arXiv subjects

David A. Kessler

Publications and source records attributed to David A. Kessler.

At least 73 records · Page 4Linked to original sources

arXiv2016

The effect of environmental stochasticity on species richness in neutral communities

Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to environmental variations due to the storage effect. This paper provides a systematic and comprehensive discussion of these two contradicting tendencies, using the metacommunity version of the recently proposed time-average neutral model of biodiversity which incorporates environmental stochasticity and demographic noise and allows for extinction and speciation. We show that the incorporation of demographic noise into the model is essential to its applicability, yielding realistic behavior of the system when fitness variations are relatively weak. The dependence of species richness on the strength of environmental stochasticity changes sign when the correlation time of the environmental variations increases. This transition marks the point at which the storage effect no longer succeeds in stabilizing the community.

q-bio.PE↗

arXiv2015

Fronts and fluctuations at a critical surface

The properties of a front between two different phases in the presence of a smoothly inhomogeneous external field that takes its critical value at the crossing point is analyzed. Two generic scenarios are studied. In the first, the system admits a bistable solution and the external field governs the rate in which one phase invades the other. The second mechanism corresponds to a second order transition that, in the case of reactive systems, takes the form of a transcritical bifurcation at the crossing point. We solve for the front shape and its response to external white noise, showing that static properties and also some of the dynamics features cannot distinguish between the two scenarios. The only reliable indicator turns out to be the fluctuation statistics. These take a Gaussian form in the bifurcation case and a double-peak shape in a bistable system. The results of a recent analysis of the morphogenesis process in Drosophila embryos are reanalyzed and we show, in contrast with the interpretation suggested by Krotov et. al., that the plausible underlying dynamics is bistable and not bifurcational.

nlin.PS↗

arXiv2015

Generic Criticality in Ecological and Neuronal Networks

We investigate the dynamics of two models of biological networks with purely suppressive interactions between the units; species interacting via niche competition and neurons via inhibitory synaptic coupling. In both of these cases, power-law scaling of the density of states with probability arises without any fine-tuning of the model parameters. These results argue against the increasingly popular notion that non-equilibrium living systems operate at special critical points, driven by there by evolution so as to enable adaptive processing of input data.

cond-mat.dis-nn↗

arXiv2015

Microbranching in mode-I fracture using large scale simulations of amorphous and perturbed lattice models

We study the high-velocity regime mode-I fracture instability when small microbranches start to appear near the main crack, using large scale simulations. Some of the features of those microbranches have been reproduced qualitatively in smaller scale studies (using ${\cal O}(10^4)$ atoms) on both a model of an amorphous materials (via the continuous random network model) and using perturbed lattice models. In this study, larger scale simulations (${\cal O}(10^6)$ atoms) were performed using multi-threading computing on a GPU device, in order to achieve more physically realistic results. First, we find that the microbranching pattern appears to be converging with the lattice width. Second, the simulations reproduce the growth of the size of a microbranch as a function of the crack velocity, as well as the increase of the amplitude of the derivative of the electrical resistance RMS with respect to the time as a function of the crack velocity. In addition, the simulations yield the correct branching angle of the microbranches, and the power law governing the shape of the microbranches seems to be lower than one, so that the side cracks turn over in the direction of propagation of the main crack as seen in experiment.

cond-mat.stat-mech↗

arXiv2015

Fluctuations of ring polymers

We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and weakly-interacting models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d greater or equal 2. A symmetry of the problem reveals that dimension d and 4 minus d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the one dimensional Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimensions 2 and 3, and are well described to a first approximation by the non-interacting excursion model in dimension 5.

cond-mat.soft↗

arXiv2014

Fractional Edgeworth Expansion: Corrections to the Gaussian-Lévy Central Limit Theorem

In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of variables with an infinite variance which converge by the generalized central limit theorem to a Lévy $α$-stable density function. Our correction may be written by means of a series of fractional derivatives of the Lévy and the conjugate Lévy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the series expansion, we introduce a new family of special functions and briefly discuss their properties. We implement our generalization to the distribution of the momentum for atoms undergoing Sisyphus cooling, and show the improvement of our leading order approximation compared to previous approximations. In vicinity of the transition between Lévy and Gauss behaviors, convergence to asymptotic results slows down.

cond-mat.stat-mech↗

arXiv2014

Deviations from Boltzmann-Gibbs equilibrium in confined optical lattices

Cold atoms in dissipative optical lattices have long been known to exhibit anomalous kinetics due to an effective nonlinear friction force. Here we show that confining the spatial motion of the atoms will lead to an anomalous non-Boltzmann-Gibbs equilibrium state, with a power law tail at large energies. Only in the limit of deep optical lattices, do we regain the Boltzmann-Gibbs state. For strong confinement relative to the damping, we find an explicit expression for the equilibrium phase-space distribution, which generally differs from the canonical Boltzmann-Gibbs state at all energies. Both in the low and high energy limits, the equilibrium distribution is a function of the system's Hamiltonian. At intermediate energies, however, the distribution is not a function of energy only and equipartition is violated.

cond-mat.stat-mech↗

arXiv2014

A generalized model of island biodiversity

The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics structure with four qualitatively distinct phases is unfolded. When the overall interspecies competition is weak, the island species are a sample of the mainland species. For higher values of the competition parameter the system still admit an equilibrium community, but now some of the mainland species are absent on the island. Further increase in competition leads to an intermittent "chaotic" phase, where the dynamics is controlled by invadable combinations of species and the turnover rate is governed by the migration. Finally, the strong competition phase is glassy, dominated by uninvadable state and noise-induced transitions. Our model contains, as a spatial case, the celebrated neutral island theories of Wilson-MacArthur and Hubbell. Moreover, we show that slight deviations from perfect neutrality may lead to each of the phases, as the Hubbell point appears to be quadracritical.

q-bio.PE↗

arXiv2014

Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process

One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $N$ is large and mutation rates are low, but not necessarily small compared to $1/N$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $α$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in shortened form.

q-bio.PE↗

arXiv2014

The Distribution of the Area under a Bessel Excursion and its Moments

A Bessel excursion is a Bessel process that begins at the origin and first returns there at some given time $T$. We study the distribution of the area under such an excursion, which recently found application in the context of laser cooling. The area $A$ scales with the time as $A \sim T^{3/2}$, independent of the dimension, $d$, but the functional form of the distribution does depend on $d$. We demonstrate that for $d=1$, the distribution reduces as expected to the distribution for the area under a Brownian excursion, known as the Airy distribution, deriving a new expression for the Airy distribution in the process. We show that the distribution is symmetric in $d-2$, with nonanalytic behavior at $d=2$. We calculate the first and second moments of the distribution, as well as a particular fractional moment. We also analyze the analytic continuation from $d<2$ to $d>2$. In the limit where $d\to 4$ from below, this analytically continued distribution is described by a one-sided Lévy $α$-stable distribution with index $2/3$ and a scale factor proportional to $[(4-d)T]^{3/2}$.

math-ph↗

arXiv2013

Transport and the first passage time problem with application to cold atoms in optical traps

Measurements of spatial diffusion of cold atoms in optical lattices have revealed anomalous super-diffusion, which is controlled by the depth of the optical lattice. We use first passage time statistics to derive the diffusion front of the atoms. In particular, the distributions of areas swept under the first passage curve till its first arrival, and of areas under the Bessel excursion are shown to be powerful tools in the analysis of the atomic cloud. A rather general relation between first passage time statistics and diffusivity is discussed, showing that first passage time analysis is a useful tool in the calculation of transport coefficients. A brief introduction to the semi-classical description of Sisyphus cooling is provided which yields a rich phase diagram for the dynamics.

cond-mat.stat-mech↗

arXiv2013

Coexistence in an inhomogeneous environment

We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an implicit cost of dispersal, due to the tendency to leave favorable locations. Then, as in the Hamilton-May model with its explicit dispersal cost, the tradeoff between dispersal case and the beneficial role of dispersal in limiting fluctuations, leads to an advantage of one dispersal rate over another, and the eventual extinction of the disadvantaged species. In two dimensions we find that while the competition leads to the elimination of one species at high and low population density, at intermediate densities the two species can coexist essentially indefinitely. This is a new phenomenon not present in either the one-dimensional form of the Kessler-Sander model nor in the totally connected Hamilton-May model, and points to the importance of geometry in the question of dispersal.

q-bio.PE↗

arXiv2013

Micro-branching in mode-I fracture in a randomly perturbed lattice

We study mode-I fracture in lattices with noisy bonds. In contrast to previous attempts, by using a small parameter that perturbs the force-law between the atoms in perfect lattices and using a 3-body force law, simulations reproduce the qualitative behavior of the beyond steady-state cracks in the high velocity regime, including reasonable micro-branching. As far as the physical properties such as the structure factor $g(r)$, the radial or angular distributions, these lattices share the physical properties of perfect lattices rather than that of an amorphous material (e.g., the continuous random network model). A clear transition can be seen between steady-state cracks, where a single crack propagates in the midline of the sample and the regime of unstable cracks, where micro-branches start to appear near the main crack, in line with previous experimental results. This is seen both in a honeycomb lattice and a fully hexagonal lattice. This model reproduces the main physical features of propagating cracks in brittle materials, including the behavior of velocity as a function of driving displacement and the increasing amplitude of oscillations of the electrical resistance. In addition, preliminary indications of power-law behavior of the micro-branch shapes can be seen, potentially reproducing one of the most intriguing experimental results of brittle fracture.

cond-mat.stat-mech↗

arXiv2013

Evolutionarily Stable Density-Dependent Dispersal

An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition and local catastrophe. We do not impose any a priori constraints on the dispersal schedule, allowing the entire schedule to evolve. We find that the system converges at long times to a unique nontrivial dispersal schedule such that the dispersal probability is a monotonically increasing function of the density. We have explored the dependence of the selected dispersal strategy on the various system parameters: mean number of offspring, site carrying capacity, dispersal cost and system size. A few general scaling laws are seen to emerge from the data.

q-bio.PE↗

arXiv2012

Neutral selection

Hubbell's neutral theory of biodiversity has successfully explained the observed composition of many ecological communities but it relies on strict demographic equivalence among species and provides no room for evolutionary processes like selection, adaptation and speciation. Here we show how to embed the neutral theory within the Darwinian framework. In a fitness landscape with a quadratic maximum, typical of quantitative traits, selection restricts the extant species to have traits close to optimal, so that the fitness differences between surviving species are small. For sufficiently small mutation steps, the community structure fits perfectly to the Fisher log-series species abundance distribution. The theory is relatively insensitive to moderate amounts of environmental noise, wherein the location of the fitness maximum changes by amounts of order the width of the noise-free distribution. Adding very large environmental noise to the model qualitatively changes the abundance distributions, converting the exponential fall-off of large species to a power-law decay, typical of a neutral model with environmental noise.

q-bio.PE↗

arXiv2012

Mass Dependence of Instabilities of an Oscillator with Multiplicative and Additive Noise

We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stiffness, the situation is more complicated and in fact the transition is reentrant for intermediate noise strength and damping. For multiplicative noise in the mass, the results depend on the implementation of the noise. One can take the velocity or the momentum to be conserved as the mass is changed. In these cases increasing the mass destabilizes the system. Alternatively, if the change in mass is caused by the accretion/loss of particles to the Brownian particle, these processes are asymmetric with momentum conserved upon accretion and velocity upon loss. In this case, there is no instability, as opposed to the other two implementations. We also study the distribution of the energy, finding a power-law cutoff at a value which increases with time.

cond-mat.stat-mech↗

arXiv2012

How input fluctuations reshape the dynamics of a biological switching system

An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuations affect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch is directly regulated by a noisy input signal, which is described as a nonnegative mean-reverting diffusion process. This continuous process can be a good approximation of the discrete birth-death process and is much more analytically tractable. Within this new setup, we apply the Feynman-Kac theorem to investigate the statistical features of the output switching dynamics. Consistent with our previous findings, the input noise is found to effectively suppress the input-dependent transitions. We show analytically that this effect becomes significant when the input signal fluctuates greatly in amplitude and reverts slowly to its mean.

q-bio.MN↗

arXiv2012

Universal Dimer in a Collisionally Opaque Medium: Experimental Observables and Efimov Resonances

A universal dimer is subject to secondary collisions with atoms when formed in a cloud of ultracold atoms via three-body recombination. We show that in a collisionally opaque medium, the value of the scattering length that results in the maximum number of secondary collisions may not correspond to the Efimov resonance at the atom-dimer threshold and thus can not be automatically associated with it. This result explains a number of controversies in recent experimental results on universal three-body states and supports the emerging evidence for the significant finite range corrections to the first excited Efimov energy level.

cond-mat.quant-gas↗