Fisher equation to bacterial population dynamics

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions, is used to provide a practical prescription to extract Fisher equation parameters from observations and to decide on the validity of the Fisher equation.

Theory of microwave interactions in ceramic materials: the phenomenon of thermal runaway

A theory of the phenomenon of thermal runaway in ceramic materials undergoing microwave heating is presented on the basis of a simple temperature-time equation. The non-linear evolution inherent in the equation is shown to arise naturally from physical arguments and it is shown how the parameters of the theory may be calculated from the microscopic absorption processes and information about the material under consideration. The theory is applied to experimental observations reported on several different materials and shown to be in good agreement with the data.

Dynamic localization of a particle in an electric field viewed in momentum space: Connection with Bloch oscillations

Abstract A recent investigation has shown that the motion of a charged particle on a discrete lattice under the action of a time-dependent electric field can exhibit a peculiar phenomenon involving the dynamic localization of the particle whenever the magnitude and frequency of the applied field are in certain ratios to each other. The connection of this phenomenon to the familiar effect of Bloch oscillations is studied by exploring the phenomenon in momentum space.