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David A. Kessler

Publications and source records attributed to David A. Kessler.

At least 91 records · Page 5Linked to original sources
arXiv2012

Theory of fractional-Lévy kinetics for cold atoms diffusing in optical lattices

Recently, anomalous superdiffusion of ultra cold 87Rb atoms in an optical lattice has been observed along with a fat-tailed, Lévy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical potential. We find, within the framework of the semiclassical theory of Sisyphus cooling, three distinct phases of the dynamics, as the optical potential depth is lowered: normal diffusion; Lévy diffusion; and x ~ t^3/2 scaling, the latter related to Obukhov's model (1959) of turbulence. The process can be formulated as a Lévy walk, with strong correlations between the length and duration of the excursions. We derive a fractional diffusion equation describing the atomic cloud, and the corresponding anomalous diffusion coefficient.

cond-mat.stat-mech↗
arXiv2012

A scaling theory for the quasi-deterministic limit

Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when the number of particles $N$ is large. Accordingly, it fails close to the extinction transition, when the amplitude of stochastic fluctuations is comparable with the size of the population. Here we present a general scaling theory of the transition regime for spatially extended systems. Two fundamental models for out-of-equilibrium phase transitions are considered: the Susceptible-Infected-Susceptible (SIS) that belongs to the directed percolation equivalence class, and the Susceptible-Infected-Recovered (SIR) model belonging to the dynamic percolation class. Implementing the Ginzburg criteria we show that the width of the fluctuation-dominated region scales like $N^{-κ}$, where $N$ is the number of individuals per site and $κ= 2/(d_u-d)$, $d_u$ is the upper critical dimension. Other exponents that control the approach to the deterministic limit are shown to depend on $κ$. The theory is supported by the results of extensive numerical simulations for systems of various dimensionalities.

cond-mat.stat-mech↗
arXiv2011

Noise Effects in Nonlinear Biochemical Signaling

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.

q-bio.MN↗
arXiv2011

Propagating mode-I fracture in amorphous materials using the continuous random network (CRN) model

We study propagating mode-I fracture in two dimensional amorphous materials using atomistic simulations. We used the continuous random network (CRN) model of an amorphous material, creating samples using a two dimensional analogue of the WWW (Wooten, Winer & Weaire) Monte-Carlo algorithm. For modeling fracture, molecular-dynamics simulations were run on the resulting samples. The results of our simulations reproduce the main experimental features. In addition to achieving a steady-state crack under a constant driving displacement (which had not yet been achieved by other atomistic models for amorphous materials), the runs show micro-branching, which increases with driving, transitioning to macro-branching for the largest drivings. Beside the qualitative visual similarity of the simulated cracks to experiment, the simulation also succeeds in explaining the experimentally observed oscillations of the crack velocity.

cond-mat.mtrl-sci↗
arXiv2010

The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it.

cond-mat.stat-mech↗
arXiv2010

Infinite invariant densities for anomalous diffusion in optical lattices and other logarithmic potentials

We solve the Fokker-Planck equation for Brownian motion in a logarithmic potential. When the diffusion constant is below a critical value the solution approaches a non-normalizable scaling state, reminiscent of an infinite invariant density. With this non-normalizable density we obtain the phase diagram of anomalous diffusion for this important process. We briefly discuss the consequence for a range of physical systems including atoms in optical lattices and charges in vicinity of long polyelectrolytes. Our work explains in what sense the infinite invariant density and not Boltzmann's equilibrium describes the long time limit of these systems.

cond-mat.stat-mech↗
arXiv2010

Non-Universal Extinction Transition for Boundary Active Site

We present a generalized model of a diffusion-reaction system where the reaction occurs only on the boundary. This model reduces to that of Barato and Hinrichsen when the occupancy of the boundary site is restricted to zero or one. In the limit when there is no restriction on the occupancy of the boundary site, the model reduces to an age dependent Galton-Watson branching process and admits an analytic solution. The model displays a boundary-induced phase transition into an absorbing state with rational critical exponents and exhibits aging at criticality below a certain fractal dimension of the diffusion process. Surprisingly the behavior in the critical regime for intermediate occupancy restriction $N$ varies with $N$. In fact, by varying the lifetime of the active boundary particle or the diffusion coefficient in the bulk, the critical exponents can be continuously modified.

cond-mat.stat-mech↗
arXiv2009

Fluctuations and Dispersal Rates in Population Dyanmics

Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V. Hutson, K. Mischaikow, et al., J. Math. Bio. 37, 61 (1998)) of two species which differ only in their dispersal rates the slow species always dominates. We demonstrate that fluctuations can change this conclusion and can lead to dominance by the fast species or to coexistence, depending on parameters. We discuss two different effects of fluctuations, and show that our results are consistent with more complex treatments that find that selected dispersal rates are not monotonic with the cost of migration.

q-bio.PE↗
arXiv2009

Globally coupled chaotic maps and demographic stochasticity

The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the equilibrium number of agents on each site, $N$, controls the strength of the discreteness-induced fluctuations. For small $N$ (large fluctuations) a period-doubling cascade appears as the coupling (migration) increases. As $N$ grows an extremely slow dynamic emerges, leading to a flow along a one-dimensional family of almost period 2 solutions. This manifold become a true solutions in the deterministic limit. The degeneracy between different attractors that characterizes the clustering phase of the deterministic system is thus the $N \to \infty$ limit of the slow dynamics manifold.

nlin.CD↗
arXiv2009

Universal features of surname distribution in a subsample of a growing population

We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions. In the first, we construct the family size distribution for the subsample from the stable distribution for the full population. This latter distribution is calculated for an arbitrary growth process in the limit of slow growth, and is seen to depend only on the average and variance of the number of children per individual, as well as the mutation rate. The distribution for the subsample is shifted left with respect to the original distribution, tending to eliminate the part of the original distribution reflecting the small families, and thus increasing the mean family size. From the subsample distribution, various bulk quantities such as the average family size and the percentage of singleton families are calculated. In the second approach, we study the past time development of these bulk quantities, deriving the statistics of the genealogical tree of the subsample. This approach reproduces that of the first when the current statistics of the subsample is considered. The surname distribution from th e 2000 U.S. Census is examined in light of these findings, and found to misrepresent the population growth rate by a factor of 1000.

q-bio.PE↗
arXiv2008

The fixation probability of rare mutators in finite asexual populations

A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100 fold have been observed to spontaneously emerge and achieve high frequencies in natural populations and in long-term laboratory evolution experiments with \textit{E. coli}. In principle, the fixation of mutator alleles is limited by (i) competition with mutations in wild-type backgrounds, (ii) additional deleterious mutational load, and (iii) random genetic drift. Using a multiple locus model and employing both simulation and analytic methods, we investigate the effects of these three factors on the fixation probability $P_{fix}$ of an initially rare mutator as a function of population size $N$, beneficial and deleterious mutation rates, and the strength of mutations $s$. Our diffusion based approximation for $P_{fix}$ successfully captures effects (ii) and (iii) when selection is fast compared to mutation ($μ/s \ll 1$). This enables us to predict the conditions under which mutators will be evolutionarily favored. Surprisingly, our simulations show that effect (i) is typically small for strong-effect mutators. Our results agree semi-quantitatively with existing laboratory evolution experiments and suggest future experimental directions.

q-bio.PE↗
arXiv2008

Non-Hermitian delocalization and the extinction transition

Logistic growth on a static heterogenous substrate is studied both above and below the drift-induced delocalization transition. Using stochastic, agent-based simulations the delocalization of the highest eigenfunction is connected with the large $N$ limit of the stochastic theory, as the localization length of the deterministic theory controls the divergence of the spatial correlation length at the transition. Any finite colony made of discrete agents is washed away from a heterogeneity with compact support in the presence of strong wind, thus the transition belongs to the directed percolation universality class. Some of the difficulties in the analysis of the extinction transition in the presence of a localized active state are discussed.

cond-mat.stat-mech↗
arXiv2008

Extinction transition on diffusive substrate: a different universality class?

The extinction transition on a one dimensional heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the fluctuating environment. At the transition point the density decays like $t^{-0.159}$, as predicted by the theory of directed percolation. However, the scaling function describing the behavior away from the transition shows significant deviations from the DP predictions; it is suggested, thus, that the off-transition behavior of the system is governed by local adaptation to favored regions.

cond-mat.stat-mech↗
arXiv2008

Singularities in Speckled Speckle: Screening

We study screening of optical singularities in random optical fields with two widely different length scales. We call the speckle patterns generated by such fields speckled speckle, because the major speckle spots in the pattern are themselves highly speckled. We study combinations of fields whose components exhibit short- and long-range correlations, and find unusual forms of screening.

physics.optics↗
arXiv2008

Singularities in Speckled Speckle: Statistics

Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary points) using analytical theory and computer simulations. We find anomalous spatial arrangements of the critical points and orders of magnitude anomalies in their relative number densities, and in the densities of the associated zero crossings.

physics.optics↗
arXiv2008

Transition Phenomena Induced by Internal Noise and Quasi-absorbing State

We study a simple chemical reaction system and effects of the internal noise. The chemical reaction system causes the same transition phenomenon discussed by Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72 (2003) 62]. By using the simpler model than Togashi-Kaneko's one, we discuss the transition phenomenon by means of a random walk model and an effective model. The discussion makes it clear that quasi-absorbing states, which are produced by the change of the strength of the internal noise, play an important role in the transition phenomenon. Stabilizing the quasi-absorbing states causes bifurcation of the peaks in the stationary probability distribution discontinuously.

cond-mat.stat-mech↗
arXiv2008

Novel exponents control the quasi-deterministic limit of the extinction transition

The quasi-deterministic limit of the generic extinction transition is considered within the framework of standard epidemiological models. The susceptible-infected-susceptible (SIS) model is known to exhibit a transition from extinction to spreading, as the infectivity is increased, described by the directed percolation equivalence class. We find that the distance from the transition point, and the prefactor controlling the divergence of the (perpendicular) correlation length, both scale with the local population size, $N$, with two novel universal exponents. Different exponents characterize the large $N$ behavior of the susceptible-infected-recovered (SIR) model, which belongs to the dynamic percolation class. Extensive numerical studies in a range of systems lead to the conjecture that these characteristics are generic and may be used in order to classify the high density limit of any stochastic process on the edge of extinction.

cond-mat.stat-mech↗