arXiv subjects

Daniel A. Beller

Publications and source records attributed to Daniel A. Beller.

At least 19 recordsLinked to original sources

arXiv2026

Topological delocalisation of confined 3D active nematics

Defect lines in 3D active nematic systems are intriguing topological singularities whose out-of-equilibrium dynamics remain elusive in confined settings. Here, we numerically study 3D active nematics confined within closed cylinders to elucidate the roles of geometry and activity. We reveal a competition between passive elasticity, which causes localisation of defects near edges, and activity, which endows defects with motility and gives rise to disorderly, delocalised dynamics. Varying boundary curvature, activity strength, and cylinder radius reveals a state space of static and dynamic localisation states, including handle-like configurations and chaotic motion bounded within the cylinder endcap. As activity is tuned to induce delocalisation, we identify phase transition signatures, including pronounced fluctuations and an emergent power law scaling of defect number and average defect length. We find that these scaling properties are strongly altered by confinement: unlike in bulk systems where activity governs length distributions, confinement tunes an activity-independent characteristic length, with an exponent reminiscent of self-avoiding confined polymers. These results establish confinement of inhomogeneous curvature as a versatile mechanism for controlling active topological dynamics.

cond-mat.soft↗

arXiv2026

Chaos-generating periodic orbits of topological defects in confined active nematics

Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile $+1/2$ disclinations. We investigate how this tendency toward chaotic fluid stirring can, counterintuitively, produce certain ordered, periodic flows in confinement, characterized by stable periodic orbits of $+1/2$ disclinations. We computationally study two-dimensional active nematics in systems with boundary conditions requiring a prescribed number $n$ of excess $+1/2$ disclinations, using Beris-Edwards nematohydrodynamics simulations alongside an agent-based simulation approach. We find that when confinement is sufficiently strong to prevent defect pair-nucleation, but not strong enough to arrest all flow, then $n=3$ defects generically follow a "golden braid" orbit as observed recently in experiments, and we predict a "silver braid" orbit of $n=4$ defects. For these results and for greater numbers of defects, we show that the periodic or chaotic nature of the dynamics is determined by a balance between the number of defects and the number of vortices in the flow field, suggesting a new design criterion for ordered flows in active nematics.

cond-mat.soft↗

arXiv2026

Dynamics of individual active elastic filaments with chiral self-propulsion

We study the over-damped dynamics of individual one-dimensional elastic filaments subjected to a chiral active force which propels each point of the filament at a fixed angle relative to the tangent vector of the filament at that point. Such a model is a reasonable starting point for describing the behavior of polymers such as microtubules in gliding assay experiments. We derive sixth-order nonlinear coupled partial differential equations for the intrinsic properties of the filament, namely, its curvature and metric, and show that these equations are capable of supporting multiple different stationary solutions in a co-moving frame, i.e.\ that chiral active elastic filaments exhibit dynamic multi-stability in their shapes. A linear stability analysis of these solutions is carried out to determine which solutions are stable and a brief analysis of the time-dependent approach to stationary shape is considered. Finally, simulations are presented which confirm many of our predictions while also revealing additional complexity.

cond-mat.soft↗

arXiv2025

Gliding microtubules exhibit tunable collective rotation driven by chiral active forces

How chirality propagates across scales remains an open question in many biological and synthetic systems. An especially clear manifestation of this propagation is found in in vitro gliding assays of cytoskeletal filaments on surfaces, driven by molecular motors. These assays have become model systems of active matter dynamics, as they spontaneously organize into diverse dynamical states, including collective motions with chiral rotation. However, the microscopic mechanisms underlying these chiral collective dynamics have remained unclear. Here, we investigate rotating active nematic order in microtubule gliding assay experiments under two stabilization conditions, each on two types of substrates. We propose that chirality in active forces exerted by motors on microtubules represents a viable mechanism for this large-scale chirality. Using Brownian dynamics simulations of self-propelled, semiflexible filaments with chiral activity, we demonstrate that coherently rotating active nematic order emerges by this mechanism even in the absence of curvature, i.e. shape chirality, of the constituent filaments. Moreover, we predict that the angular speed and handedness of the collective rotation can be tuned by modulating filament stiffness. Our findings identify a new set of sufficient microscopic ingredients for predictable propagation of chiral handedness from the molecular to the material scale in living and active matter.

cond-mat.soft↗

arXiv2025

Modeling active nematics via the nematic locking principle

Active nematic systems consist of rod-like internally driven subunits that interact with one another to form large-scale coherent flows. They are important examples of far-from-equilibrium fluids, which exhibit a wealth of nonlinear behavior. This includes active turbulence, in which topological defects braid around one another in a chaotic fashion. One of the most studied examples of active nematics is a dense two-dimensional layer of microtubules, crosslinked by kinesin molecular motors that inject extensile deformations into the fluid. Though numerous studies have modeled microtubule-based active nematics, no consensus has emerged on how to fully capture the features of the experimental system. To better understand the foundations for modeling this system, we propose a fundamental principle we call the nematic locking principle: individual microtubules cannot rotate without all neighboring microtubules also rotating. Physically, this is justified by the high density of the microtubules, their elongated nature, and their corresponding steric interactions. We assert that nematic locking holds throughout the majority of the material but breaks down in the neighborhood of topological defects and other regions of low density. We derive the most general nematic transport equation consistent with this principle and also derive the most general term that violates it. We examine the standard Beris-Edwards approach used to model this system and show that it violates nematic locking throughout the majority of the material. We then propose a modification to the Beris-Edwards model that enforces nematic locking nearly everywhere. This modification shuts off fracturing except in regions where the order parameter is reduced. The resulting simulations show strong nematic locking throughout the bulk of the material, consistent with experimental observation.

cond-mat.soft↗

arXiv2025

Spontaneous spatial sorting by cell shape in growing colonies of rod-like bacteria

Mechanical interactions among cells in a growing microbial colony can significantly influence the colony's spatial genetic structure and, thus, evolutionary outcomes such as the fates of rare mutations. Here, we computationally investigate how this spatial genetic structure changes as a result of heritable phenotypic variations in cell shape. By modeling rod-like bacterial cells as lengthening and dividing circo-rectangles in a 2D Brownian dynamics framework, we simulate the growth of a colony containing two populations with different aspect ratios. Compared to monodisperse colonies, such bidisperse colonies exhibit diminished intermixing between sub-populations when the less elongated cells are too short to nematically order, instead forming large clusters. We find that the cells with longer aspect ratio gradually segregate to the colony periphery. We present evidence that this demixing is related to nematic order in the bulk and to active nematic mixing dynamics near the periphery. These findings are qualitatively robust across different growth rate protocols and initial conditions. Because the periphery is often an advantageous position when nutrients are limited, our results suggest a possible evolutionary selective pressure of mechanical origin that favors large cell aspect ratio.

cond-mat.soft↗

arXiv2024

Geometry-Induced Competitive Release in a Meta-Population Model of Range Expansions in Disordered Environments

Rare evolutionary events, such as the rise to prominence of deleterious mutations, can have drastic impacts on the evolution of growing populations. Heterogeneous environments may reduce the influence of selection on evolutionary outcomes through various mechanisms, including pinning of genetic lineages and of the population fronts. These effects play significant roles in enabling competitive release of otherwise trapped mutations. In this work we show that environments containing random arrangements of "hotspot" patches, where locally abundant resources enhance growth rates equally for all sub-populations, give rise to massively enriched deleterious mutant clones. We derive a geometrical optics description of mutant bubbles, which result from interactions with hotspots, that successfully predicts the observed increase in mutant survival. This prediction requires no fitting parameters and holds well in scenarios of rare mutations and of adaptation from standing variation. In addition, we find that the influence of environmental noise in shaping the fate of rare mutations is maximal near a percolation transition of overlapping discs, beyond which mutant survival decreases.

q-bio.PE↗

arXiv2024

Symmetry and stability of orientationally ordered collective motions of self-propelled, semiflexible filaments

Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when the active units are sufficiently anisotropic to produce liquid crystalline order and thus active nematic phenomena, with important biophysical examples provided by cytoskeletal filaments including microtubules and actin. Gliding assay experiments have provided a testbed to study the collective motions of these cytoskeletal filaments and unlocked diverse collective active phases, including states with long-range orientational order. However, it is not well-understood how such long-range order emerges from the interplay of passive and active aligning mechanisms. We use Brownian dynamics simulations to study the collective motions of semiflexible filaments that self-propel in quasi-two dimensions, in order to gain insights into the aligning mechanisms at work in these gliding assay systems. We find that, without aligning torques in the microscopic model, long-range orientational order can only be achieved when the filaments are able to overlap. The symmetry (nematic or polar) of the long-range order that first emerges is shown to depend on the energy cost of filament overlap and on filament flexibility. However, our model also predicts that a long-range-ordered active nematic state is merely transient, whereas long-range polar order is the only active dynamical steady state in systems with finite filament rigidity.

cond-mat.soft↗

arXiv2024

Connecting the Dots: Range Expansions across Landscapes with Quenched Noise

When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also significantly influence the competition between sub-populations vying for space. Little is known about the interplay of these intrinsic and extrinsic sources of noise in population dynamics: When does environmental heterogeneity dominate over genetic drift or vice versa, and what distinguishes their population genetics signatures? Here, in the context of neutral evolution, we examine the interplay between a population's intrinsic, demographic noise and an extrinsic, quenched random noise provided by a heterogeneous environment. Using a multi-species Eden model, we simulate a population expanding over a landscape with random variations in local growth rates and measure how this variability affects genealogical tree structure, and thus genetic diversity. We find that, for strong heterogeneity, the genetic makeup of the expansion front is to a great extent predetermined by the set of fastest paths through the environment. The landscape-dependent statistics of these optimal paths then supersede those of the population's intrinsic noise as the main determinant of evolutionary dynamics. Remarkably, the statistics for coalescence of genealogical lineages, derived from those deterministic paths, strongly resemble the statistics emerging from demographic noise alone in uniform landscapes. This cautions interpretations of coalescence statistics and raises new challenges for inferring past population dynamics.

q-bio.PE↗

arXiv2023

Sequences of dislocation reactions and helicity transformations in tubular crystals

Freestanding tubular crystals offer a general description of crystalline order on deformable surfaces with cylindrical topology, such as single-walled carbon nanotubes, microtubules, and recently reported colloidal assemblies. These systems exhibit a rich interplay between the crystal's helicity on its periodic surface, the deformable geometry of that surface, and the motions of topological defects within the crystal. Previously, in simulations of tubular crystals as elastic networks, we found that dislocations in nontrivial patterns can co-stabilize with kinks in the tube shape, producing mechanical multistability. Here, we extend that work with detailed Langevin dynamics simulations, in order to explore defect dynamics efficiently and without the constraints imposed by elastic network models. Along with the predicted multistability of dislocation glide, we find a variety of irreversible defect transformations, including vacancy formation, particle extrusions, and "reactions" that reorient dislocation pairs. Moreover, we report spontaneous sequences of several such defect transformations, which are unique to tubular crystals. We demonstrate a simple method for controlling these sequences through a time-varying external force.

cond-mat.soft↗

arXiv2023

Maximally mixing active nematics

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rod-like components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this Letter shows that this system can exhibit stable periodic motion when sufficiently confined to a square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) ``topological entropy'' -- the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.

cond-mat.soft↗

arXiv2023

Templated self-assembly of gold nanoparticles in smectic liquid crystals confined at 3D printed curved surfaces

The fabrication of assembled structures of topological defects in liquid crystals (LCs) has attracted much attention during the last decade, stemming from the potential application of these defects in modern technologies. A range of techniques can be employed to create large areas of engineered defects in LCs, including mechanical shearing, chemical surface treatment, external fields, or geometric confinement. The technology of 3D printing has recently emerged as a powerful method to fabricate novel patterning topographies inaccessible by other microfabrication techniques, especially confining geometries with curved topographies. In this work, we show the advantages of using 3D-printed curved surfaces and controlled anchoring properties to confine LCs and engineer new structures of topological defects, whose structure we elucidate by comparison with a novel application of Landau-de Gennes free energy minimization to the smectic A-nematic phase transition. We also demonstrate the ability of these defects to act as a scaffold for assembling gold (Au) nanoparticles (NPs) into reconfigurable 3D structures. We discuss the characteristics of this templated self-assembly (TSA) approach and explain the relationship between NP concentrations and defect structures with insights gained from numerical modeling. This work paves the way for a versatile platform of LC defect-templated assembly of a range of functional nanomaterials useful in the field of energy technology.

cond-mat.soft↗

arXiv2022

Do active nematic self-mixing dynamics help growing bacterial colonies to maintain local genetic diversity?

Recent studies have shown that packings of cells, both eukaryotic cellular tissues and growing or swarming bacterial colonies, can often be understood as active nematic fluids. A key property of volume-conserving active nematic model systems is chaotic self-mixing characterized by motile topological defects. However, for active nematics driven by growth rather than motility, less is understood about mixing and defect motion. Mixing could affect evolutionary outcomes in bacterial colonies by counteracting the tendency to spatially segregate into monoclonal sectors, which reduces the local genetic diversity and confines competition between subpopulations to the boundaries between neighboring sectors. To examine whether growth-driven active nematic physics could influence this genetic demixing process, we conduct agent-based simulations of growing, dividing, and sterically repelling rod-like bacteria of various aspect ratios, and we analyze colony morphology using tools from both soft matter physics and population genetics. We find that despite measurable defect self-propulsion in growth-driven active nematics, the radial expansion flow prevents chaotic mixing. Even so, at biologically relevant cell aspect ratios, self-mixing is more effective in growing active nematics of rod-like cells compared to growing isotropic colonies of round cells. This suggests potential evolutionary consequences associated with active nematic dynamics.

cond-mat.soft↗

arXiv2021

Shape multistability in flexible tubular crystals through interactions of mobile dislocations

We study avenues to shape multistability and shape-morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium presenting a wide variety of tubular crystal deformation geometries, due to an interplay of effective defect interactions with out-of-tangent-plane deformations that reorient the tube axis. Importantly, this interplay often stabilizes defect configurations quite distinct from those predicted for a two-dimensional crystal confined to the surface of a rigid cylinder. We find that relative and absolute stability of competing states depend strongly on control parameters such as bending rigidity, applied stress, and spontaneous curvature. Using stable dislocation pair arrangements as building blocks, we demonstrate that targeted macroscopic three-dimensional conformations of thin crystalline tubes can be programmed by imposing certain sparse patterns of defects. Our findings reveal a broad design space for controllable and reconfigurable colloidal tube geometries, with potential relevance also to carbon nanotubes and microtubules.

cond-mat.soft↗

arXiv2019

Fast, scalable, and interactive software for Landau-de Gennes numerical modeling of nematic topological defects

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.

cond-mat.soft↗

arXiv2019

Topological structure and dynamics of three dimensional active nematics

Point-like motile topological defects control the universal dynamics of diverse two-dimensional active nematics ranging from shaken granular rods to cellular monolayers. A comparable understanding in higher dimensions has yet to emerge. We report the creation of three-dimensional active nematics by dispersing extensile microtubule bundles in a passive colloidal liquid crystal. Light-sheet microscopy reveals the millimeter-scale structure of active nematics with a single bundle resolution and the temporal evolution of the associated nematic director field. The dominant excitations of three-dimensional active nematics are extended charge-neutral disclination loops that undergo complex dynamics and recombination events. These studies introduce a new class of non-equilibrium systems whose turbulent-like dynamics arises from the interplay between internally generated active stresses, the chaotic flows and the topological structure of the constituent defects.

cond-mat.soft↗

arXiv2018

Evolution in range expansions with competition at rough boundaries

When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic \textit{spatial} wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations.

physics.bio-ph↗

arXiv2018

Evolution of populations expanding on curved surfaces

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.

q-bio.PE↗