arXiv subjects

M. J. Bowick

Publications and source records attributed to M. J. Bowick.

14 recordsLinked to original sources

arXiv2019

Folding pathways to crumpling in thermalized elastic frames

The mechanical properties of thermally excited two-dimensional crystalline membranes can depend dramatically on their geometry and topology. A particularly relevant example is the effect on the crumpling transition of holes in the membrane. Here we use molecular dynamics simulations to study the case of elastic frames (sheets with a single large hole in the center) and find that the system approaches the crumpled phase through a sequence of origami-like folds at decreasing length scales when temperature is increased. We use normal-normal correlation functions to quantify the temperature-dependent number of folds.

cond-mat.soft↗

arXiv2017

Thermal crumpling of perforated two-dimensional sheets

Thermalized elastic membranes without distant self-avoidance are believed to undergo a crumpling transition when the microscopic bending stiffness is comparable to $kT$, the scale of thermal fluctuations. Most potential physical realizations of such membranes have a bending stiffness well in excess of experimentally achievable temperatures and are therefore unlikely ever to access the crumpling regime. We propose a mechanism to tune the onset of the crumpling transition by altering the geometry and topology of the sheet itself. We carry out extensive molecular dynamics simulations of perforated sheets with a dense periodic array of holes and observe that the critical temperature is controlled by the total fraction of removed area, independent of the precise arrangement and size of the individual holes. The critical exponents for the perforated membrane are compatible with those of the standard crumpling transition.

cond-mat.soft↗

arXiv2015

Shape-shifting droplet networks

We consider a three-dimensional network of aqueous droplets joined by single lipid bilayers to form a cohesive, tissue-like material. The droplets in these networks can be programmed to have distinct osmolarities so that osmotic gradients generate internal stresses via local fluid flows to cause the network to change shape. We discover, using molecular dynamics simulations, a reversible folding-unfolding process by adding an osmotic interaction with the surrounding environment which necessarily evolves dynamically as the shape of the network changes. This discovery is the next important step towards osmotic robotics in this system. We also explore analytically and numerically how the networks become faceted via buckling and how quasi-one-dimensional networks become three-dimensional.

cond-mat.soft↗

arXiv2015

Viral nematics in confined geometries

Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid crystals, we examine the competition between bulk elasticity and surface anchoring, mediated by the formation of topological defects. We show analytically that bulk defects are unstable with respect to defects sitting at the boundary. Moreover, in case of an annulus, whose topology does not require the presence of topological defects, under weak anchoring conditions we find that nematic textures with boundary defects are stable compared to the defect free configurations. Thus our simple approach, with no fitting parameters, suggests a possible symmetry breaking mechanism responsible for the formation of one-, two- and three-fold textures under annular confinement.

cond-mat.soft↗

arXiv2015

Thick smectic shells

The known ground state of ultrathin smectic films confined to the surface of a sphere is described by four +1/2 defects assembled on a great circle and a director which follows geodesic lines. Using a simple perturbative approach we show that for thick smectic films on a sphere with planar anchoring this solution breaks down, distorting the smectic layers. The instability happens when the bend elastic constant exceeds the anchoring strength times the radius of the inner sphere. Above this threshold, the formation of a periodic chevron-like structure, observed experimentally as well, relieves geometric frustration. We quantify the effect of thickness and curvature of smectic shells and provide insight into the wavelength of the observed texture.

cond-mat.soft↗

arXiv2015

Forming a cube from a sphere with tetratic order

Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form solution for 1/4-disclinations in planar geometry. Applying the same covariant formalism to a sphere we show analytically that within the one elastic constant approximation eight +1/4-disclinations favor positions defining the vertices of a cube. The interplay between defect-defect interactions and bending energy results in a flattening of the sphere towards superspheroids with the symmetry of a cube.

cond-mat.soft↗

arXiv2014

On the modeling of endocytosis in yeast

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Experiments on endocytosis in yeast all agree that (i) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it and (ii) the large scale membrane deformation is tubular in shape. There are three competing proposals, in contrast, for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: (i) initiation, where clathrin interacts with the membrane via adaptor proteins, (ii) elongation, where the membrane is then further deformed by polymerizing actin filaments, followed by (iii) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could possibly be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed.

q-bio.CB↗

arXiv2003

Grain Boundary Scars and Spherical Crystallography

We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the minimum energy configurations of particles with arbitrary repulsive interactions on curved surfaces. Above a critical system size we find that crystals develop distinctive high-angle grain boundaries, or scars, not found in planar crystals. The number of excess defects in a scar is shown to grow linearly with the dimensionless system size. The observed slope is expected to be universal, independent of the microscopic potential.

cond-mat.soft↗

arXiv1997

Minimal Dynamical Triangulations of Random Surfaces

We introduce and investigate numerically a minimal class of dynamical triangulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the local coordination number, or equivalently intrinsic scalar curvature, leaves intact the fractal structure characteristic of generic dynamically triangulated random surfaces. Furthermore the Ising model coupled to minimal two-dimensional gravity still possesses a continuous phase transition. The critical exponents of this transition correspond to the usual KPZ exponents associated with coupling a central charge c=1/2 model to two-dimensional gravity.

hep-th↗

arXiv1996

Suppressing Curvature Fluctuations in Dynamical Triangulations

We study numerically the dynamical triangulation formulation of two-dimensional quantum gravity using a restricted class of triangulation, so-called minimal triangulations, in which only vertices of coordination number 5, 6, and 7 are allowed. A real-space RG analysis shows that for pure gravity (central charge c = 0) this restriction does not affect the critical behavior of the model. Furthermore, we show that the critical behavior of an Ising model coupled to minimal dynamical triangulations (c = 1/2) is still governed by the KPZ-exponents.

hep-lat↗

arXiv1996

The flat phase of fixed-connectivity membranes

The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system \cite{BCFTA}. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.

hep-lat↗

arXiv1995

The Phase Diagram of Crystalline Surfaces

We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to $128^2$ nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.

hep-lat↗

arXiv1992

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

We have observed the production of strings (disclination lines and loops) via the Kibble mechanism of domain (bubble) formation in the isotropic to nematic phase transition of a sample of uniaxial nematic liquid crystal. The probablity of string formation per bubble is measured to be $0.33 \pm 0.01$. This is in good agreement with the theoretical value $1/ π$ expected in two dimensions for the order parameter space $S^2/{\bf Z}_2$ of a simple uniaxial nematic liquid crystal.

hep-ph↗

arXiv1992

Unitary One Matrix Models: String Equations and Flows

We review the Symmetric Unitary One Matrix Models. In particular we discuss the string equation in the operator formalism, the mKdV flows and the Virasoro Constraints. We focus on the $\t$-function formalism for the flows and we describe its connection to the (big cell of the) Sato Grassmannian $\Gr$ via the Plucker embedding of $\Gr$ into a fermionic Fock space. Then the space of solutions to the string equation is an explicitly computable subspace of $\Gr\times\Gr$ which is invariant under the flows.

hep-th↗