arXiv subjects

Daniel A. Beller

Publications and source records attributed to Daniel A. Beller.

32 records · Page 2Linked to original sources

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↗

arXiv2018

Tunable colloid trajectories in nematic liquid crystals near wavy walls

The ability to dictate colloid motion is an important challenge in fields ranging from materials science to living systems. Here, by embedding energy landscapes in confined nematic liquid crystals, we design a versatile platform to define colloidal migration. This is achieved by placing a wavy wall, with alternating hills and wells, in nematic liquid crystals, to impose a smooth elastic energy field with alternating splay and bend distortions. This domain generates (meta) stable loci that act as attractors and unstable loci that repel colloids over distances large compared to the colloid radius. Energy gradients in the vicinity of these loci are exploited to dictate colloid trajectories. We demonstrate several aspects of this control, by studying transitions between defect configurations, propelling particles along well defined paths and exploiting multistable systems to send particles to particular sites within the domain. Such tailored landscapes have promise in reconfigurable systems and in microrobotics applications

cond-mat.soft↗

arXiv2018

Elastocapillary driven assembly of particles at free-standing smectic-A films

Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetting conditions of particles at the smectic film, are reported. This work paves the way to exploiting LC interfaces as a means to direct spontaneously formed, reconfigurable, and optically active materials.

cond-mat.soft↗

arXiv2016

Lassoing saddle splay and the geometrical control of topological defects

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): both point and ring topological defects can occur within each hole and around the system, while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create novel defect structures, including an array of disclination lines, reminiscent of those found in liquid crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.

cond-mat.soft↗

arXiv2016

Plastic deformation of tubular crystals by dislocation glide

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical phyllotaxis, describing the spiral packings on cylinders commonly found in nature, have found application in all these systems. Several recent studies have examined defects in tubular crystals associated with crystalline packings that must accommodate a fixed tube radius. Here, we study the mechanics of tubular crystals with variable tube radius, with dislocations interposed between regions of different phyllotactic packings. Unbinding and separation of dislocation pairs with equal and opposite Burgers vectors allow the growth of one phyllotactic domain at the expense of another. In particular, glide separation of dislocations offers a low-energy mode for plastic deformations of solid tubes in response to external stresses, reconfiguring the lattice step by step. Through theory and simulation, we examine how the tube's radius and helicity affects, and is in turn altered by, the mechanics of dislocation glide. We also discuss how a sufficiently strong bending rigidity can alter or arrest the deformations of tubes with small radii.

cond-mat.soft↗

arXiv2014

Shape-controlled orientation and assembly of colloids with sharp edges in nematic liquid crystals

The assembly of colloids in nematic liquid crystals via topological defects has been extensively studied for spherical particles, and investigations of other colloid shapes have revealed a wide array of new assembly behaviors. We show, using Landau-de Gennes numerical modeling, that nematic defect configurations and colloidal assembly can be strongly influenced by fine details of colloid shape, in particular the presence of sharp edges. For cylinder, microbullet, and cube colloid geometries, we obtain the particles' equilibrium alignment directions and effective pair interaction potentials as a function of simple shape parameters. We find that defects pin at sharp edges, and that the colloid consequently orients at an oblique angle relative to the far-field nematic director that depends on the colloid's shape. This shape-dependent alignment, which we confirm in experimental measurements, raises the possibility of selecting self-assembly outcomes for colloids in liquid crystals by tuning particle geometry.

cond-mat.soft↗

arXiv2014

The Geometry of the Cholesteric Phase

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot be, in general, translated from one phase to the other.

cond-mat.soft↗

arXiv2014

Elasticity-Dependent Self-assembly of Micro-Templated Chromonic Liquid Crystal Films

We explore micropatterned director structures of aqueous lyotropic chromonic liquid crystal (LCLC) films created on square lattice cylindrical-micropost substrates. The structures are manipulated by modulating the LCLC mesophases and their elastic properties via concentration through drying. Nematic LCLC films exhibit preferred bistable alignment along the diagonals of the micropost lattice. Columnar LCLC films, dried from nematics, form two distinct director and defect configurations: a diagonally aligned director pattern with local squares of defects, and an off-diagonal configuration with zig-zag defects. The formation of these states appears to be tied to the relative splay and bend free energy costs of the initial nematic films. The observed nematic and columnar configurations are understood numerically using a Landau-de Gennes free energy model. Among other attributes, the work provide first examples of quasi-2D micropatterning of LC films in the columnar phase and lyotropic LC films in general, and it demonstrates alignment and configuration switching of typically difficult-to-align LCLC films via bulk elastic properties.

cond-mat.soft↗

arXiv2013

Focal Conic Flower Textures at Curved Interfaces

Focal conic domains (FCDs) in smectic-A liquid crystals have drawn much attention both for their exquisitely structured internal form and for their ability to direct the assembly of micro- and nanomaterials in a variety of patterns. A key to directing FCD assembly is control over the eccentricity of the domain. Here, we demonstrate a new paradigm for creating spatially varying FCD eccentricity by confining a hybrid-aligned smectic with curved interfaces. In particular, we manipulate interface behavior with colloidal particles in order to experimentally produce two examples of what has recently been dubbed the flower texture, where the focal hyperbolae diverge radially outward from the center of the texture, rather than inward as in the canonical eventail or fan texture. We explain how this unconventional assembly can arise from appropriately curved interfaces. Finally, we present a model for this system that applies the law of corresponding cones, showing how FCDs may be embedded smoothly within a "background texture" of large FCDs and concentric spherical layers, in a manner consistent with the qualitative features of the smectic flower. Such understanding could potentially lead to disruptive liquid crystal technologies beyond displays, including patterning, smart surfaces, microlens arrays, sensors and nanomanufacturing.

cond-mat.soft↗

arXiv2013

Exploiting imperfections: Directed assembly of surface colloids via bulk topological defects

We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals to assemble colloidal particles trapped at the liquid crystal interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic liquid crystal 5CB create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. Here we report on complex, open structures organized via interactions with defects in the bulk. Specifically, by confining the nematic liquid crystal in an array of microposts with homeotropic anchoring conditions, we cause defect rings to form at well-defined locations in the bulk of the sample. These defects source elastic deformations that direct the assembly of the interfacially-trapped colloids into ring-like assemblies, which recapitulate the defect geometry even when the microposts are completely immersed in the nematic. When the surface density of the colloids is high, they form a ring near the defect and a hexagonal lattice far from it. Since topographically complex substrates are easily fabricated and liquid crystal defects are readily reconfigured, this work lays the foundation for a new, robust mechanism to dynamically direct assembly over large areas by controlling surface anchoring and associated bulk defect structure.

cond-mat.soft↗

arXiv2013

Ring around the colloid

In this work, we show that Janus washers, genus-one colloids with hybrid anchoring conditions, form topologically required defects in nematic liquid crystals. Experiments under crossed polarizers reveal the defect structure to be a rigid disclination loop confined within the colloid, with an accompanying defect in the liquid crystal. When confined to a homeotropic cell, the resulting colloid-defect ring pair tilts relative to the far field director, in contrast to the behavior of toroidal colloids with purely homeotropic anchoring. We show that this tilting behavior can be reversibly suppressed by the introduction of a spherical colloid into the center of the toroid, creating a new kind of multi-shape colloidal assemblage.

cond-mat.soft↗

arXiv2013

Micro-Bullet Assembly: Interactions of Oriented Dipoles in Confined Nematic Liquid Crystal

Microbullet particles, cylinders with one blunt and one spherical end, offer a novel platform to study the effects of anisotropy and curvature on colloidal assembly in complex fluids. Here, we disperse microbullets in 4-cyano-4'-pentylbiphenyl (5CB) nematic liquid crystal (NLC) cells and form oriented elastic dipoles with a nematic point defect located near the curved end. This feature allows us to study particle interactions as a function of dipole alignment. By careful control of the surface anchoring at the particle surface and the confining boundaries, we study the interactions and assembly of microbullets under various conditions. When microbullets with homeotropic surface anchoring are dispersed in a planar cell, parallel dipoles form linear chains parallel to the director, similar to the observations of spherical particles in a planar cell, while antiparallel dipoles orient side-to-side. In a homeotropic cell, however, particles rotate to orient their long axis parallel to the director. When so aligned, parallel dipoles repel and form 2D ordered assemblies with hexagonal symmetry that ripen over time owing to attraction between antiparallel neighbors. Further, we show that the anchoring conditions inside the cell can be altered by application of an electrical field, allowing us to flip microbullets to orient parallel to the director, an effect driven by an elastic torque. Finally, we detail the mechanisms that control the formation of 1D chains and hexagonal lattices with respect to the elasticity of the NLC.

cond-mat.soft↗

arXiv2012

Breaking the Rules for Topological Defects: Smectic Order on Conical Substrates

Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are grown on real surfaces; eventually, surface imperfections are on the same scale as the lattice constant. Here, we gain insights into this general problem by studying two-dimensional smectic order on substrates with highly localized intrinsic curvature, constructed from cones and their intersections with planes. In doing so we take advantage of fully tractable "paper and tape" constructions, allowing us to understand, in detail, the induced cusps and singularities.

cond-mat.soft↗