arXiv subjects

V. M. Kenkre

Publications and source records attributed to V. M. Kenkre.

At least 37 records · Page 2Linked to original sources

arXiv2008

Molecular motion in cell membranes: analytic study of fence-hindered random walks

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, 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. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G-protein coupled mu-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

physics.bio-ph↗

arXiv2007

Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks

An analytic formulation of memory-possessing random walks introduced recently [Cressoni et al., Phys. Rev. Lett. 98, 070603 (2007) and Schütz and Trimper, Phys. Rev. E 70, 045101 (2004)] for Alzheimer behavior and related phenomena is provided along with exact solutions on the basis of Fokker-Planck equations. The solution of a delay-differential equation derived for the purpose is shown to produce log-periodic oscillations and to coincide rather accurately with previously published computer simulation results. Generalizations along several directions are also constructed on the basis of the formalism.

cond-mat.stat-mech↗

arXiv2007

Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and across network shortcuts ($f$). For fast shortcuts ($f/F\gg 1 $) and low shortcut densities, traversal time data collapse onto an universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.

cond-mat.dis-nn↗

arXiv2007

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

An important characteristic of flocks of birds, school 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.

cond-mat.stat-mech↗

arXiv2006

Study of transients in the propagation of nonlinear waves in some reaction diffusion systems

We study the transient dynamics of single species reaction diffusion systems whose reaction terms $f(u)$ vary nonlinearly near $u\approx 0$, specifically as $f(u)\approx u^{2}$ and $f(u)\approx u^{3}$. We consider three cases, calculate their traveling wave fronts and speeds \emph{analytically} and solve the equations numerically with different initial conditions to study the approach to the asymptotic front shape and speed. Observed time evolution is found to be quite sensitive to initial conditions and to display in some cases nonmonotonic behavior. Our analysis is centered on cases with $f'(0)=0$, and uncovers findings qualitatively as well quantitatively different from the more familiar reaction diffusion equations with $f'(0)>0$. These differences are ascribable to the disparity in time scales between the evolution of the front interior and the front tail.

nlin.PS↗

arXiv2006

Diffusion and Home Range Parameters for Rodents: Peromyscus maniculatus in New Mexico

We analyze data from a long term field project in New Mexico, consisting of repeated sessions of mark-recaptures of Peromyscus maniculatus (Rodentia: Muridae), the host and reservoir of Sin Nombre Virus (Bunyaviridae: Hantavirus). The displacements of the recaptured animals provide a means to study their movement from a statistical point of view. We extract two parameters from the data with the help of a simple model: the diffusion constant of the rodents, and the size of their home range. The short time behavior shows the motion to be approximately diffusive and the diffusion constant to be 470+/-50m^2/day. The long time behavior provides an estimation of the diameter of the rodent home ranges, with an average value of 100+/-25m. As in previous investigations directed at Zygodontomys brevicauda observations in Panama, we use a box model for home range estimation. We also use a harmonic model in the present investigation to study the sensitivity of the conclusions to the model used and find that both models lead to similar estimates.

q-bio.PE↗

arXiv2006

Solitons of Bose-Fermi mixtures in a strongly elongated trap

It is shown that a Bose-Fermi mixture of a degenerate gas of spin-polarized fermions, whose number significantly exceeds the number of bosons, embedded in a strongly anisotropic trap, is described by the one-dimensional coupled nonlinear Schrodinger equation for the boson component and the wave equation with external source for the fermion component. Depending on the type of boson-fermion interaction, the system may display modulational instability and the existence of solitons in the fermion and boson components respectively. Such solitons represent either a local decrease (increase) of the density of both the components or a decrease of the density in one component and an increase of the density in the other component. It is shown that the type of the effective interactions can be easily managed by varying the trap geometry or by means of Feshbach resonance.

cond-mat.other↗

arXiv2005

Effect of Predators of Juvenile Rodents on the Spread of the Hantavirus Epidemic

Effects of predators of juvenile mice on the spread of the Hantavirus are analyzed in the context of a recently proposed model. Two critical values of the predation probability are identified. When the smaller of them is exceeded, the hantavirus infection vanishes without extinguishing the mice population. When the larger is exceeded, the entire mice population vanishes. These results suggest the possibility of control of the spread of the epidemic by introducing predators in areas of mice colonies in a suitable way so that such control does not kill all the mice but lowers the epidemic spread.

q-bio.PE↗

arXiv2005

Theory of Hantavirus Infection Spread Incorporating Localized Adult and Itinerant Juvenile Mice

A generalized model of the spread of the Hantavirus in mice populations is presented on the basis of recent observational findings concerning the movement characteristics of the mice that carry the infection. The factual information behind the generalization is based on mark-recapture observations reported in Giuggioli et al. [Bull. Math. Biol. 67, 1135 (2005)] that have necessitated the introduction of home ranges in the simple model of Hantavirus spread presented by Abramson and Kenkre [Phys. Rev. E 66, 11912 (2002)]. The essential feature of the model presented here is the existence of adult mice that remain largely confined to locations near their home ranges, and itinerant juvenile mice that are not so confined, and, during their search for their own homes, move and infect both other juveniles and adults that they meet during their movement. The model is presented at three levels of description: mean field, kinetic and configuration. Results of calculations are shown explicitly from the mean field equations and the simulation rules, and are found to agree in some respects and to differ in others. The origin of the differences is shown to lie in spatial correlations. It is indicated how mark-recapture observations in the field may be employed to verify the applicability of the theory.

q-bio.PE↗

arXiv2005

Diffusion and Home Range Parameters from Rodent Population Measurements in Panama

Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, \emph{Zygodontomys brevicauda}. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.

q-bio.PE↗

arXiv2005

Theory of Home Range Estimation from Mark-Recapture Measurements of Animal Populations

A theory is provided for the estimation of home ranges of animals from the standard mark-recapture technique in which data are collected by capturing, tagging and recapturing the animals. The theoretical tool used is the Fokker-Planck equation, its characteristic quantities being the diffusion constant which describes the motion of the animals, and the attractive potential which addresses their tendency to live near their burrows. The measurement technique is shown to correspond to the calculation of a certain kind of mean square displacement of the animals relevant to the specific probing window in space corresponding to the trapping region. The output of the theory is a sigmoid curve of the observable mean square displacement as a function of the ratio of distances characteristic of the home range and the trapping region, along with an explicit prescription to extract the home range form observations. Applications of the theory to rodent movement in Panama and New Mexico are pointed out. An analysis is given of the sensitivity of our theory to the choice of the confining potential via the use of various representative cases. A comparison is provided between home range size inferred from our method and from other procedures employed in the literature. Consequences of home range overlap are also discussed.

q-bio.PE↗

arXiv2005

Traversal Times for Random Walks on Small-World Networks

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world connections. When f >> F, the mean time to traverse the network exhibits a transition associated with percolation of the random graph (i.e., small-world) part of the network, and a collapse of the data onto a universal curve. This transition was not observed in earlier studies in which equal transition rates were assumed for all allowed steps. We develop a simple self-consistent effective medium theory and show that it gives a quantitatively correct description of the traversal time in all parameter regimes except the immediate neighborhood of the transition, as is characteristic of most effective medium theories.

cond-mat.dis-nn↗

arXiv2005

Study of Arbitrary Nonlinearities in Convective Population Dynamics with Small Diffusion

Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for the evolution of population densities. The initial value problem is solved explicitly for some cases and for others it is shown how to find traveling wave solutions analytically. The effect of adding diffusion to the convective equations is first studied through exact analysis through a piecewise linear representation of the nonlinearity. Using an appropriate small parameter suggested by that analysis, a perturbative treatment is developed to treat the case in which the convective evolution is augmented by a small amount of diffusion.

q-bio.PE↗

arXiv2005

Static Pairwise Annihilation in Complex Networks

We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e. Poisson) and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the ``hubs'' have been annihilated, the network disintegrates and only isolated sites are left.

cond-mat.stat-mech↗

arXiv2005

Bistability and Hysteresis in the Sliding Friction of a Dimer

The sliding friction of a dimer moving over a periodic substrate and subjected to an external force is studied in the steady state for arbitrary temperatures within a one-dimensional model. Nonlinear phenomena that emerge include dynamic bistability and hysteresis, and can be related to earlier observations for extended systems such as the Frenkel-Kontorova model. Several observed features can be satisfactorily explained in terms of the resonance of a driven-damped nonlinear oscillator. Increasing temperature tends to lower the resonant peak and wash out the hysteresis.

cond-mat.mtrl-sci↗

arXiv2004

Periodically Varying Externally Imposed Environmental Effects on Population Dynamics

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatio-temporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.

nlin.AO↗

arXiv2004

A Theoretical Framework for the Analysis of the West Nile Virus Epidemic

We present a model for the growth of West Nile virus in mosquito and bird populations based on observations of the initial epidemic in the U.S. Increase of bird mortality as a result of infection, which is a feature of the epidemic, is found to yield an effect which is observable in principle, viz., periodic variations in the extent of infection. The vast difference between mosquito and bird lifespans, another peculiarity of the system, is shown to lead to interesting consequences regarding delay in the onset of the steady-state infection. An outline of a framework is provided to treat mosquito diffusion and bird migration.

q-bio.PE↗

arXiv2003

Analytic considerations in the study of spatial patterns arising from non-local interaction effects in population dynamics

Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We first show how stability arguments yield a condition for pattern formation involving the ratio of the pattern wavelength and the effective diffusion length of the individuals. We develop a mode-mode coupling analysis which might be useful in shedding some light on the observed formation of small-amplitude versus large-amplitude patterns.

nlin.PS↗