arXiv subjects

Carl D. Modes

Publications and source records attributed to Carl D. Modes.

25 records · Page 2Linked to original sources

arXiv2014

Structural Self-Assembly and Glassy Dynamics in Locally Adaptive Networks

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs and find in simulation that these networks ultimately develop a hierarchical organization of the final weighted architecture accompanied by the formation of a system-spanning backbone. In addition, we find that the long term equilibration dynamics exhibit glassy behavior characterized by long periods of slow changes punctuated by bursts of reorganization events.

nlin.AO↗

arXiv2013

A Geometric Knotspace Template

Early last century witnessed both the complete classification of 2-dimensional manifolds and a proof that classification of 4-dimensional manifolds is undecidable, setting up 3-dimensional manifolds as a central battleground of topology to this day. A rather important subset of the 3-manifolds has turned out to be the knotspaces, the manifolds left when a thin tube around a knot in 3D space is excised. Given a knot diagram it would be desirable to provide as compact a description of its knotspace as feasible; hitherto this has been done by computationally tessellating the knotspace of a given knot into polyhedral complexes using ad hoc methods of uncontrolled computational complexity. Here we present an extremely compact representation of the knotspace obtainable directly from a knot diagram; more technically, an explicit, geometrically-inspired polygonal tessellation of a deformation retract of the knotspace of arbitrary knots and links. Our template can be constructed directly from a planar presentation of the knot with C crossings using at most 12C polygons bounded by 64C edges, in time O(C). We show the utility of our template by deriving a novel presentation of the fundamental group, from which we motivate a measure of complexity of the knot diagram.

math.GT↗

arXiv2011

Blueprinting Nematic Glass: Systematically Constructing and Combining Active Points of Curvature for Emergent Morphology

Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture domains in nematic glasses that are simple to synthesize, and explore the ways that these simple domains may be compatibly combined to yield analogs of the traditional smooth disclination defect textures seen in standard liquid crystals. We calculate the deformation properties of these constructed textures, and show that, subject to the compatibility constraints of the construction, these textures may be further combined to achieve shape blueprinting of 3-D structures from flat sheets.

cond-mat.soft↗

arXiv2010

Disclination-mediated thermo-optical response in nematic glass sheets

Nematic solids respond strongly to changes in ambient heat or light, significantly differently parallel and perpendicular to the director. This phenomenon is well characterized for uniform director fields, but not for defect textures. We analyze the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for some disclination defects with an eye towards reversibly inducing three-dimensional shapes from flat sheets of material, at the nano-scale all the way to macroscopic objects, including non-developable surfaces. The latter offers a new paradigm to actuation via switchable stretch in thin systems.

cond-mat.soft↗

arXiv2008

Spherical Foams in Flat Space

Regular tesselations of space are characterized through their Schlafli symbols {p,q,r}, where each cell has regular p-gonal sides, q meeting at each vertex, and r meeting on each edge. Regular tesselations with symbols {p,3,3} all satisfy Plateau's laws for equilibrium foams. For general p, however, these regular tesselations do not embed in Euclidean space, but require a uniform background curvature. We study a class of regular foams on S^3 which, through conformal, stereographic projection to R^3 define irregular cells consistent with Plateau's laws. We analytically characterize a broad classes of bulk foam bubbles, and extend and explain recent observations on foam structure and shape distribution. Our approach also allows us to comment on foam stability by identifying a weak local maximum of A^(3/2)/V at the maximally symmetric tetrahedral bubble that participates in T2 rearrangements.

cond-mat.soft↗

arXiv2008

Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard Disc Fluid in Negative Curvature

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space. Additionally, we investigate packing and dynamics on triply periodic, negatively curved surfaces with an eye toward real biological and polymeric systems.

cond-mat.soft↗

arXiv2007

Hard Discs on the Hyperbolic Plane

cond-mat.stat-mech↗