arXiv subjects

David R. Nelson

Publications and source records attributed to David R. Nelson.

At least 19 recordsLinked to original sources

arXiv2026

Liquid Crystal Ground States on Hyperbolic Cones

We generalize the analytic theory and simulation models for liquid crystal ground states on conventional cones with positive apex Gaussian curvature and study liquid crystal ground states on hyperbolic cones with a delta function of negative apex Gaussian curvature. While both the local apex curvature on a conventional cone and a hyperbolic cone lead to a fixed unquantized pseudodefect in the conformal domain and behave like conventional disclinations with opposite topological charges, there are fundamental differences in the ground states as well, which can be viewed as a violation of charge conjugation symmetry in a liquid crystal phase. To illustrate the violated charge conjugation symmetry on curved surfaces, we study two simple examples: (a) $p$-atic liquid crystals on a hyperbolic cone with free boundary conditions at the cone base. (b) $p$-atic liquid crystals on a hyperbolic cone with tangential boundary conditions at the cone base. In the simple case of $p=1$ liquid crystals (a vector order parameter field) on a hyperbolic cone with tangential boundary conditions, the positive pseudocharge caused by the apex curvature can be stably bound with a topological charge of the same sign despite their repulsive interaction, in sharp contrast to the charge conjugated situation associated with conventional cones.

cond-mat.soft↗

arXiv2026

The Allee Effect in Compressible Flows

Microbes in marine environments are often confined to thin near-surface layers while being advected by turbulent flows. Because such constrained advection generates an effectively compressible flow, reproduction and transport interact in a nontrivial way. Here, we focus on populations whose growth is governed by an Allee effect and show that sinks and sources, generated by the compressible flow, have dramatic consequences for the survival of such species. We derive analytical expressions for the carrying capacity as a function of the Allee strength in the limit of small and large Damk\"ohler number, which measures the product of the large eddy turnover time and the organism growth rate. Numerical simulations reveal how these two limits connect. In the limit of small Damk\"ohler number, we find a maximal Allee strength, set by the statistics of the compressible flow, that leads to species extinction in fully developed turbulence.

physics.bio-ph↗

arXiv2026

Banded non-Hermitian random matrices, neural networks, and eigenvalue degeneracies

We study two-banded, non-Hermitian random matrices inspired by sparse neural networks with a circular, 1d topology. We focus on two paradigmatic models, an SSH chain and a ladder model, which have both non-Hermitian directional bias and random sign disorder in the hoppings. The random sign disorder, which follows Dale's Law, leads to localization of the eigenstates, while the directional bias drives a delocalization transition in these states. The competition between disorder and directional bias results in rich eigenspectra with loops of extended states in the complex plane surrounded by regions of localized ones, and the eigenvalues are all confined to an annular region. Furthermore, the distinct band structures of the SSH chain and ladder model lead to different delocalization phenomena. Even in the absence of disorder, tuning the directional bias can lead to an eigenvalue degeneracy, which is an exceptional point for the SSH chain but a diabolic point for the ladder. In the presence of the disorder, these special eigenvalue degeneracies are preserved and also highlight key stages in the delocalization process. For both models, increasing the directional bias initially delocalizes states starting from within the bands. For the SSH chain, for large enough directional bias, the delocalized states open up a hole in the spectrum in the complex plane, similar to prior results for single band systems. But for the ladder model, as the directional bias is increased, the states delocalize in two stages, leading to two separate loops of extended states with localized states in between. The precise contours on which the extended states reside can be predicted from the Lyapunov exponents associated with products of random transfer matrices, in agreement with direct numerical diagonalization. Although we focus on periodic boundaries, results are discussed for open boundaries as well.

cond-mat.dis-nn↗

arXiv2026

Thermalized buckling of extensible, semiflexible polymers

The Euler buckling of rods is a long-studied mechanical instability, and it remains relevant to this day, as the constituent components in many biological and physical systems are linear polymers, such as microtubules or carbon nanotubes. At finite temperature, if a polymer is shorter than its persistence length, the polymer is semiflexible, and its elasticity remains rod-like. But polymers can also stretch due to their finite extensibility, which can couple to energetically cheap bending deformations in nonlinear ways when a load is applied to the system. We show how the interplay between thermal fluctuations and nonlinear elasticity dramatically modifies the Euler buckling instability for compressed semiflexible polymers in a fixed strain ensemble. We identify a Ginzburg-like length scale beyond which thermally excited undulations lead to a softened Young's modulus, while the polymer nevertheless remains semiflexible. Both perturbative calculations and numerical Monte Carlo simulations suggest a qualitative change in several scaling properties of the buckling transition. The critical compressional strain for thermal buckling now increases with system size, in contrast to athermal buckling, where it decreases with system size. Renormalization group calculations confirm this picture, and also show that thermal buckling is controlled by a new fixed point with different critical exponents compared to classical Euler buckling.

cond-mat.stat-mech↗

arXiv2025

Genetic interfaces at the frontier of expanding microbial colonies

We study the genetic interfaces between two species of an expanding colony that consists of individual microorganisms that reproduce and undergo diffusion, both at the frontier and in the interior. Within the bulk of the colony, the genetic interface is controlled in a simple way via interspecies interactions. However, at the frontier of the colony, the genetic interface width saturates at finite values for long times, both for neutral strains and interspecies interactions such as antagonism. This finite width arises from geometric effects: genetic interfaces drift toward local minima at an undulating colony frontier, where a focusing mechanism induced by curvature impedes diffusive mixing. Numerical simulations support a logarithmic dependence of the genetic interface width on the strength of the number fluctuations.

physics.bio-ph↗

arXiv2025

Transition to chaos with conical billiards

We adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane, with tilt angle $\gamma$. We explore the dynamics as a function of $\gamma$ and the cone deficit angle $\chi$ that controls the sharpness of the apex, where a point source of positive Gaussian curvature is concentrated. We find regions of the ($\gamma, \chi$) plane where, depending on the initial conditions, either (A) the trajectories sample the entire cone base and avoid the apex region; (B) sample only a portion of the base region while again avoiding the apex; or (C) sample the entire cone surface much more uniformly, suggestive of ergodicity. The special case of an untilted cone displays only type A trajectories which form a ring caustic at the distance of closest approach to the apex. However, we observe an intricate transition to chaotic dynamics dominated by Type (C) trajectories for sufficiently large $\chi$ and $\gamma$. A Poincar\'e map that summarizes trajectories decomposed into the geodesic segments interrupted by specular reflections provides a powerful method for visualizing the transition to chaos. We then analyze the similarities and differences of the path to chaos for conical billiards with other area-preserving conservative maps.

nlin.CD↗

arXiv2024

Liquid Crystal Ground States on Cones with Anti-Twist Boundary Conditions

Geometry and topology play a fundamental role in determining pattern formation on 2D surfaces in condensed matter physics. For example, local positive Gaussian curvature of a 2D surface attracts positive topological defects in a liquid crystal phase confined to the curved surface while repelling negative topological defects. Although the cone geometry is flat on the flanks, the concentrated Gaussian curvature at the cone apex geometrically frustrates liquid crystal orientational fields arbitrarily far away. The apex acts as an unquantized pseudo-defect interacting with the topological defects on the flank. By exploiting the conformal mapping methods of F. Vafa et al., we explore a simple theoretical framework to understand the ground states of liquid crystals with $p$-fold rotational symmetry on cones, and uncover important finite size effects for the ground states with boundary conditions that confine both plus and minus defects to the cone flanks. By combining the theory and simulations, we present new results for liquid crystal ground states on cones with anti-twist boundary conditions at the cone base, which enforce a total topological charge of $-1$. We find that additional quantized negative defects are created on the flank as the cone apex becomes sharper via a defect unbinding process, such that an equivalent number of quantized positive defects become trapped at the apex, thus partially screening the apex charge, whose magnitude is a continuous function of cone angle.

cond-mat.soft↗

arXiv2024

LA4SR: illuminating the dark proteome with generative AI

AI language models (LMs) show promise for biological sequence analysis. We re-engineered open-source LMs (GPT-2, BLOOM, DistilRoBERTa, ELECTRA, and Mamba, ranging from 70M to 12B parameters) for microbial sequence classification. The models achieved F1 scores up to 95 and operated 16,580x faster and at 2.9x the recall of BLASTP. They effectively classified the algal dark proteome - uncharacterized proteins comprising about 65% of total proteins - validated on new data including a new, complete Hi-C/Pacbio Chlamydomonas genome. Larger (>1B) LA4SR models reached high accuracy (F1 > 86) when trained on less than 2% of available data, rapidly achieving strong generalization capacity. High accuracy was achieved when training data had intact or scrambled terminal information, demonstrating robust generalization to incomplete sequences. Finally, we provide custom AI explainability software tools for attributing amino acid patterns to AI generative processes and interpret their outputs in evolutionary and biophysical contexts.

q-bio.GN↗

arXiv2024

Turbulent mixing controls fixation of growing antagonistic populations

Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria, baker's yeast) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing strains, while being spatially advected by turbulent flows? By using numerical simulations of a continuum model, we study the dynamics of two antagonistic strains that are dispersed by incompressible turbulent flows in two spatial dimensions. A key parameter is the ratio of the fluid transport time to that of biological reproduction, which determines the winning strain that ultimately takes over the whole population from an initial heterogeneous state. By quantifying the probability and mean time for fixation along with the spatial structure of concentration fluctuations, we demonstrate how turbulence raises the threshold for biological nucleation and antagonism suppresses flow-induced mixing by depleting the population at interfaces. Our work highlights the unusual biological consequences of the interplay of turbulent fluid flows with antagonistic population dynamics, with potential implications for marine microbial ecology and origins of biological chirality.

q-bio.PE↗

arXiv2024

Defect ground states for liquid crystals on cones and hyperbolic cones

This contribution is intended for Journal of Physics A: Mathematical and Theoretical Special issue on Non-equilibrium Dynamics in Complex Systems: Celebrating the Contributions of Uwe Täuber on his 60th Birthday. Cones with orientational order in the local tangent plane provide a soft matter analog of the Aharonov-Bohm effect. We first review recent work on 2D liquid crystals with $p$-fold rotational symmetry on cones. We exploit an analogy with electrostatics to determine the ground state as a function of both the cone angle and the liquid crystal symmetry for both free and tangential boundary conditions applied at the cone base. There is an effective topological charge $-χ$ at the apex, where $2πχ$ is the deficit angle. The ground states are in general frustrated due to parallel transport along the azimuthal direction on the cone. In the case of tangential boundary conditions, the ground state changes as a function of $χ$, where the apex absorbs and emits quantized defect charges, with intricate dependence on both the deficit angle and $p$. We check our predictions numerically for a set of commensurate cone angles, whose surfaces can be polygonized as a perfect triangular or square mesh, and find excellent agreement. Cones with both free and tangential boundary conditions can also exhibit metastable states distinguished by quantized screening of the apex charge. We also present preliminary work on hyperbolic cones, where the Gaussian curvature singularity is negative at the apex. When free boundary conditions are applied at the base, the ground states are characterized by an effective topological charge at the apex, similarly to the case of conventional cones. However, when tangential boundary conditions are applied, decreasing the deficit angle (which is now negative) induces neutral defect pair nucleation at the apex followed by emission of a positive defect.

cond-mat.soft↗

arXiv2023

Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the time scales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a a rich phase diagram of multi-defect dynamics including exotic periodic orbits of one or two $+1/2$ flank defects, depending on activity and non-quantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we can understand (i) defect unbinding, (ii) defect absorption and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.

cond-mat.soft↗

arXiv2023

Geometric frustration of hard-disk packings on cones

Conical surfaces pose an interesting challenge to crystal growth: a crystal growing on a cone can wrap around and meet itself at different radii. We use a disk-packing algorithm to investigate how this closure constraint can geometrically frustrate the growth of single crystals on cones with small opening angles. By varying the crystal seed orientation and cone angle, we find that -- except at special commensurate cone angles -- crystals typically form a seam that runs along the axial direction of the cone, while near the tip, a disordered particle packing forms. We show that the onset of disorder results from a finite-size effect that depends strongly on the circumference and not on the seed orientation or cone angle. This finite-size effect occurs also on cylinders, and we present evidence that on both cylinders and cones, the defect density increases exponentially as circumference decreases. We introduce a simple model for particle attachment at the seam that explains the dependence on the circumference. Our findings suggest that the growth of single crystals can become frustrated even very far from the tip when the cone has a small opening angle. These results may provide insights into the observed geometry of conical crystals in biological and materials applications.

cond-mat.soft↗

arXiv2023

Remembrances of Michael E. Fisher

This contribution will be published in '50 years of the renormalization group', dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora Entin-Wohlman, David Huse, and Leo Radzihovsky, World Scientific. These personal remembrances come in three parts. The first contains a brief personal perspective on Michael E. Fisher's contributions to science. The second tells how I came to work with Michael and describes events while I was under his supervision during my graduate years at Cornell University. The third part summarizes recent work, done in collaboration with Suraj Shankar, on thermalized buckling of isotopically compressed thin (perhaps atomically thin) sheets of materials such as graphene or MoS$_2$. These investigations were inspired by Michael's beautiful work on the effect of constraints at critical points, with fluctuations at all length scales, which leads to 'Fisher renormalization' of critical exponents. [1] Thin fluctuating sheets embedded in three dimensions, when they are tensionless as in a cantilever or 'diving board' geometry, are automatically at a critical point everywhere in a low temperature flat phase. However, when we consider thin sheets supported on multiple sides in various ways, Fisher's ideas lead to the inequivalence of isotensional and isometric thermodynamic ensembles, which triggers dramatic differences in some of the critical exponents associated with the two types of boundary conditions. [2] Readers not interested in my experiences while a student at Cornell University may only want to read parts I and III. There are also some concluding remarks.

cond-mat.stat-mech↗

arXiv2023

Vibrations and tunneling of strained nanoribbons at finite temperature

Crystalline sheets (e.g., graphene and transition metal dichalcogenides) liberated from a substrate are a paradigm for materials at criticality because flexural phonons can fluctuate into the third dimension. Although studies of static critical behaviors (e.g., the scale-dependent elastic constants) are plentiful, investigations of dynamics remain limited. Here, we use molecular dynamics to study the time dependence of the midpoint (the height center-of-mass) of doubly clamped nanoribbons, as prototypical graphene resonators, under a wide range of temperature and strain conditions. By treating the ribbon midpoint as a Brownian particle confined to a nonlinear potential (which assumes a double-well shape beyond the buckling transition), we formulate an effective theory describing the ribbon's tunneling rate across the two wells and its oscillations inside a given well. We find that, for nanoribbbons compressed above the Euler buckling point and thermalized above a temperature at which the non-linear effects due to thermal fluctuations become significant, the exponential term (the ratio between energy barrier and temperature) depends only on the geometry, but not the temperature, unlike the usual Arrhenius behavior. Moreover, we find that the natural oscillation time for small strain shows a non-trivial scaling $τ_{\rm o}\sim L_0^{\,z}T^{-η/4}$, with $L_0$ being the ribbon length, $z=2-η/2$ being the dynamic critical exponent, $η=0.8$ being the scaling exponent describing scale-dependent elastic constants, and $T$ being the temperature. These unusual scale- and temperature-dependent dynamics thus exhibit dynamic criticality and could be exploited in the development of graphene-based nanoactuators.

cond-mat.mtrl-sci↗

arXiv2023

Active topological defect absorption by a curvature singularity

Using the Born-Oppenheimer approximation, we present a general description of topological defects dynamics in $p$-atic materials on curved surfaces, and simplify it in the case of active nematics. We find that activity induces a geometric contribution to the motility of the $+1/2$ defect. Moreover, in the case of a cone, the simplest example of a geometry with curvature singularity, we find that the motility depends on the deficit angle of the cone and changes sign when the deficit angle is bigger than $π$, leading to the change in active behavior from contractile (extensile) to extensile (contractile) behavior. Using our analytical framework, we then identify for positively charged defects the basin of attraction to the cone apex and present closed-form predictions for defect trajectories near the apex. The analytical results are quantitatively corroborated against full numerical simulations. Provided the capture radius is small compared to the cone size, the agreement is excellent.

cond-mat.soft↗

arXiv2022

Curvature as an external field in mechanical antiferromagnets

A puckered sheet is a freestanding crystalline membrane with an embedded array of bistable buckled units. Recent work has shown that the bistable units behave like spins in a two-dimensional compressible Ising antiferromagnet with, however, a coupling to flexural phonons. At finite temperature, this purely mechanical system displays Ising-like phase transitions, which drive anomalous thermal expansion. Here, we show that geometry can be used to control phase behavior: curvature produces a radius-dependent "external field" that encourages alignment between neighboring "spins," disrupting the ordered checkerboard ground state of antialigned neighbors. The effective field strength scales as the inverse of the radius of curvature. We identify this effective field theoretically with both a discrete real space model and a nonlinear continuum elastic model. We then present molecular dynamics simulations of puckered sheets in cylindrical geometries at zero and finite temperature, probing the influence of curvature on the stability of configurations and phase transitions. Our work demonstrates how curvature and temperature can be used to design and operate a responsive and tunable metamaterial at either the macroscale or nanoscale.

cond-mat.soft↗

arXiv2022

Spatial population genetics with fluid flow

The growth and evolution of microbial populations is often subjected to advection by fluid flows in spatially extended environments, with immediate consequences for questions of spatial population genetics in marine ecology, planktonic diversity and origin of life scenarios. Here, we review recent progress made in understanding this rich problem in the simplified setting of two competing genetic microbial strains subjected to fluid flows. As a pedagogical example we focus on antagonsim, i.e., two killer microorganism strains, each secreting toxins that impede the growth of their competitors (competitive exclusion), in the presence of stationary fluid flows. By solving two coupled reaction-diffusion equations that include advection by simple steady cellular flows composed of characteristic flow motifs in two dimensions (2d), we show how local flow shear and compressibility effects can interact with selective advantage to have a dramatic influence on genetic competition and fixation in spatially distributed populations. We analyze several 1d and 2d flow geometries including sources, sinks, vortices and saddles, and show how simple analytical models of the dynamics of the genetic interface can be used to shed light on the nucleation, coexistence and flow-driven instabilities of genetic drops. By exploiting an analogy with phase separation with nonconserved order parameters, we uncover how these genetic drops harness fluid flows for novel evolutionary strategies, even in the presence of number fluctuations, as confirmed by agent-based simulations as well.

q-bio.PE↗

arXiv2022

Defect absorption and emission for $p$-atic liquid crystals on cones

We investigate the ground state configurations of $p$-atic liquid crystals on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are particularly convenient as they explicitly encode a geometric contribution to the elastic potential. In the special case of a cone with half-angle $β$, the apex develops an effective topological charge of $-χ$, where $2πχ= 2π(1-\sinβ)$ is the deficit angle of the cone, and a topological defect of charge $σ$ behaves as if it had an effective topological charge $Q_\mathrm{eff} = (σ- σ^2/2)$ when interacting with the apex. The effective charge of the apex leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. For total topological defect charge 1, e.g. imposed by tangential boundary conditions at the edge, we find that for a disk the ground state configuration consists of $p$ defects each of charge $+1/p$ lying equally spaced on a concentric ring of radius $d = (\frac{p-1}{3p-1})^{\frac{1}{2p}} R$, where $R$ is the radius of the disk. In the case of a cone with tangential boundary conditions at the base, we find three types of ground state configurations as a function of cone angle: (1) for sharp cones, all of the $+1/p$ defects are absorbed by the apex; (2) at intermediate cone angles, some of the $+1/p$ defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (3) for nearly flat cones, all of the $+1/p$ defects lie equally spaced along a concentric ring on the flank. Here the defect positions and the absorption transitions depend intricately on $p$ and the deficit angle which we analytically compute. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement.

cond-mat.soft↗