5,990 research outputs found
Self-force via Green functions and worldline integration
A compact object moving in curved spacetime interacts with its own
gravitational field. This leads to both dissipative and conservative
corrections to the motion, which can be interpreted as a self-force acting on
the object. The original formalism describing this self-force relied heavily on
the Green function of the linear differential operator that governs
gravitational perturbations. However, because the global calculation of Green
functions in non-trivial black hole spacetimes has been an open problem until
recently, alternative methods were established to calculate self-force effects
using sophisticated regularization techniques that avoid the computation of the
global Green function. We present a method for calculating the self-force that
employs the global Green function and is therefore closely modeled after the
original self-force expressions. Our quantitative method involves two stages:
(i) numerical approximation of the retarded Green function in the background
spacetime; (ii) evaluation of convolution integrals along the worldline of the
object. This novel approach can be used along arbitrary worldlines, including
those currently inaccessible to more established computational techniques.
Furthermore, it yields geometrical insight into the contributions to
self-interaction from curved geometry (back-scattering) and trapping of null
geodesics. We demonstrate the method on the motion of a scalar charge in
Schwarzschild spacetime. This toy model retains the physical history-dependence
of the self-force but avoids gauge issues and allows us to focus on basic
principles. We compute the self-field and self-force for many worldlines
including accelerated circular orbits, eccentric orbits at the separatrix, and
radial infall. This method, closely modeled after the original formalism,
provides a promising complementary approach to the self-force problem.Comment: 18 pages, 9 figure
Measurability of kinetic temperature from metal absorption-line spectra formed in chaotic media
We present a new method for recovering the kinetic temperature of the
intervening diffuse gas to an accuracy of 10%. The method is based on the
comparison of unsaturated absorption-line profiles of two species with
different atomic weights. The species are assumed to have the same temperature
and bulk motion within the absorbing region. The computational technique
involves the Fourier transform of the absorption profiles and the consequent
Entropy-Regularized chi^2-Minimization [ERM] to estimate the model parameters.
The procedure is tested using synthetic spectra of CII, SiII and FeII ions. The
comparison with the standard Voigt fitting analysis is performed and it is
shown that the Voigt deconvolution of the complex absorption-line profiles may
result in estimated temperatures which are not physical. We also successfully
analyze Keck telescope spectra of CII1334 and SiII1260 lines observed at the
redshift z = 3.572 toward the quasar Q1937--1009 by Tytler {\it et al.}.Comment: 25 pages, 6 Postscript figures, aaspp4.sty file, submit. Ap
Wavelets and their use
This review paper is intended to give a useful guide for those who want to
apply discrete wavelets in their practice. The notion of wavelets and their use
in practical computing and various applications are briefly described, but
rigorous proofs of mathematical statements are omitted, and the reader is just
referred to corresponding literature. The multiresolution analysis and fast
wavelet transform became a standard procedure for dealing with discrete
wavelets. The proper choice of a wavelet and use of nonstandard matrix
multiplication are often crucial for achievement of a goal. Analysis of various
functions with the help of wavelets allows to reveal fractal structures,
singularities etc. Wavelet transform of operator expressions helps solve some
equations. In practical applications one deals often with the discretized
functions, and the problem of stability of wavelet transform and corresponding
numerical algorithms becomes important. After discussing all these topics we
turn to practical applications of the wavelet machinery. They are so numerous
that we have to limit ourselves by some examples only. The authors would be
grateful for any comments which improve this review paper and move us closer to
the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh
A method for the estimation of p-mode parameters from averaged solar oscillation power spectra
A new fitting methodology is presented which is equally well suited for the
estimation of low-, medium-, and high-degree mode parameters from -averaged
solar oscillation power spectra of widely differing spectral resolution. This
method, which we call the "Windowed, MuLTiple-Peak, averaged spectrum", or
WMLTP Method, constructs a theoretical profile by convolving the weighted sum
of the profiles of the modes appearing in the fitting box with the power
spectrum of the window function of the observing run using weights from a
leakage matrix that takes into account both observational and physical effects,
such as the distortion of modes by solar latitudinal differential rotation. We
demonstrate that the WMLTP Method makes substantial improvements in the
inferences of the properties of the solar oscillations in comparison with a
previous method that employed a single profile to represent each spectral peak.
We also present an inversion for the internal solar structure which is based
upon 6,366 modes that we have computed using the WMLTP method on the 66-day
long 2010 SOHO/MDI Dynamics Run. To improve both the numerical stability and
reliability of the inversion we developed a new procedure for the
identification and correction of outliers in a frequency data set. We present
evidence for a pronounced departure of the sound speed in the outer half of the
solar convection zone and in the subsurface shear layer from the radial sound
speed profile contained in Model~S of Christensen-Dalsgaard and his
collaborators that existed in the rising phase of Solar Cycle~24 during
mid-2010
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