arXiv subjects

Nigel Goldenfeld

Publications and source records attributed to Nigel Goldenfeld.

At least 37 records · Page 2Linked to original sources

arXiv2019

Mechanisms of rapid evolution

The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid evolution. The first example focuses primarily on population dynamics: anomalies in population cycles can reflect the influence of strong selection and the interplay with mutations. The second focuses primarily on the way in which ecological structure can potentially be influenced by what is arguably the most powerful source of genetic novelty: horizontal gene transfer. We review the status of rapid evolution and also enumerate the current and future challenges of achieving a full understanding of rapid evolution in all its manifestations.

q-bio.PE↗

arXiv2019

Three-body Interactions Drive the Transition to Polar Order in a Simple Flocking Model

A large class of mesoscopic or macroscopic flocking theories are coarse-grained from microscopic models that feature binary interactions as the chief aligning mechanism. However while such theories seemingly predict the existence of polar order with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. To resolve this paradox, here we introduce a solvable one-dimensional flocking model and derive its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless the noise is non-Gaussian. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density.

cond-mat.soft↗

arXiv2018

Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La$_{2-x}$Ba$_x$CuO$_4$

Charge order is universal among high-T$_c$ cuprates but its relevance to superconductivity is not established. It is widely believed that, while static order competes with superconductivity, dynamic order may be favorable and even contribute to Cooper pairing. We use time-resolved resonant soft x-ray scattering to study the collective dynamics of the charge order in the prototypical cuprate, La$_{2-x}$Ba$_x$CuO$_4$. We find that, at energy scales $0.4$ meV $ \lesssim ω\lesssim 2$ meV, the excitations are overdamped and propagate via Brownian-like diffusion. At energy scales below 0.4 meV the charge order exhibits dynamic critical scaling, displaying universal behavior arising from propagation of topological defects. Our study implies that charge order is dynamic, so may participate tangibly in superconductivity.

cond-mat.str-el↗

arXiv2018

Biophysical constraints determine the selection of phenotypic fluctuations during directed evolution

Phenotypes of individuals in a population of organisms are not fixed. Phenotypic fluctuations, which describe temporal variation of the phenotype of an individual or individual-to-individual variation across a population, are present in populations from microbes to higher animals. Phenotypic fluctuations can provide a basis for adaptation and be the target of selection. Here we present a theoretical and experimental investigation of the fate of phenotypic fluctuations in directed evolution experiments where phenotypes are subject to constraints. We show that selecting bacterial populations for fast migration through a porous environment drives a reduction in cell-to-cell variation across the population. Using sequencing and genetic engineering we study the genetic basis for this reduction in phenotypic fluctuations. We study the generality of this reduction by developing a simple, abstracted, numerical simulation model of the evolution of phenotypic fluctuations subject to constraints. Using this model we find that strong and weak selection generally lead respectively to increasing or decreasing cell-to-cell variation as a result of a bound on the selected phenotype under a wide range of parameters. However, other behaviors are also possible, and we describe the outcome of selection simulations for different model parameters and suggest future experiments. We analyze the mechanism of the observed reduction of phenotypic fluctuations in our experimental system, discuss the relevance of our abstract model to the experiment and explore its broader implications for evolution.

q-bio.PE↗

arXiv2017

Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model

The "Kill the Winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the "Kill the Winner" paradigm and show that the stable coexistence state of the deterministic "Kill the Winner" model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promotes high diversity of the ecosystem by generating a persistent population flux of species.

physics.bio-ph↗

arXiv2016

Turbulence as a problem in non-equilibrium statistical mechanics

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a non-equilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.

physics.flu-dyn↗

arXiv2016

Stochastic predator-prey dynamics of transposons in the human genome

Transposable elements, or transposons, are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some transposons are parasitic, relying on the enzymes produced by the regular transposons. In this case, we show that a stochastic model, which takes into account the small copy numbers of the transposons in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.

q-bio.PE↗

arXiv2016

Giant amplification of noise in fluctuation-induced pattern formation

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially-extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and non-orthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism provides a robust basis for fluctuation-induced biological pattern formation based on the Turing mechanism, without requiring fine tuning of diffusion constants.

cond-mat.stat-mech↗

arXiv2015

Enhanced Microfluidic Mixing via a Tricritical Spiral Vortex Instability

Experimental measurements and numerical simulations are made on fluid flow through cross-slot devices with a range of aspect (depth:width) ratios, 0.4 < alpha < 3.87. For low Reynolds numbers Re, the flow is symmetric and a sharp boundary exists between fluid streams entering the cross-slot from opposite directions. Above an alpha-dependent critical value Re_c, the flow undergoes a symmetry-breaking bifurcation (though remains steady and laminar) and a spiral vortex structure develops about the central axis of the outflow channel. An order parameter characterizing the instability grows according to a sixth-order Landau potential, and shows a progression from second order to first order transitions as alpha increases. A tricritical point occurs for alpha ~ 0.55. The spiral vortex acts as a mixing region in the flow field and this phenomenon can be used to drive enhanced mixing in microfluidic devices.

physics.flu-dyn↗

arXiv2015

A noise-induced mechanism for biological homochirality of early life self-replicators

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially-extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

q-bio.PE↗

arXiv2015

Ecological collapse and the emergence of traveling waves at the onset of shear turbulence

The transition to turbulence exhibits remarkable spatio-temporal behavior that continues to defy detailed understanding. Near the onset to turbulence in pipes, transient turbulent regions decay either directly or, at higher Reynolds numbers through splitting, with characteristic time-scales that exhibit a super-exponential dependence on Reynolds number. Here we report numerical simulations of transitional pipe flow, showing that a zonal flow emerges at large scales, activated by anisotropic turbulent fluctuations; in turn, the zonal flow suppresses the small-scale turbulence leading to stochastic predator-prey dynamics. We show that this "ecological" model of transitional turbulence reproduces the super-exponential lifetime statistics and phenomenology of pipe flow experiments. Our work demonstrates that a fluid on the edge of turbulence is mathematically analogous to an ecosystem on the edge of extinction, and provides an unbroken link between the equations of fluid dynamics and the directed percolation universality class.

physics.flu-dyn↗

arXiv2015

A framework for analyzing ecological trait-based models in multi-dimensional niche spaces

We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are described by sequences of strings, which allows us to describe multiple traits. We define the mathematical framework for analyzing pattern forming instabilities in these models, showing surprisingly that the analytic linear theory predicts the asymptotically long time population distributions of niches in the model. We propose a test for identifying ecological drivers in biodiversity distributions, based on representing ecosystem data by means of a certain transform introduced in the theory.

q-bio.PE↗

arXiv2015

Crystal plasticity as a mean field depinning transition: results from a phase field crystal model

Until now, most of our knowledge about the universality class of crystal plasticity has come from simulations using discrete dislocation dynamics. These are force-controlled, typically at zero temperature, and deal with the creation and annihilation of dislocations phenomenologically. In this work, we go beyond these limitations by using phase field crystal simulations in two dimensions at finite temperature to extract the avalanche statistics of a simulated crystal under constant shear velocity. In addition to the avalanche size and energy distributions we extract the avalanche duration distributions and power spectra. All exponents and scaling functions extracted here for the statics and dynamics of crystal plasticity, belong to the mean field elastic depinning universality class, confirming earlier findings based on discrete dislocation dynamics.

cond-mat.mtrl-sci↗

arXiv2014

Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model

Plastic deformation mediated by collective dislocation dynamics is investigated in the two-dimensional phase-field crystal model of sheared single crystals. We find that intermittent fluctuations in the dislocation population number accompany bursts in the plastic strain-rate fluctuations. Dislocation number fluctuations exhibit a power-law spectral density $1/f^2$ at high frequencies $f$. The probability distribution of number fluctuations becomes bimodal at low driving rates corresponding to a scenario where low density of defects alternate at irregular times with high population of defects. We propose a simple stochastic model of dislocation reaction kinetics that is able to capture these statistical properties of the dislocation density fluctuations as a function of shear rate.

cond-mat.mtrl-sci↗

arXiv2014

Path integral calculation for emergence of rapid evolution from demographic stochasticity

Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in population dynamics, including a $π$ phase shift between predator and prey (evolutionary cycles) and even undetectable prey oscillations compared to those of the predator (cryptic cycles). Here we present a generic individual-level stochastic model of interacting populations that includes a subpopulation of low nutritional value to the predator. Using a master equation formalism, and by mapping to a coherent state path integral solved by a system-size expansion, we show that evolutionary and cryptic quasicycles can emerge generically from the combination of intrinsic demographic fluctuations and clonal mutations alone, without additional biological mechanisms.

q-bio.PE↗

arXiv2013

Determination of the universality class of crystal plasticity

Although scaling phenomena have long been documented in crystalline plasticity, the universality class has been difficult to identify due to the rarity of avalanche events, which require large system sizes and long times in order to accurately measure scaling exponents and functions. Here we present comprehensive simulations of two-dimensional dislocation dynamics under shear, using finite-size scaling to extract scaling exponents and the avalanche profile scaling function from time-resolved measurements of slip-avalanches. Our results provide compelling evidence that both the static and dynamic universality classes are consistent with the mean-field interface depinning model.

cond-mat.mtrl-sci↗

arXiv2013

Universal fluctuations and extreme statistics of avalanches near the depinning transtition

We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.

cond-mat.dis-nn↗

arXiv2013

Distribution of maximum velocities in avalanches near the depinning transition

We report exact predictions for universal scaling exponents and scaling functions associated with the distribution of the maximum collective avalanche propagation velocities $v_m$ in the mean field theory of the interface depinning transition. We derive the extreme value distribution $P(v_m|T)$ for the maximum velocities in avalanches of fixed duration $T$, and verify the results by numerical simulation near the critical point. We find that the tail of the distribution of maximum velocity for an arbitrary avalanche duration, $v_m$, scales as $P(v_m)\sim v_m^{-2}$ for large $v_m$. These results account for the observed power-law distribution of the maximum amplitudes in acoustic emission experiments of crystal plasticity, and are also broadly applicable to other systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.

cond-mat.dis-nn↗