arXiv subjects

Nigel Goldenfeld

Publications and source records attributed to Nigel Goldenfeld.

At least 55 records · Page 3Linked to original sources

arXiv2013

Extrinsic noise driven phenotype switching in a self-regulating gene

Due to inherent noise in intracellular networks cellular decisions can be random, so genetically identical cells can display different phenotypic behavior even in identical environments. Most previous work in understanding the decision-making process has focused on the role of intrinsic noise in these systems. Yet, especially in the high copy-number regime, extrinsic noise has been shown to be much more significant. Here, using a prototypical example of a bistable self-regulating gene model, we develop a theoretical framework describing the combined effect of intrinsic and extrinsic noise on the dynamics of stochastic genetic switches. Employing our theory and Monte Carlo simulations, we show that extrinsic noise not only significantly alters the lifetimes of the phenotypic states, but can induce bistability in unexpected regions of parameter space, and may fundamentally change the escape mechanism. These results have implications for interpreting experimentally observed heterogeneity in cellular populations and for stochastic modeling of cellular decision processes.

q-bio.MN↗

arXiv2012

Effect of weak rotation on large-scale circulation cessations in turbulent convection

We investigate the effect of weak rotation on the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection, using the theory for cessations in a low-dimensional stochastic model of the flow previously studied. We determine the cessation frequency of the LSC as a function of rotation, and calculate the statistics of the amplitude and azimuthal velocity fluctuations of the LSC as a function of the rotation rate for different Rayleigh numbers. Furthermore, we show that the tails of the reorientation probability distribution function remain unchanged for rotating systems, while the distribution of the LSC amplitude and correspondingly the cessation frequency are strongly affected by rotation. Our results are in close agreement with experimental observations.

physics.flu-dyn↗

arXiv2012

Avalanche statistics and intermittency in topological defect-mediated flows

Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling arguments and a systematic cluster expansion method to account for density correlations. We find that the distribution has power-law tails with an exponent that takes the value -3 for $v\rightarrow \infty$, but a value -2 for intermediate values of $v$. We relate these regimes to the theory of avalanches, by directly computing the known avalanche scaling exponents.

cond-mat.stat-mech↗

arXiv2012

Anisotropic velocity statistics of topological defects under shear flow

We report numerical results on the velocity statistics of topological defects during the dynamics of phase ordering and non-relaxational evolution assisted by an external shear ow. We propose a numerically efficient tracking method for finding the position and velocity of defects, and apply it to vortices in a uniform field and dislocations in anisotropic stripe patterns. During relaxational dynamics, the distribution function of the velocity fuctuations is characterized by a dynamical scaling with a scaling function that has a robust algebraic tail with an inverse cube power law. This is characteristic to defects of codimension two, e.g. point defects in two dimensions and filaments in three dimensions, regardless of whether the motion is isotropic (as for vortices) or highly anisotropic (as for dislocations). However, the anisotropic dislocation motion leads to anisotropic statistical properties when the interaction between defects and their motion is in infuenced by the presence of an external shear flow transverse to the stripe orientation.

cond-mat.stat-mech↗

arXiv2011

Theory of cooperation in a micro-organismal snow-drift game

We present a mean field model for the phase diagram of a community of micro-organisms, interacting through their metabolism so that they are, in effect, engaging in a cooperative social game. We show that as a function of the concentration of the nutrients glucose and histidine, the community undergoes a phase transition separating a state in which one strain is dominant to a state which is characterized by coexisting populations. Our results are in good agreement with recent experimental results, correctly predicting quantitative trends and the phase diagram.

physics.bio-ph↗

arXiv2011

Directed percolation describes lifetime and growth of turbulent puffs and slugs

We show that Directed Percolation (DP) simulations in a pipe geometry in 3+1 dimensions fully capture the observed complex phenomenology of the transition to turbulence. At low Reynolds numbers (Re), turbulent puffs form and spontaneously relaminarize. At high Re, turbulent slugs expand uniformly into the laminar regions. In a spatiotemporally intermittent state between these two regimes of Re, puffs split and turbulent regions exhibit laminar patches. DP also captures the main quantitative features of the transition, with a superexponentially diverging characteristic lifetime below the transition. Above the percolation threshold, active (turbulent) clusters expand into the inactive (laminar) phase with a well-defined velocity whose scaling with control parameter (Reynolds number or percolation probability) is consistent with experimental results. Our results provide strong evidence in favor of a conjecture of Pomeau.

physics.flu-dyn↗

arXiv2011

The effect of Coulombic friction on spatial displacement statistics

The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the corresponding Fokker-Planck equation including both velocity and spatial components, exhibiting a formal connection to a quantum mechanical harmonic oscillator in the presence of a delta potential. Numerical solutions for the resulting spatial displacement statistics show a crossover from exponential to Gaussian displacement statistics. We identify a transient intermediate regime that exhibits multiscaling properties arising from the contribution of Coulombic friction. The possible role of these effects during observations in diffusion experiments is shortly discussed.

physics.data-an↗

arXiv2011

Rare fluctuations and large-scale circulation cessations in turbulent convection

In turbulent Rayleigh-Benard convection, a large-scale circulation (LSC) develops in a nearly vertical plane, and is maintained by rising and falling plumes detaching from the unstable thermal boundary layers. Rare but large fluctuations in the LSC amplitude can lead to extinction of the LSC (a cessation event), followed by the re-emergence of another LSC with a different (random) azimuthal orientation. We extend previous models of the LSC dynamics to include momentum and thermal diffusion in the azimuthal plane, and calculate the tails of the probability distributions of both the amplitude and azimuthal angle. Our analytical results are in very good agreement with experimental data.

physics.flu-dyn↗

arXiv2011

Dislocations Jam At Any Density

Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic response, while above this critical stress the dislocations are mobile (the unjammed phase) and the material fails. We use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress grows with the square root of the dislocation density. Consequently, dislocations jam at any density, in contrast to granular materials, which only jam below a critical density.

cond-mat.soft↗

arXiv2011

Fluctuation-driven Turing patterns

Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ecological pattern formation, we show that the inclusion of intrinsic noise in Turing models leads to the formation of "quasi-patterns" that form in generic regions of parameter space and are experimentally distinguishable from standard Turing patterns. The existence of quasi-patterns removes the need for unphysical fine tuning or separation of scales in the application of Turing models to real systems.

q-bio.OT↗

arXiv2011

The dynamics of gene duplication and transposons in microbial genomes following a sudden environmental change

A variety of genome transformations can occur as a microbial population adapts to a large environmental change. In particular, genomic surveys indicate that, following the transition to an obligate, host-dependent symbiont, the density of transposons first rises, then subsequently declines over evolutionary time. Here, we show that these observations can be accounted for by a class of generic stochastic models for the evolution of genomes in the presence of continuous selection and gene duplication. The models use a fitness function that allows for partial contributions from multiple gene copies, is an increasing but bounded function of copy number, and is optimal for one fully adapted gene copy. We use Monte Carlo simulation to show that the dynamics result in an initial rise in gene copy number followed by a subsequent fall due to adaptation to the new environmental parameters. These results are robust for reasonable gene duplication and mutation parameters when adapting to a novel target sequence. Our model provides a generic explanation for the dynamics of microbial transposon density following a large environmental changes such as host restriction.

q-bio.PE↗

arXiv2010

Statistical Mechanics of Horizontal Gene Transfer in Evolutionary Ecology

The biological world, especially its majority microbial component, is strongly interacting and may be dominated by collective effects. In this review, we provide a brief introduction for statistical physicists of the way in which living cells communicate genetically through transferred genes, as well as the ways in which they can reorganize their genomes in response to environmental pressure. We discuss how genome evolution can be thought of as related to the physical phenomenon of annealing, and describe the sense in which genomes can be said to exhibit an analogue of information entropy. As a direct application of these ideas, we analyze the variation with ocean depth of transposons in marine microbial genomes, predicting trends that are consistent with recent observations using metagenomic surveys.

q-bio.PE↗

arXiv2010

Life is physics: evolution as a collective phenomenon far from equilibrium

Evolution is the fundamental physical process that gives rise to biological phenomena. Yet it is widely treated as a subset of population genetics, and thus its scope is artificially limited. As a result, the key issues of how rapidly evolution occurs, and its coupling to ecology have not been satisfactorily addressed and formulated. The lack of widespread appreciation for, and understanding of, the evolutionary process has arguably retarded the development of biology as a science, with disastrous consequences for its applications to medicine, ecology and the global environment. This review focuses on evolution as a problem in non-equilibrium statistical mechanics, where the key dynamical modes are collective, as evidenced by the plethora of mobile genetic elements whose role in shaping evolution has been revealed by modern genomic surveys. We discuss how condensed matter physics concepts might provide a useful perspective in evolutionary biology, the conceptual failings of the modern evolutionary synthesis, the open-ended growth of complexity, and the quintessentially self-referential nature of evolutionary dynamics.

q-bio.PE↗

arXiv2010

Plasticity and Dislocation Dynamics in a Phase Field Crystal Model

The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal (PFC) model. In the model, dislocations are naturally created, without any \textit{ad hoc} creation rules, by applying a shearing force to the perfectly periodic ground state. These dislocations diffuse, interact and annihilate with one another, forming avalanche events. By data collapsing the event energy probability density function for different shearing rates, a connection to interface depinning dynamics is confirmed. The relevant critical exponents agree with mean field theory predictions.

cond-mat.mtrl-sci↗

arXiv2010

Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible states of the system, identifying a novel limit cycle, which we interpret physically. To test the robustness of our mean field calculations to demographic fluctuations, we have compared our results with stochastic simulations using the Gillespie algorithm. Finally, we estimate the range of parameters that delineate the various steady states of our model.

q-bio.PE↗

arXiv2010

Emergence of foams from the breakdown of the phase field crystal model

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams, and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously-reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.

nlin.PS↗

arXiv2010

Extreme fluctuations and the finite lifetime of the turbulent state

We argue that the transition to turbulence is controlled by large amplitude events that follow extreme distribution theory. The theory suggests an explanation for recent observations of the turbulent state lifetime which exhibit super-exponential scaling behaviour with Reynolds number.

physics.flu-dyn↗

arXiv2009

Nonlinear Elasticity of the Phase Field Crystal Model from the Renormalization Group

The rotationally-covariant renormalization group equations of motion for the density wave amplitudes in the phase field crystal model are shown to follow from a dynamical equation driven by an effective free energy density that we derive. We show that this free energy can be written purely as a function of the strain tensor and thence derive the corresponding equations governing the nonlinear elastic response.

cond-mat.mtrl-sci↗