95 research outputs found
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.Comment: Specific results for spiral defects now added. References to Witten,
Mahadevan and Ben Amar now added
Negative Gaussian curvature from induced metric changes.
We revisit the light or heat-induced changes in topography of initially flat sheets of a solid that elongate or contract along patterned in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated-so-called "anticones." We show that azimuthal material displacements are required for the distorted state to be stretch free and bend minimizing. The resultant shapes are smooth and asterlike and can become reentrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, although the former offer huge deformations.This is the author accepted manuscript. The final version is available from American Physical Society via http://dx.doi.org/10.1103/PhysRevE.92.01040
Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard-Disk Fluid in Negative Curvature
We examine a simple hard-disk 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, one-parameter model of disordered monodisperse hard disks. 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 simulations 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
How to Pare a Pair: Topology Control and Pruning in Intertwined Complex Networks
Recent work on self-organized remodeling of vasculature in slime-mold, leaf
venation systems and vessel systems in vertebrates has put forward a plethora
of potential adaptation mechanisms. All these share the underlying hypothesis
of a flow-driven machinery, meant to alter rudimentary vessel networks in order
to optimize the system's dissipation, flow uniformity, or more, with different
versions of constraints. Nevertheless, the influence of environmental factors
on the long-term adaptation dynamics as well as the networks structure and
function have not been fully understood. Therefore, interwoven capillary
systems such as found in the liver, kidney and pancreas, present a novel
challenge and key opportunity regarding the field of coupled distribution
networks. We here present an advanced version of the discrete Hu--Cai model,
coupling two spatial networks in 3D. We show that spatial coupling of two
flow-adapting networks can control the onset of topological complexity in
concert with short-term flow fluctuations. We find that both
fluctuation-induced and spatial coupling induced topology transitions undergo
curve collapse obeying simple functional rescaling. Further, our approach
results in an alternative form of Murray's law, which incorporates local vessel
interactions and flow interactions. This geometric law allows for the
estimation of the model parameters in ideal Kirchhoff networks and respective
experimentally acquired network skeletons
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.Comment: 4 pages, 4 included figures, RevTe
Frame, metric and geodesic evolution in shape-changing nematic shells.
Non-uniform director fields in flat, responsive, glassy nematic sheets lead to the induction of shells with non-trivial topography on the application of light or heat. Contraction along the director causes metric change, with, in general, the induction of Gaussian curvature, that drives the topography change. We describe the metric change, the evolution of the director field, and the transformation of reference state material curves, e.g. spirals into radii, as curvature develops. The non-isometric deformations associated with heat or light change the geodesics of the surface, intriguingly even in regions where no Gaussian curvature results
Impossible ecologies: Interaction networks and stability of coexistence in ecological communities
Does an ecological community allow stable coexistence? Identifying the
general principles that determine the answer to this question is a central
problem of theoretical ecology. Random matrix theory approaches have uncovered
the general trends of the effect of competitive, mutualistic, and predator-prey
interactions between species on stability of coexistence. However, an
ecological community is determined not only by the counts of these different
interaction types, but also by their network arrangement. This cannot be
accounted for in a direct statistical description that would enable random
matrix theory approaches. Here, we therefore develop a different approach, of
exhaustive analysis of small ecological communities, to show that this
arrangement of interactions can influence stability of coexistence more than
these general trends. We analyse all interaction networks of
species with Lotka-Volterra dynamics by combining exact results for species and numerical exploration. Surprisingly, we find that a very small
subset of these networks are "impossible ecologies", in which stable
coexistence is non-trivially impossible. We prove that the possibility of
stable coexistence in general ecologies is determined by similarly rare
"irreducible ecologies". By random sampling of interaction strengths, we then
show that the probability of stable coexistence varies over many orders of
magnitude even in ecologies that differ only in the network arrangement of
identical ecological interactions. Finally, we demonstrate that our approach
can reveal the effect of evolutionary or environmental perturbations of the
interaction network. Overall, this work reveals the importance of the full
structure of the network of interactions for stability of coexistence in
ecological communities.Comment: 14 pages, 6 figures, 3 supplementary figure
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