4,213 research outputs found
An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis
This paper outlines an energy-minimization finite-element approach to the
computational modeling of equilibrium configurations for nematic liquid
crystals under free elastic effects. The method targets minimization of the
system free energy based on the Frank-Oseen free-energy model. Solutions to the
intermediate discretized free elastic linearizations are shown to exist
generally and are unique under certain assumptions. This requires proving
continuity, coercivity, and weak coercivity for the accompanying appropriate
bilinear forms within a mixed finite-element framework. Error analysis
demonstrates that the method constitutes a convergent scheme. Numerical
experiments are performed for problems with a range of physical parameters as
well as simple and patterned boundary conditions. The resulting algorithm
accurately handles heterogeneous constant coefficients and effectively resolves
configurations resulting from complicated boundary conditions relevant in
ongoing research.Comment: 31 pages, 3 figures, 3 table
Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
We prove that the smooth solutions to the Cauchy problem for the compressible
general three-dimensional Ericksen--Leslie system modeling nematic liquid
crystal flow with conserved mass, linear momentum, and dissipating total
energy, generally lose classical smoothness within a finite time.Comment: 7 pages. arXiv admin note: text overlap with arXiv:1206.2850,
arXiv:1105.2180 by other author
Symmetry breaking in the self-consistent Kohn-Sham equations
The Kohn-Sham (KS) equations determine, in a self-consistent way, the
particle density of an interacting fermion system at thermal equilibrium. We
consider a situation when the KS equations are known to have a unique solution
at high temperatures and this solution is a uniform particle density. We show
that, at zero temperature, there are stable solutions that are not uniform. We
provide the general principles behind this phenomenon, namely the conditions
when it can be observed and how to construct these non-uniform solutions. Two
concrete examples are provided, including fermions on the sphere which are
shown to crystallize in a structure that resembles the C molecule.Comment: a few typos eliminate
Statistical mechanics of glass transition in lattice molecule models
Lattice molecule models are proposed in order to study statistical mechanics
of glass transition in finite dimensions. Molecules in the models are
represented by hard Wang tiles and their density is controlled by a chemical
potential. An infinite series of irregular ground states are constructed
theoretically. By defining a glass order parameter as a collection of the
overlap with each ground state, a thermodynamic transition to a glass phase is
found in a stratified Wang tiles model on a cubic lattice.Comment: 18 pages, 8 figure
Winterbottom Construction for Finite Range Ferromagnetic Models: An L_1 Approach
We provide a rigorous microscopic derivation of the thermodynamic description
of equilibrium crystal shapes in the presence of a substrate, first studied by
Winterbottom. We consider finite range ferromagnetic Ising models with pair
interactions in dimensions greater or equal to 3, and model the substrate by a
finite-range boundary magnetic field acting on the spins close to the bottom
wall of the box
A Multiscale Approach for Modeling Crystalline Solids
In this paper we present a modeling approach to bridge the atomistic with
macroscopic scales in crystalline materials. The methodology combines
identification and modeling of the controlling unit processes at microscopic
level with the direct atomistic determination of fundamental material
properties. These properties are computed using a many body Force Field derived
from ab initio quantum-mechanical calculations. This approach is exercised to
describe the mechanical response of high-purity Tantalum single crystals,
including the effect of temperature and strain-rate on the hardening rate. The
resulting atomistically informed model is found to capture salient features of
the behavior of these crystals such as: the dependence of the initial yield
point on temperature and strain rate; the presence of a marked stage I of easy
glide, specially at low temperatures and high strain rates; the sharp onset of
stage II hardening and its tendency to shift towards lower strains, and
eventually disappear, as the temperature increases or the strain rate
decreases; the parabolic stage II hardening at low strain rates or high
temperatures; the stage II softening at high strain rates or low temperatures;
the trend towards saturation at high strains; the temperature and strain-rate
dependence of the saturation stress; and the orientation dependence of the
hardening rate.Comment: 25 pages, 15 figures, LaTe
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