4,973 research outputs found
Solving seismic wave propagation in elastic media using the matrix exponential approach
Three numerical algorithms are proposed to solve the time-dependent
elastodynamic equations in elastic solids. All algorithms are based on
approximating the solution of the equations, which can be written as a matrix
exponential. By approximating the matrix exponential with a product formula, an
unconditionally stable algorithm is derived that conserves the total elastic
energy density. By expanding the matrix exponential in Chebyshev polynomials
for a specific time instance, a so-called ``one-step'' algorithm is constructed
that is very accurate with respect to the time integration. By formulating the
conventional velocity-stress finite-difference time-domain algorithm (VS-FDTD)
in matrix exponential form, the staggered-in-time nature can be removed by a
small modification, and higher order in time algorithms can be easily derived.
For two different seismic events the accuracy of the algorithms is studied and
compared with the result obtained by using the conventional VS-FDTD algorithm.Comment: 13 pages revtex, 6 figures, 2 table
Multimodal Interaction in a Haptic Environment
In this paper we investigate the introduction of haptics in a multimodal tutoring environment. In this environment a haptic device is used to control a virtual piece of sterile cotton and a virtual injection needle. Speech input and output is provided to interact with a virtual tutor, available as a talking head, and a virtual patient. We introduce the haptic tasks and how different agents in the multi-agent system are made responsible for them. Notes are provided about the way we introduce an affective model in the tutor agent
The Partial Averaging method
The partial averaging technique is defined and used in conjunction with the
random series implementation of the Feynman-Kac formula. It enjoys certain
properties such as good rates of convergence and convergence for potentials
with coulombic singularities. In this work, I introduce the reader to the
technique and I analyze the basic mathematical properties of the method. I show
that the method is convergent for all Kato-class potentials that have finite
Gaussian transform.Comment: 9 pages, no figures; one reference correcte
Morphological Image Analysis of Quantum Motion in Billiards
Morphological image analysis is applied to the time evolution of the
probability distribution of a quantum particle moving in two and
three-dimensional billiards. It is shown that the time-averaged Euler
characteristic of the probability density provides a well defined quantity to
distinguish between classically integrable and non-integrable billiards. In
three dimensions the time-averaged mean breadth of the probability density may
also be used for this purpose.Comment: Major revision. Changes include a more detailed discussion of the
theory and results for 3 dimensions. Now: 10 pages, 9 figures (some are
colored), 3 table
Beyond the poor man's implementation of unconditionally stable algorithms to solve the time-dependent Maxwell Equations
For the recently introduced algorithms to solve the time-dependent Maxwell
equations (see Phys.Rev.E Vol.64 p.066705 (2001)), we construct a variable grid
implementation and an improved spatial discretization implementation that
preserve the property of the algorithms to be unconditionally stable by
construction. We find that the performance and accuracy of the corresponding
algorithms are significant and illustrate their practical relevance by
simulating various physical model systems.Comment: 18 pages, 16 figure
Dynamics of Ordered Active Columns: Flows, Twists, and Waves
We formulate the hydrodynamics of active columnar phases, with
two-dimensional translational order in the plane perpendicular to the columns
and no elastic restoring force for relative sliding of the columns, using the
general formalism of an active model H. Our predictions include:
two-dimensional odd elasticity coming from three-dimensional plasmon-like
oscillations of the columns in chiral polar phases with a frequency that is
independent of wavenumber and non-analytic; a buckling instability coming from
the generic force-dipole active stress analogous to the mechanical
Helfrich-Hurault instability in passive materials; the selection of helical
column undulations by apolar chiral activity
Distribution of nearest distances between nodal points for the Berry function in two dimensions
According to Berry a wave-chaotic state may be viewed as a superposition of
monochromatic plane waves with random phases and amplitudes. Here we consider
the distribution of nodal points associated with this state. Using the property
that both the real and imaginary parts of the wave function are random Gaussian
fields we analyze the correlation function and densities of the nodal points.
Using two approaches (the Poisson and Bernoulli) we derive the distribution of
nearest neighbor separations. Furthermore the distribution functions for nodal
points with specific chirality are found. Comparison is made with results from
from numerical calculations for the Berry wave function.Comment: 11 pages, 7 figure
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