29,709 research outputs found
Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects
Numerical modeling of nematic liquid crystals using the tensorial Landau-de
Gennes (LdG) theory provides detailed insights into the structure and
energetics of the enormous variety of possible topological defect
configurations that may arise when the liquid crystal is in contact with
colloidal inclusions or structured boundaries. However, these methods can be
computationally expensive, making it challenging to predict (meta)stable
configurations involving several colloidal particles, and they are often
restricted to system sizes well below the experimental scale. Here we present
an open-source software package that exploits the embarrassingly parallel
structure of the lattice discretization of the LdG approach. Our
implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate
simulations using both CPU and GPU resources in either single- or multiple-core
configurations. We make use of an efficient minimization algorithm, the Fast
Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale
parallelization, requiring little additional memory or computational cost while
offering performance competitive with other commonly used methods. In
multi-core operation we are able to scale simulations up to supra-micron length
scales of experimental relevance, and in single-core operation the simulation
package includes a user-friendly GUI environment for rapid prototyping of
interfacial features and the multifarious defect states they can promote. To
demonstrate this software package, we examine in detail the competition between
curvilinear disclinations and point-like hedgehog defects as size scale,
material properties, and geometric features are varied. We also study the
effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph
Simulated Annealing for Topological Solitons
The search for solutions of field theories allowing for topological solitons
requires that we find the field configuration with the lowest energy in a given
sector of topological charge. The standard approach is based on the numerical
solution of the static Euler-Lagrange differential equation following from the
field energy. As an alternative, we propose to use a simulated annealing
algorithm to minimize the energy functional directly. We have applied simulated
annealing to several nonlinear classical field theories: the sine-Gordon model
in one dimension, the baby Skyrme model in two dimensions and the nuclear
Skyrme model in three dimensions. We describe in detail the implementation of
the simulated annealing algorithm, present our results and get independent
confirmation of the studies which have used standard minimization techniques.Comment: 31 pages, LaTeX, better quality pics at
http://www.phy.umist.ac.uk/~weidig/Simulated_Annealing/, updated for
publicatio
Topological solitons in highly anisotropic two dimensional ferromagnets
e study the solitons, stabilized by spin precession in a classical
two--dimensional lattice model of Heisenberg ferromagnets with non-small
easy--axis anisotropy. The properties of such solitons are treated both
analytically using the continuous model including higher then second powers of
magnetization gradients, and numerically for a discrete set of the spins on a
square lattice. The dependence of the soliton energy on the number of spin
deviations (bound magnons) is calculated. We have shown that the
topological solitons are stable if the number exceeds some critical value
. For and the intermediate values of anisotropy
constant ( is an exchange constant), the soliton
properties are similar to those for continuous model; for example, soliton
energy is increasing and the precession frequency is decreasing
monotonously with growth. For high enough anisotropy we found some fundamentally new soliton features absent for continuous
models incorporating even the higher powers of magnetization gradients. For
high anisotropy, the dependence of soliton energy E(N) on the number of bound
magnons become non-monotonic, with the minima at some "magic" numbers of bound
magnons. Soliton frequency have quite irregular behavior with
step-like jumps and negative values of for some regions of . Near
these regions, stable static soliton states, stabilized by the lattice effects,
exist.Comment: 17 page
Stable topological textures in a classical 2D Heisenberg model
We show that stable localized topological soliton textures (skyrmions) with
topological charge exist in a classical 2D Heisenberg
model of a ferromagnet with uniaxial anisotropy. For this model the soliton
exist only if the number of bound magnons exceeds some threshold value depending on and the effective anisotropy constant .
We define soliton phase diagram as the dependence of threshold energies and
bound magnons number on anisotropy constant. The phase boundary lines are
monotonous for both and , while the solitons with
reveal peculiar nonmonotonous behavior, determining the transition regime from
low to high topological charges. In particular, the soliton energy per
topological charge (topological energy density) achieves a minimum neither for
nor high charges, but rather for intermediate values or
.Comment: 8 pages, 4 figure
On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification
We present a new approach to convexification of the Tikhonov regularization
using a continuation method strategy. We embed the original minimization
problem into a one-parameter family of minimization problems. Both the penalty
term and the minimizer of the Tikhonov functional become dependent on a
continuation parameter.
In this way we can independently treat two main roles of the regularization
term, which are stabilization of the ill-posed problem and introduction of the
a priori knowledge. For zero continuation parameter we solve a relaxed
regularization problem, which stabilizes the ill-posed problem in a weaker
sense. The problem is recast to the original minimization by the continuation
method and so the a priori knowledge is enforced.
We apply this approach in the context of topology-to-shape geometry
identification, where it allows to avoid the convergence of gradient-based
methods to a local minima. We present illustrative results for magnetic
induction tomography which is an example of PDE constrained inverse problem
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