arXiv subjects

Nigel Goldenfeld

Publications and source records attributed to Nigel Goldenfeld.

At least 73 records · Page 4Linked to original sources

arXiv2009

Emergence of heterogeneity and political organization in information exchange networks

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases, corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics, and may have applications in a variety of systems including social insects and microbial communities.

nlin.AO↗

arXiv2009

The turbulent mean-velocity profile: it is all in the spectrum

It has long been surmised that the mean-velocity profile (MVP) of a pipe flow is closely related to the spectrum of turbulent energy. Here we perform a spectral analysis to identify the eddies that dominate the production of shear stress via momentum transfer. This analysis allows us to express the MVP as a functional of the spectrum. Each part of the MVP relates to a specific spectral range: the buffer layer to the dissipative range, the log layer to the inertial range, and the wake to the energetic range. The parameters of the spectrum set the thickness of the viscous layer, the amplitude of the buffer layer, and the amplitude of the wake.

physics.flu-dyn↗

arXiv2009

Macroscopic effects of the spectral structure in turbulent flows

Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent α(the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent α= 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent α= 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of αby using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.

physics.flu-dyn↗

arXiv2009

Robust ecological pattern formation induced by demographic noise

We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing instability in mean field theory, demographic noise greatly enlarges the region of parameter space where pattern formation occurs. To distinguish between patterns generated by fluctuations and those present at the mean field level in real ecosystems, we calculate the power spectrum in the noise-driven case and predict the presence of fat tails not present in the mean field case. These results may account for the prevalence of large-scale ecological patterns, beyond that expected from traditional non-stochastic approaches.

q-bio.PE↗

arXiv2009

Biology's next revolution

The interpretation of recent environmental genomics data exposes the far-reaching influence of horizontal gene transfer, and is changing our basic concepts of organism, species and evolution itself.

q-bio.PE↗

arXiv2009

Optimality Properties of a Proposed Precursor to the Genetic Code

We calculate the optimality of a doublet precursor to the canonical genetic code with respect to mitigating the effects of point mutations and compare our results to corresponding ones for the canonical genetic code. We find that the proposed precursor has much less optimality than that of the canonical code. Our results render unlikely the notion that the doublet precursor was an intermediate state in the evolution of the canonical genetic code. These findings support the notion that code optimality reflects evolutionary dynamics, and that if such a doublet code originally had a biochemical significance, it arose before the emergence of translation.

q-bio.OT↗

arXiv2009

The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.

physics.flu-dyn↗

arXiv2009

Molecular Dynamics on Diffusive Time Scales from the Phase Field Crystal Equation

We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time-scales. To illustrate this approach, we calculate the two-point correlation function of a liquid.

physics.comp-ph↗

arXiv2008

Lambda-prophage induction modeled as a cooperative failure mode of lytic repression

We analyze a system-level model for lytic repression of lambda-phage in E. coli using reliability theory, showing that the repressor circuit comprises 4 redundant components whose failure mode is prophage induction. Our model reflects the specific biochemical mechanisms involved in regulation, including long-range cooperative binding, and its detailed predictions for prophage induction in E. coli under ultra-violet radiation are in good agreement with experimental data.

q-bio.MN↗

arXiv2008

Extreme genetic code optimality from a molecular dynamics calculation of amino acid polar requirement

A molecular dynamics calculation of the amino acid polar requirement is presented and used to score the canonical genetic code. Monte Carlo simulation shows that this computational polar requirement has been optimized by the canonical genetic code more than any previously-known measure. These results strongly support the idea that the genetic code evolved from a communal state of life prior to the root of the modern ribosomal tree of life.

q-bio.PE↗

arXiv2007

Cascade of Complexity in Evolving Predator-Prey Dynamics

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.

q-bio.PE↗

arXiv2007

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match well the measured shapes near the vent at the top of observed travertine domes. Closer to the base of the dome, the solutions deviate from observations, and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane, and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

nlin.PS↗

arXiv2007

Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model

We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field crystal model to provide the underlying equations for the complex amplitude of the atomic density field--a quantity that is spatially uniform except near topological defects, grain boundaries and other lattice imperfections. Our algorithm is a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline domain formation in two dimensions.

cond-mat.mtrl-sci↗

arXiv2007

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics.

physics.flu-dyn↗

arXiv2006

Critical behavior of Griffiths ferromagnets

From a heuristic calculation of the leading order essential singularity in the distribution of Yang-Lee zeroes, we obtain new scaling relations near the ferromagnetic-Griffiths transition, including the prediction of a discontinuity on the analogue of the critical isotherm. We show that experimental data for the magnetization and heat capacity of $\mathrm{La_{0.7}Ca_{0.3}MnO_3}$ are consistent with these predictions, thus supporting its identification as a Griffiths ferromagnet.

cond-mat.dis-nn↗

arXiv2006

Ordering dynamics in Type-II superconductors

We use analytic and numerical methods to analyze the dynamics of vortices following the quench of a Type-II superconductor under the application of an external magnetic field. In three dimensions, in the absence of a field, the spacing between vortices scales with time t with an exponent phi=0.414 +/- 0.01, In a thin sheet of superconductor, the scaling exponent is phi=0.294 +/- 0.01. When an external magnetic field h is applied, the vortices are confined with respect to the length scale of the Abrikosov lattice, leading to a crossover between the power-law scaling length scale and the lattice length scale. From this we suggest a one-parameter scaling of dr/dt with h and r that is consistent with numerical data.

cond-mat.supr-con↗

arXiv2006

Renormalization group theory for the phase field crystal equation

We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two dimensional phase field crystal (PFC) model by a variety of renormalization group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple scales techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.

nlin.PS↗

arXiv2006

Dynamics of precipitation pattern formation at geothermal hot springs

We formulate and model the dynamics of spatial patterns arising during the precipitation of calcium carbonate from a supersaturated shallow water flow. The model describes the formation of travertine deposits at geothermal hot springs and rimstone dams of calcite in caves. We find explicit solutions for travertine domes at low flow rates, identify the linear instabilities which generate dam and pond formation on sloped substrates, and present simulations of statistical landscape evolution.

nlin.PS↗