Publications (248)508.49 Total impact
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ABSTRACT: A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a Smoluchowski equation in 2ndimensional space that combines diffusion with confinement of each animal to its particular home range. An additional (reaction) term that comes into play when the animals are in close proximity describes the process of infection. Analytic solutions are obtained, confirmed by numerical procedures, and shown to predict a surprising effect of confinement. The effect is that infection spread has a nonmonotonic dependence on the diffusion constant and/or the extent of the attachment of the animals to the home ranges. Optimum values of these parameters exist for any given distance between the attractive centers. Any change from those values, involving faster/slower diffusion or shallower/steeper confinement, hinders the transmission of infection. A physical explanation is provided by the theory. Reduction to the simpler case of no home ranges is demonstrated. Effective infection rates are calculated and it is shown how to use them in complex systems consisting of dense populations.Bulletin of mathematical biology. 08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even an animal such as a mouse carrying an epidemic. Theoretical considerations have almost always assumed that the particle motion is translationally invariant. We study here the case when that assumption is relaxed, in that the particle is additionally subjected to a harmonic potential. This tethering to a center modifies the reactiondiffusion phenomenon. Using a Smoluchowski equation to describe the system, we carry out a study which is explicit in one dimension but can be easily extended for arbitrary dimensions. Interesting features emerge depending on the relative location of the trap, the attractive center, and the initial placement of the diffusing particle.Physical Review E 12/2013; 88(61):062142. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effects of interaction with a reservoir. One stems from the randomization of phases and the other from phase space considerations. Even the meaning of the word `phase' differs drastically in the two instances in which it appears in the previous statement. In the first case it normally refers to quantum phases whereas in the second it describes the multiplicity of reservoir states that corresponds to each system state. The generalized master equation theory for the time evolution of such systems is here developed in a transparent manner and both effects of reservoir interactions are addressed in a unified fashion. The formalism is illustrated in simple cases including in the standard spinboson situation wherein a quantum dimer is in interaction with a bath consisting of harmonic oscillators. The theory has been constructed for application in energy transfer in molecular aggregates and in photosynthetic reaction centers.The European Physical Journal B 08/2013; 87(4). · 1.28 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Motivated currently by the problem of coalescence of receptor clusters in mast cells in the general subject of immune reactions, and formerly by the investigation of exciton trapping and sensitized luminescence in molecular systems and aggregates, we present analytic expressions for survival probabilities of moving entities undergoing diffusion and reaction on encounter. Results we provide cover several novel situations in simple 1d systems as well as higherdimensional counterparts along with a useful compendium of such expressions in chemical physics and allied fields. We also emphasize the importance of the relationship of discrete sink term analysis to continuum boundary condition studies.The Journal of Physical Chemistry B 07/2013; · 3.61 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Wave propagation can be clearly discerned in data collected on mouse populations in the Cibola National Forest (New Mexico, USA) related to seasonal changes. During an exploration of the construction of a methodology for investigations of the spread of the Hantavirus epidemic in mice we have built a system of interacting reaction diffusion equations of the FisherKolmogorovPetrovskiiPiskunov type. Although that approach has met with clear success recently in explaining Hantavirus refugia and other spatiotemporal correlations, we have discovered that certain observed features of the wave propagation observed in the data we mention are impossible to explain unless modifications are made. However, we have found that it is possible to provide a tentative explanation/description of the observations on the basis of an assumed Allee effect proposed to exist in the dynamics. Such incorporation of the Allee effect has been found useful in several of our recent investigations both of population dynamics and pattern formation and appears to be natural to the observed system. We report on our investigation of the observations with our extended theory.Journal of Theoretical Biology 12/2012; · 2.35 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study electron tunneling between two infinte potential square wells connected via an opaque barrier and find that time evolution of the probability of the presence of a Gaussian wave packet, localized initially in one of the wells, shares the fractal behavior of tunneling in a quartic potential, discovered by Dekker (H. Dekker, Phys. Rev.A35, 1825 (1987). However, the fractal dimensions are found to be closer to those of a conventional Weierstrass function than those appropriate to the quasiWeierstrass behavior of Dekker. It is argued that the usual exponential decay predicted by conventional relaxation processes can be recovered only as an effect of thermal fluctuations.Fractals 11/2011; 06(01). · 0.36 Impact Factor  Biophysical Journal 02/2011; 100(3). · 3.67 Impact Factor
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ABSTRACT: We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations. The result we obtain helps in the understanding of the onset of abrupt transitions leading to the extinction of biological populations. The result is expressed in terms of Airy functions and sheds light on the behavior of bacteria in a Petri dish as well as of large animals such as rodents moving over a landscape.Physica A: Statistical Mechanics and its Applications 01/2011; 390(2):257262. · 1.68 Impact Factor 
Article: Effects of rotation on the nonlinear friction of a damped dimer sliding on a periodic substrate.
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ABSTRACT: Rotational effects on the nonlinear sliding friction of a damped dimer moving over a substrate are studied within a largely onedimensional model. The model consists of two masses connected rigidly, internally damped, and sliding over a sinusoidal (substrate) potential while being free to rotate in the plane containing the masses and the direction of sliding. Numerical simulations of the dynamics performed by throwing the dimer with an initial center of mass velocity along the substrate direction show a richness of phenomena including the appearance of three separate regimes of motion. The orientation of the dimer performs tiny oscillations around values that are essentially constant in each regime. The constant orientations form an intricate pattern determined by the ratio of the dimer length to the substrate wavelength as well as by the initial orientations chosen. Corresponding evolution of the center of mass velocity consists, respectively, of regular oscillations in the first and the third regimes, but a power law decay in the second regime; the center of mass motion is effectively damped in this regime because of the coupling to the rotation. Depending on the initial orientation of the dimer, there is considerable variation in the overall behavior. For small initial angles to the vertical, an interesting formal connection can be established to earlier results known in the literature for a vibrating, rather than rotating, dimer. But for large angles, on which we focus in the present paper, quite different evolution occurs. Some of the numerical observations are explained successfully on the basis of approximate analytical arguments but others pose puzzling problems.Physical Review E 10/2010; 82(4 Pt 2):046601. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present an analytic study of traveling fronts, localized colonies, and extended patterns arising from a reactiondiffusion equation which incorporates simultaneously two features: the wellknown Allee effect and spatially nonlocal competition interactions. The former is an essential ingredient of most systems in population dynamics and involves extinction at low densities, growth at higher densities, and saturation at still higher densities. The latter feature is also highly relevant, particularly to biological systems, and goes beyond the unrealistic assumption of zerorange interactions. We show via exact analytic methods that the combination of the two features yields a rich diversity of phenomena and permits an understanding of a variety of issues including spontaneous appearance of colonies.Physical Review E 09/2010; 82(3 Pt 2):036210. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A fieldinduced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Physics of Condensed Matter 08/2010; · 1.28 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We predict an abrupt observable transition, on the basis of numerical studies, of hantavirus infection in terrain characterized by spatially dependent environmental resources. The underlying framework of the analysis is that of Fisher equations with an internal degree of freedom, the state of infection. The unexpected prediction is of the sudden disappearance of refugia of infection in spite of the existence of supercritical (favorable) food resources, brought about by reduction of their spatial extent. Numerical results are presented and a theoretical explanation is provided on analytic grounds on the basis of the competition of diffusion of rodents carrying the hantavirus and nonlinearity present in the resource interactions.Physical Review E 07/2010; 82(1 Pt 1):011920. · 2.31 Impact Factor  Biophysical Journal 01/2010; 98(3). · 3.67 Impact Factor
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ABSTRACT: Anomalous diffusion of random walks has been extensively studied for the case of noninteracting particles. Here we study the evolution of nonlinear partial differential equations by interpreting them as Fokker–Planck equations arising from interactions among random walkers. We extend the formalism of generalized Hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples. They include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable: the usual Fisher equation which contains a quadratic nonlinearity, a generalization of the Fisher equation with densitydependent diffusion constant, and the Nagumo equation which incorporates a cubic rather than a quadratic nonlinearity. We estimate the generalized Hurst exponents.Physica A: Statistical Mechanics and its Applications 09/2009; 388(18):36873694. · 1.68 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We propose a comprehensive dynamical model for cooperative motion of selfpropelled particles, e.g., flocking, by combining wellknown elements such as velocityalignment interactions, spatial interactions, and angular noise into a unified Lagrangian treatment. Noise enters into our model in an especially realistic way: it incorporates correlations, is highly nonlinear, and it leads to a unique collective behavior. Our results show distinct stability regions and an apparent change in the nature of one class of noiseinduced phase transitions, with respect to the mean velocity of the group, as the range of the velocityalignment interaction increases. This phasetransition change comes accompanied with drastic modifications of the microscopic dynamics, from nonintermittent to intermittent. Our results facilitate the understanding of the origin of the phase transitions present in other treatments.Physical Review E 06/2009; 79(5 Pt 1):051115. · 2.31 Impact Factor 
Article: Theory of possible effects of the Allee phenomenon on the population of an epidemic reservoir.
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ABSTRACT: We investigate possible effects of highorder nonlinearities on the shapes of infection refugia of the reservoir of an infectious disease. We replace Fishertype equations that have been recently used to describe, among others, the Hantavirus spread in mouse populations by generalizations capable of describing Allee effects that are a consequence of the highorder nonlinearities. After analyzing the equations to calculate steadystate solutions, we study the stability of those solutions and compare to the earlier Fishertype case. Finally, we consider the spatial modulation of the environment and find that unexpected results appear, including a bifurcation that has not been studied before.Physical Review E 05/2009; 79(4 Pt 1):041902. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a theoretical calculation to describe the confined motion of transmembrane molecules in cell membranes. Understanding the motion of membraneassociated molecules, e.g. various types of receptors, has great modern relevance in cell biology. Our study is divided into two parts. In the first, we consider motion in an ordered system and in the second, we investigate the effects of disorder by employing an effective medium approximation. Both are based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. As a result, the calculations make possible, in principle, the extraction of confinement parameters such as mean compartment sizes and mean intercompartmental transition rates from experimentally reported published observations.03/2009;  [Show abstract] [Hide abstract]
ABSTRACT: The effectivemedium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a onedimensional system with bond disorder for specificity, a transformation procedure is developed to deduce explicit expressions for the memory functions from given distribution functions characterizing the system disorder. It is shown how to use the memory functions in the Laplace domain forms in which they first appear, and in the time domain forms which are obtained via numerical inversion algorithms, to address time evolution of the system beyond the asymptotic domain of large times normally treated. An analytic but approximate procedure is provided to obtain the memories, in addition to the inversion algorithm. Good agreement of effectivemedium theory predictions with numerically computed exact results is found for all time ranges for the distributions used except near the percolation limit, as expected. The use of ensemble averages is studied for normal as well as correlation observables. The effect of size on effectivemedium theory is explored and it is shown that, even in the asymptotic limit, finitesize corrections develop to the wellknown harmonic mean prescription for finding the effective rate. A percolation threshold is shown to arise even in one dimension for finite (but not infinite) systems at a concentration of broken bonds related to the system size. Spatially longrange transfer rates are shown to emerge naturally as a consequence of the replacement of spatial disorder by temporal memories, in spite of the fact that the original rates possess nearest neighbor character. Pausing time distributions in continuoustime random walks corresponding to the effectivemedium memories are calculated.Physical Review E 02/2009; 79(1 Pt 1):011114. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present some models of random walks with internal degrees of freedom that have the potential to find application in the context of animal movement and stochastic search. The formalism we use is based on the generalized master equation which is particularly convenient here because of its inherent coarsegraining procedure whereby a random walker position is averaged over the internal degrees of freedom. We show some instances in which nonlocal jump probabilities emerge from the coupling of the motion to the internal degrees of freedom, and how the tuning of one parameter can give rise to sub, superand normal diffusion at long times. Remarks on the relation between the generalized master equation, continuous time random walks and fractional diffusion equations are also presented.Journal of Physics A Mathematical and Theoretical 01/2009; 4220. · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the timeindependent Schr\"{o}dinger equation for a quantum particle subjected to a uniform gravitational field. Despite the linear character of the Schr\"{o}dinger equation, the result we obtain helps in the understanding of the onset of abrupt transitions leading to extinction of biological populations. The result is expressed in terms of Airy functions and sheds light on the behavior of bacteria in a Petri dish as well as of large animals such as rodents moving over a landscape.12/2008;
Publication Stats
4k  Citations  
508.49  Total Impact Points  
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Institutions

1985–2013

University of New Mexico
 • Department of Physics & Astronomy
 • Department of Biology
Albuquerque, New Mexico, United States


2005–2010

University of Chile
 Departamento de Física (Ciencias)
Santiago, Region Metropolitana de Santiago, Chile


1986

Charles University in Prague
 Faculty of Mathematics and Physics
Praha, Praha, Czech Republic 
Massachusetts Institute of Technology
Cambridge, Massachusetts, United States


1974–1985

University of Rochester
 Department of Physics and Astronomy
Rochester, NY, United States


1983

French National Centre for Scientific Research
Lutetia Parisorum, ÎledeFrance, France 
University of Strasbourg
Strasburg, Alsace, France


1982

The Catholic University of America
 Department of Physics
Washington, D. C., DC, United States


1978–1979

Indian Institute of Technology Bombay
 Department of Physics
Mumbai, Mahārāshtra, India
