191,052 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
Global semantic typing for inductive and coinductive computing
Inductive and coinductive types are commonly construed as ontological
(Church-style) types, denoting canonical data-sets such as natural numbers,
lists, and streams. For various purposes, notably the study of programs in the
context of global semantics, it is preferable to think of types as semantical
properties (Curry-style). Intrinsic theories were introduced in the late 1990s
to provide a purely logical framework for reasoning about programs and their
semantic types. We extend them here to data given by any combination of
inductive and coinductive definitions. This approach is of interest because it
fits tightly with syntactic, semantic, and proof theoretic fundamentals of
formal logic, with potential applications in implicit computational complexity
as well as extraction of programs from proofs. We prove a Canonicity Theorem,
showing that the global definition of program typing, via the usual (Tarskian)
semantics of first-order logic, agrees with their operational semantics in the
intended model. Finally, we show that every intrinsic theory is interpretable
in a conservative extension of first-order arithmetic. This means that
quantification over infinite data objects does not lead, on its own, to
proof-theoretic strength beyond that of Peano Arithmetic. Intrinsic theories
are perfectly amenable to formulas-as-types Curry-Howard morphisms, and were
used to characterize major computational complexity classes Their extensions
described here have similar potential which has already been applied
Approximate Zero Modes for the Pauli Operator on a Region
Let denoted the Pauli operator on a bounded open
region with Dirichlet boundary conditions and
magnetic potential scaled by some . Assume that the corresponding
magnetic field satisfies where and is an open subset of
of full measure (note that, the Orlicz space
contains for any ). Let
denote the corresponding eigenvalue counting function. We establish the strong
field asymptotic formula as , whenever
for some and . The
corresponding eigenfunctions can be viewed as a localised version of the
Aharonov-Casher zero modes for the Pauli operator on .Comment: 28 pages; for the sake of clarity the main results have been
reformulated and some minor presentational changes have been mad
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Rhetoric and the origins of the human sciences: A Foucauldian tale untold
Fixed-Target CP-Violation Experiments at Fermilab
Studies of CP violation, for 30 years focused primarily on the neutral K
meson, are on the threshold of a new era as experiments approach Standard-Model
sensitivities in decays of beauty, charm, and hyperons. The array of
heavy-quark experiments approved and planned at Fermilab may lead to a
significant breakthrough in the next five to ten years.Comment: Revised and expanded for greater clarity and completeness. 15 pages,
6 PostScript figure
Remarks on Muon Experiments and Possible CP Violation in Decay
The first experimental limit on CP violation in pi -> mu -> e decay is
extracted from published results of the CERN g-2 experiment.Comment: 2 pages, LaTeX, submitted to Phys. Rev.
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