2,118 research outputs found
Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators
The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionally and spatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4
Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey
This paper provides a tutorial and survey for a specific kind of illustrative
visualization technique: feature lines. We examine different feature line
methods. For this, we provide the differential geometry behind these concepts
and adapt this mathematical field to the discrete differential geometry. All
discrete differential geometry terms are explained for triangulated surface
meshes. These utilities serve as basis for the feature line methods. We provide
the reader with all knowledge to re-implement every feature line method.
Furthermore, we summarize the methods and suggest a guideline for which kind of
surface which feature line algorithm is best suited. Our work is motivated by,
but not restricted to, medical and biological surface models.Comment: 33 page
A literature survey of low-rank tensor approximation techniques
During the last years, low-rank tensor approximation has been established as
a new tool in scientific computing to address large-scale linear and
multilinear algebra problems, which would be intractable by classical
techniques. This survey attempts to give a literature overview of current
developments in this area, with an emphasis on function-related tensors
A Proposal for a Differential Calculus in Quantum Mechanics
In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics,
we develop a {\it quantum-deformed} exterior calculus on the phase-space of an
arbitrary hamiltonian system. Introducing additional bosonic and fermionic
coordinates we construct a super-manifold which is closely related to the
tangent and cotangent bundle over phase-space. Scalar functions on the
super-manifold become equivalent to differential forms on the standard
phase-space. The algebra of these functions is equipped with a Moyal super-star
product which deforms the pointwise product of the classical tensor calculus.
We use the Moyal bracket algebra in order to derive a set of quantum-deformed
rules for the exterior derivative, Lie derivative, contraction, and similar
operations of the Cartan calculus.Comment: TeX file with phyzzx macro, 43 pages, no figure
The Kummer tensor density in electrodynamics and in gravity
Guided by results in the premetric electrodynamics of local and linear media,
we introduce on 4-dimensional spacetime the new abstract notion of a Kummer
tensor density of rank four, . This tensor density is, by
definition, a cubic algebraic functional of a tensor density of rank four
, which is antisymmetric in its first two and its last two
indices: . Thus,
, see Eq.(46). (i) If is identified with the
electromagnetic response tensor of local and linear media, the Kummer tensor
density encompasses the generalized {\it Fresnel wave surfaces} for propagating
light. In the reversible case, the wave surfaces turn out to be {\it Kummer
surfaces} as defined in algebraic geometry (Bateman 1910). (ii) If is
identified with the {\it curvature} tensor of a Riemann-Cartan
spacetime, then and, in the special case of general
relativity, reduces to the Kummer tensor of Zund (1969). This is related to the {\it principal null directions} of the curvature. We
discuss the properties of the general Kummer tensor density. In particular, we
decompose irreducibly under the 4-dimensional linear group
and, subsequently, under the Lorentz group .Comment: 54 pages, 6 figures, written in LaTex; improved version in accordance
with the referee repor
PICPANTHER: A simple, concise implementation of the relativistic moment implicit Particle-in-Cell method
A three-dimensional, parallelized implementation of the electromagnetic
relativistic moment implicit particle-in-cell method in Cartesian geometry
(Noguchi et. al., 2007) is presented. Particular care was taken to keep the
C++11 codebase simple, concise, and approachable. GMRES is used as a field
solver and during the Newton-Krylov iteration of the particle pusher. Drifting
Maxwellian problem setups are available while more complex simulations can be
implemented easily. Several test runs are described and the code's numerical
and computational performance is examined. Weak scaling on the SuperMUC system
is discussed and found suitable for large-scale production runs.Comment: 29 pages, 8 figure
Bulgac-Kusnezov-Nos\'e-Hoover thermostats
In this paper we formulate Bulgac-Kusnezov constant temperature dynamics in
phase space by means of non-Hamiltonian brackets. Two generalized versions of
the dynamics are similarly defined: one where the Bulgac-Kusnezov demons are
globally controlled by means of a single additional Nos\'e variable, and
another where each demon is coupled to an independent Nos\'e-Hoover thermostat.
Numerically stable and efficient measure-preserving time-reversible algorithms
are derived in a systematic way for each case. The chaotic properties of the
different phase space flows are numerically illustrated through the
paradigmatic example of the one-dimensional harmonic oscillator. It is found
that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic,
both of the Nos\'e-Hoover controlled dynamics sample the canonical distribution
correctly
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