33,898 research outputs found
Non-linear modeling of active biohybrid materials
Recent advances in engineered muscle tissue attached to a synthetic substrate motivates the development of appropriate constitutive and numerical models. Applications of active materials can be expanded by using robust, non-mammalian muscle cells, such as those of Manduca sexta. In this study, we propose a model to assist in the analysis of biohybrid constructs by generalizing a recently proposed constitutive law for Manduca muscle tissue. The continuum model accounts (i) for the stimulation of muscle fibers by introducing multiple stress-free reference configurations for the active and passive states and (ii) for the hysteretic response by specifying a pseudo-elastic energy function. A simple example representing uniaxial loading-unloading is used to validate and verify the characteristics of the model. Then, based on experimental data of muscular thin films, a more complex case shows the qualitative potential of Manduca muscle tissue in active biohybrid constructs
Superquadrics and Angle-Preserving Transformations
Over the past 20 years, a great deal of interest has developed in the use of computer graphics and numerical methods for three-dimensional design. Significant progress in geometric modeling is being made, predominantly for objects best represented by lists of edges, faces, and vertices. One long-term goal of this work is a unified mathematical formalism, to form the basis of an interactive and intuitive design environment in which designers can simulate three-dimensional scenes with shading and texture, produce usable design images, verify numerical machining-control commands, and set up finite-element meshwork for structural and dynamic analysis.
A new collection of smooth parametric objects and a new set of three-dimensional parametric modifiers show potential for helping to achieve this goal. The superquadric primitives and angle-preserving transformations extend the traditional geometric primitives-quadric surfaces and parametric patches-used in existing design packages, producing a new spectrum of flexible forms. Their chief advantage is that they allow complex solids and surfaces to be constructed and altered easily from a few interactive parameters
Regular Tessellation Link Complements
By regular tessellation, we mean any hyperbolic 3-manifold tessellated by
ideal Platonic solids such that the symmetry group acts transitively on
oriented flags. A regular tessellation has an invariant we call the cusp
modulus. For small cusp modulus, we classify all regular tessellations. For
large cusp modulus, we prove that a regular tessellations has to be infinite
volume if its fundamental group is generated by peripheral curves only. This
shows that there are at least 19 and at most 21 link complements that are
regular tessellations (computer experiments suggest that at least one of the
two remaining cases likely fails to be a link complement, but so far we have no
proof). In particular, we complete the classification of all principal
congruence link complements given in Baker and Reid for the cases of
discriminant D=-3 and D=-4. We only describe the manifolds arising as
complements of links here with a future publication "Regular Tessellation
Links" giving explicit pictures of these links.Comment: 35 pages, 19 figures, 4 tables; version 2: minor chages; fixed title
in arxiv's metadata; version3: addresses referee's comments, in particular,
rewrite of discussion section; including ancillary file
Emergence of Long-range Correlations and Rigidity at the Dynamic Glass Transition
At the microscopic level, equilibrium liquid's translational symmetry is
spontaneously broken at the so-called dynamic glass transition predicted by the
mean-field replica approach. We show that this fact implies the emergence of
Goldstone modes and long-range density correlations. We derive and evaluate a
new statistical mechanical expression for the glass shear modulus.Comment: 4 page
Exactly isochoric deformations of soft solids
Many materials of contemporary interest, such as gels, biological tissues and
elastomers, are easily deformed but essentially incompressible. Traditional
linear theory of elasticity implements incompressibility only to first order
and thus permits some volume changes, which become problematically large even
at very small strains. Using a mixed coordinate transformation originally due
to Gauss, we enforce the constraint of isochoric deformations exactly to
develop a linear theory with perfect volume conservation that remains valid
until strains become geometrically large. We demonstrate the utility of this
approach by calculating the response of an infinite soft isochoric solid to a
point force that leads to a nonlinear generalization of the Kelvin solution.
Our approach naturally generalizes to a range of problems involving
deformations of soft solids and interfaces in 2 dimensional and axisymmetric
geometries, which we exemplify by determining the solution to a distributed
load that mimics muscular contraction within the bulk of a soft solid
Solid Holography and Massive Gravity
Momentum dissipation is an important ingredient in condensed matter physics
that requires a translation breaking sector. In the bottom-up gauge/gravity
duality, this implies that the gravity dual is massive. We start here a
systematic analysis of holographic massive gravity (HMG) theories, which admit
field theory dual interpretations and which, therefore, might store interesting
condensed matter applications. We show that there are many phases of HMG that
are fully consistent effective field theories and which have been left
overlooked in the literature. The most important distinction between the
different HMG phases is that they can be clearly separated into solids and
fluids. This can be done both at the level of the unbroken spacetime symmetries
as well as concerning the elastic properties of the dual materials. We extract
the modulus of rigidity of the solid HMG black brane solutions and show how it
relates to the graviton mass term. We also consider the implications of the
different HMGs on the electric response. We show that the types of response
that can be consistently described within this framework is much wider than
what is captured by the narrow class of models mostly considered so far.Comment: 43 pages, 4 figure
Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
Systems of hard nonspherical particles exhibit a variety of stable phases
with different degrees of translational and orientational order, including
isotropic liquid, solid crystal, rotator and a variety of liquid crystal
phases. In this paper, we employ a Monte Carlo implementation of the
adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to
ascertain with high precision the equilibrium phase behavior of systems of
congruent Archimedean truncated tetrahedra over the entire range of possible
densities up to the maximal nearly space-filling density. In particular, we
find that the system undergoes two first-order phase transitions as the density
increases: first a liquid-solid transition and then a solid-solid transition.
The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase
at intermediate densities. At higher densities, we find that the CT phase
undergoes another first-order phase transition to one associated with the
densest-known crystal. We find no evidence for stable rotator (or plastic) or
nematic phases. We also generate the maximally random jammed (MRJ) packings of
truncated tetrahedra, which may be regarded to be the glassy end state of a
rapid compression of the liquid. We find that such MRJ packings are
hyperuniform with an average packing fraction of 0.770, which is considerably
larger than the corresponding value for identical spheres (about 0.64). We
conclude with some simple observations concerning what types of phase
transitions might be expected in general hard-particle systems based on the
particle shape and which would be good glass formers
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