2,058 research outputs found
Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
We introduce a new method, the Local Monge Parametrizations (LMP) method, to
approximate tensor fields on general surfaces given by a collection of local
parametrizations, e.g.~as in finite element or NURBS surface representations.
Our goal is to use this method to solve numerically tensor-valued partial
differential equations (PDE) on surfaces. Previous methods use scalar
potentials to numerically describe vector fields on surfaces, at the expense of
requiring higher-order derivatives of the approximated fields and limited to
simply connected surfaces, or represent tangential tensor fields as tensor
fields in 3D subjected to constraints, thus increasing the essential number of
degrees of freedom. In contrast, the LMP method uses an optimal number of
degrees of freedom to represent a tensor, is general with regards to the
topology of the surface, and does not increase the order of the PDEs governing
the tensor fields. The main idea is to construct maps between the element
parametrizations and a local Monge parametrization around each node. We test
the LMP method by approximating in a least-squares sense different vector and
tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply
the LMP method to two physical models on surfaces, involving a tension-driven
flow (vector-valued PDE) and nematic ordering (tensor-valued PDE). The LMP
method thus solves the long-standing problem of the interpolation of tensors on
general surfaces with an optimal number of degrees of freedom.Comment: 16 pages, 6 figure
A standard format and a graphical user interface for spin system specification
We introduce a simple and general XML format for spin system description that
is the result of extensive consultations within Magnetic Resonance community
and unifies under one roof all major existing spin interaction specification
conventions. The format is human-readable, easy to edit and easy to parse using
standard XML libraries. We also describe a graphical user interface that was
designed to facilitate construction and visualization of complicated spin
systems. The interface is capable of generating input files for several popular
spin dynamics simulation packages.Comment: Submitted for publicatio
Resource Letter: Dark Energy and the Accelerating Universe
This Resource Letter provides a guide to the literature on dark energy and
the accelerating universe. It is intended to be of use to researchers,
teachers, and students at several levels. Journal articles, books, and websites
are cited for the following topics: Einstein's cosmological constant,
quintessence or dynamical scalar fields, modified cosmic gravity, relations to
high energy physics, cosmological probes and observations, terrestrial probes,
calculational tools and parameter estimation, teaching strategies and
educational resources, and the fate of the universe.Comment: Resource Letter for AAPT/AJP, 11 pages, 99 reference
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