55,847 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
An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics
In plasma simulations, where the speed of light divided by a characteristic
length is at a much higher frequency than other relevant parameters in the
underlying system, such as the plasma frequency, implicit methods begin to play
an important role in generating efficient solutions in these multi-scale
problems. Under conditions of scale separation, one can rescale Maxwell's
equations in such a way as to give a magneto static limit known as the Darwin
approximation of electromagnetics. In this work, we present a new approach to
solve Maxwell's equations based on a Method of Lines Transpose (MOL)
formulation, combined with a fast summation method with computational
complexity , where is the number of grid points (particles).
Under appropriate scaling, we show that the proposed schemes result in
asymptotic preserving methods that can recover the Darwin limit of
electrodynamics
Chern-Simons Modified General Relativity
Chern-Simons modified gravity is an effective extension of general relativity
that captures leading-order, gravitational parity violation. Such an effective
theory is motivated by anomaly cancelation in particle physics and string
theory. In this review, we begin by providing a pedagogical derivation of the
three distinct ways such an extension arises: (1) in particle physics, (2) from
string theory and (3) geometrically. We then review many exact and approximate,
vacuum solutions of the modified theory, and discuss possible matter couplings.
Following this, we review the myriad astrophysical, solar system, gravitational
wave and cosmological probes that bound Chern-Simons modified gravity,
including discussions of cosmic baryon asymmetry and inflation. The review
closes with a discussion of possible future directions in which to test and
study gravitational parity violation.Comment: 104 pages, 2 figures, 186 references, Invited Review accepted for
publication in Phys. Repts. This version corrects a minor typo in Eq. (174)
of the published versio
Visco-potential free-surface flows and long wave modelling
In a recent study [DutykhDias2007] we presented a novel visco-potential free
surface flows formulation. The governing equations contain local and nonlocal
dissipative terms. From physical point of view, local dissipation terms come
from molecular viscosity but in practical computations, rather eddy viscosity
should be used. On the other hand, nonlocal dissipative term represents a
correction due to the presence of a bottom boundary layer. Using the standard
procedure of Boussinesq equations derivation, we come to nonlocal long wave
equations. In this article we analyse dispersion relation properties of
proposed models. The effect of nonlocal term on solitary and linear progressive
waves attenuation is investigated. Finally, we present some computations with
viscous Boussinesq equations solved by a Fourier type spectral method.Comment: 29 pages, 13 figures. Some figures were updated. Revised version for
European Journal of Mechanics B/Fluids. Other author's papers can be
downloaded from http://www.lama.univ-savoie.fr/~dutyk
Exact analytical solution of viscous Korteweg-deVries equation for water waves
The evolution of a solitary wave with very weak nonlinearity which was
originally investigated by Miles [4] is revisited. The solution for a
one-dimensional gravity wave in a water of uniform depth is considered. This
leads to finding the solution to a Korteweg-de Vries (KdV) equation in which
the nonlinear term is small. Also considered is the asymptotic solution of the
linearized KdV equation both analytically and numerically. As in Miles [4], the
asymptotic solution of the KdV equation for both linear and weakly nonlinear
case is found using the method of inversescattering theory. Additionally
investigated is the analytical solution of viscous-KdV equation which reveals
the formation of the Peregrine soliton that decays to the initial sech^2(\xi)
soliton and eventually growing back to a narrower and higher amplitude
bifurcated Peregrine-type soliton.Comment: 15 page
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