arXiv subjects

David R. Nelson

Publications and source records attributed to David R. Nelson.

At least 73 records · Page 4Linked to original sources

arXiv2013

Elastic Platonic Shells

On microscopic scales, the crystallinity of flexible tethered or cross linked membranes determines their mechanical response. We show that by controlling the type, number and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical Platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading-unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.

cond-mat.soft↗

arXiv2013

Defects on cylinders: superfluid helium films and bacterial cell walls

There is a deep analogy between the physics of crystalline solids and the behavior of superfluids, dating back to pioneering work of Phillip Anderson, Paul Martin and others. The stiffness to shear deformations in a periodic crystal resembles the superfluid density that controls the behavior of supercurrents in neutral superfluids such as He^4. Dislocations in solids have a close analogy with quantized vortices in superfluids. Remarkable recent experiments on the way rod-shaped bacteria elongate their cell walls have focused attention on the dynamics and interactions of point-like dislocation defects in partially ordered cylindrical crystalline monolayers. In these lectures, we review the physics of superfluid helium films on cylinders and discuss how confinement in one direction affects vortex interactions with supercurrents. Although there are similarities with the way dislocations respond to strains on cylinders, important differences emerge, due to the vector nature of the topological charges characterizing the dislocations.

cond-mat.soft↗

arXiv2013

Theory of interacting dislocations on cylinders

We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twist-induced Peach-Koehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature.

cond-mat.soft↗

arXiv2013

Radial Domany-Kinzel Models with Mutation and Selection

We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, etc. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. "Inflation" at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius $R_0$ expanding at velocity $v$, significant genetic demixing, caused by local genetic drift, only occurs up to a finite time $t^* = R_0/v$, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.

cond-mat.stat-mech↗

arXiv2012

Growth, competition and cooperation in spatial population genetics

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.

q-bio.PE↗

arXiv2012

Fluctuating shells under pressure

Thermal fluctuations strongly modify the large length-scale elastic behavior of crosslinked membranes, giving rise to scale-dependent elastic moduli. While thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic {\it shells}. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependent coupling between the in-plane stretching modes and the out-of-plane undulations. In addition, a shell can support a pressure difference between its interior and exterior. Little is known about the effect of thermal fluctuations on the elastic properties of shells. Here, we study the statistical mechanics of shape fluctuations in a pressurized spherical shell using perturbation theory and Monte Carlo computer simulations, explicitly including the effects of curvature and an inward pressure. We predict novel properties of fluctuating thin shells under point indentations and pressure-induced deformations. The contribution due to thermal fluctuations increases with increasing ratio of shell radius to thickness, and dominates the response when the product of this ratio and the thermal energy becomes large compared to the bending rigidity of the shell. Thermal effects are enhanced when a large uniform inward pressure acts on the shell, and diverge as this pressure approaches the classical buckling transition of the shell. Our results are relevant for the elasticity and osmotic collapse of microcapsules.

cond-mat.soft↗

arXiv2012

How Does A Porous Shell Collapse? Delayed Buckling And Guided Folding Of Inhomogeneous Capsules

Colloidal capsules can sustain an external osmotic pressure; however, for a sufficiently large pressure, they will ultimately buckle. This process can be strongly influenced by structural inhomogeneities in the capsule shells. We explore how the time delay before the onset of buckling decreases as the shells are made more inhomogeneous; this behavior can be quantitatively understood by coupling shell theory with Darcy's law. In addition, we show that the shell inhomogeneity can dramatically change the folding pathway taken by a capsule after it buckles.

cond-mat.soft↗

arXiv2012

Dislocation-mediated growth of bacterial cell walls

Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference (Garner et al., Science (2011), Dominguez-Escobar et al. Science (2011), van Teeffelen et al. PNAS (2011). We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall.

physics.bio-ph↗

arXiv2012

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to another

q-bio.PE↗

arXiv2011

A Quantitative Test of Population Genetics Using Spatio-Genetic Patterns in Bacterial Colonies

It is widely accepted that population genetics theory is the cornerstone of evolutionary analyses. Empirical tests of the theory, however, are challenging because of the complex relationships between space, dispersal, and evolution. Critically, we lack quantitative validation of the spatial models of population genetics. Here we combine analytics, on and off-lattice simulations, and experiments with bacteria to perform quantitative tests of the theory. We study two bacterial species, the gut microbe Escherichia coli and the opportunistic pathogen Pseudomonas aeruginosa, and show that spatio-genetic patterns in colony biofilms of both species are accurately described by an extension of the one-dimensional stepping-stone model. We use one empirical measure, genetic diversity at the colony periphery, to parameterize our models and show that we can then accurately predict another key variable: the degree of short-range cell migration along an edge. Moreover, the model allows us to estimate other key parameters including effective population size (density) at the expansion frontier. While our experimental system is a simplification of natural microbial community, we argue it is a proof of principle that the spatial models of population genetics can quantitatively capture organismal evolution.

q-bio.PE↗

arXiv2011

Cumulative compressibility effects on population dynamics in turbulent flows

Bacteria and plankton populations living in oceans and lakes reproduce and die under the in- fluence of turbulent currents. Turbulent transport interacts in a complex way with the dynamics of populations because the typical reproduction time of microorganism is within the inertial range of turbulent time scales. In the present manuscript we quantitatively investigate the effect of flow compressibility on the dynamics of populations. While a small compressibility can be induced by several physical mechanisms, like density mismatch or the finite size of microorganisms with respect to the fluid turbulence, its effect on the the carrying capacity of the ecosystem can be dramatic. We report, for the first time, how a small compressibility can produce a sizeable reduction in the carrying capacity, due to an integrated effect made possible by the long replication times of the organisms with respect to turbulent time scales. A full statistical quantification of the fluctuations of population concentration field leads to data collapse over a broad range in parameter space.

nlin.CD↗

arXiv2011

Population genetics in compressible flows

We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field and fitness advantage, number fluctuations lead to a coarsening dynamics typical of the stochastic Fisher equation. We then study three examples of compressible advecting fields: a shell model of turbulence, a sinusoidal velocity field and a linear velocity sink. In all cases, advection leads to a striking drop in the fixation time, as well as a large reduction in the global carrying capacity. Despite localization on convergence zones, one species goes extinct much more rapidly than in well-mixed populations. For a weak harmonic potential, one finds a bimodal distribution of fixation times. The long-lived states in this case are demixed configurations with a single boundary, whose location depends on the fitness advantage.

q-bio.PE↗

arXiv2011

Competition and cooperation in one-dimensional stepping stone models

Cooperative mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well-known, their effects on mutualism are not fully understood. With range expansions of microbes in mind, we show that, even when mutualism confers a distinct selective advantage, it persists only in populations with high density and frequent migrations. When these parameters are reduced, mutualism is generically lost via a directed percolation process, with a phase diagram strongly influenced by an exceptional DP2 transition.

q-bio.PE↗

arXiv2011

Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model

We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to "voter models" of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of microorganisms undergoing a range expansion on a Petri dish. We find that the population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or "zero dimensional") model occurs exponentially in time, it occurs only algebraically fast in the one-dimensional model. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. We also find an unusual sublinear increase in the variance of the spatially averaged allele frequency with time. Although we focus on two alleles or variants, q-allele Potts-like models of gene segregation are considered as well. We also investigate the effects of geometry at the frontier by considering growth of circular colonies. Our analytical results are checked with simulations, and could be tested against recent spatial experiments on range expansions off linear inoculations of Escherichia coli and Saccharomyces cerevisiae.

q-bio.PE↗

arXiv2010

Population dynamics at high Reynolds number

We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. We show that the interplay between turbulent dynamics and population growth and saturation leads to quasi-localization and a remarkable reduction in the carrying capacity. The statistical properties of the population density are investigated and quantified via multifractal scaling analysis. We also investigate numerically the singular limit of negligibly small growth rates and delocalization of population ridges triggered by uniform advection.

physics.flu-dyn↗

arXiv2010

Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures, dubbed "grain boundary scars", that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background. We investigate the structure and the dynamics of these grain boundary scars.

cond-mat.stat-mech↗

arXiv2009

Localization behavior of vibrational modes in granular packings

We study the localization of vibrational modes of frictionless granular media. We introduce a new method, motivated by earlier work on non-Hermitian quantum problems, which works well both in the localized regime where the localization length $ξ$ is much less than the linear size $L$ and in the regime $ξ$ grater or of order $L$ when modes are extended throughout our finite system. Our very lowest frequency modes show "quasi-localized" resonances away from the jamming point; the spatial extent of these regions increases as the jamming point is approached, as expected theoretically. Throughout the remaining frequency range, our data show no signature of the nearness of the jamming point and collapse well when properly rescaled with the system size. Using Random Matrix Theory we derive the scaling relation $ξ$ ~ $L^{d/2}$ for the regime $ξ$ >> $L$ in $d$ dimensions.

cond-mat.soft↗

arXiv2009

Shear Unzipping of DNA

We study theoretically the mechanical failure of a simple model of double stranded DNA under an applied shear. Starting from a more microscopic Hamiltonian that describes a sheared DNA, we arrive at a nonlinear generalization of a ladder model of shear unzipping proposed earlier by deGennes [deGennes P. G. C. R. Acad. Sci., Ser. IV; Phys., Astrophys. 2001, 1505]. Using this model and a combination of analytical and numerical methods, we study the DNA "unzipping" transition when the shearing force exceeds a critical threshold at zero temperature. We also explore the effects of sequence heterogeneity and finite temperature and discuss possible applications to determine the strength of colloidal nanoparticle assemblies functionalized by DNA.

cond-mat.soft↗