6,938 research outputs found
Energy Spectrum Evolution of a Diffuse Field in Elastic Body Caused by Weak Nonlinearity
We study the evolution of diffuse elastodynamic spectral energy density under
the influence of weak nonlinearity. It is shown that the rate of change of this
quantity is given by a convolution of the linear energy at two frequencies.
Quantitative estimates are given for sample aluminum and fused silica blocks of
experimental interest.Comment: 9 pages, 3 figures; revised for better presentatio
Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of
The recursion and path-integral methods are applied to analytically study the
electronic structure of a neutral molecule. We employ a tight-binding
Hamiltonian which considers both the and valence electrons of carbon.
From the recursion method, we obtain closed-form {\it analytic} expressions for
the and eigenvalues and eigenfunctions, including the highest
occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital
(LUMO) states, and the Green's functions. We also present the local densities
of states around several ring clusters, which can be probed experimentally by
using, for instance, a scanning tunneling microscope. {}From a path-integral
method, identical results for the energy spectrum are also derived. In
addition, the local density of states on one carbon atom is obtained; from this
we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques
Gaussian random waves in elastic media
Similar to the Berry conjecture of quantum chaos we consider elastic analogue
which incorporates longitudinal and transverse elastic displacements with
corresponding wave vectors. Based on that we derive the correlation functions
for amplitudes and intensities of elastic displacements. Comparison to numerics
in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure
Continuous symmetry of C60 fullerene and its derivatives
Conventionally, the Ih symmetry of fullerene C60 is accepted which is
supported by numerous calculations. However, this conclusion results from the
consideration of the molecule electron system, of its odd electrons in
particular, in a close-shell approximation without taking the electron spin
into account. Passing to the open-shell approximation has lead to both the
energy and the symmetry lowering up to Ci. Seemingly contradicting to a
high-symmetry pattern of experimental recording, particularly concerning the
molecule electronic spectra, the finding is considered in the current paper
from the continuous symmetry viewpoint. Exploiting both continuous symmetry
measure and continuous symmetry content, was shown that formal Ci symmetry of
the molecule is by 99.99% Ih. A similar continuous symmetry analysis of the
fullerene monoderivatives gives a reasonable explanation of a large variety of
their optical spectra patterns within the framework of the same C1 formal
symmetry exhibiting a strong stability of the C60 skeleton.Comment: 11 pages. 5 figures. 6 table
Nonlinear collective nuclear motion
For each real number a Lie algebra of nonlinear vector fields on
three dimensional Euclidean space is reported. Although each algebra is
mathematically isomorphic to , only the vector
fields correspond to the usual generators of the general linear group. The
vector fields integrate to a nonstandard action of the general
linear group; the case integrates to a local Lie semigroup. For
each , a family of surfaces is identified that is invariant with
respect to the group or semigroup action. For positive the surfaces
describe fissioning nuclei with a neck, while negative surfaces
correspond to exotic bubble nuclei. Collective models for neck and bubble
nuclei are given by irreducible unitary representations of a fifteen
dimensional semidirect sum spectrum generating algebra spanned by its
nonlinear subalgebra plus an abelian nonlinear inertia tensor
subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request
Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on
A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the
singularity in generic gravitational collapse is locally oscillatory is tested
numerically in vacuum, U(1) symmetric cosmological spacetimes on . If the velocity term dominated (VTD) solution to Einstein's equations is
substituted into the Hamiltonian for the full Einstein evolution equations, one
term is found to grow exponentially. This generates a prediction that
oscillatory behavior involving this term and another (which the VTD solution
causes to decay exponentially) should be observed in the approach to the
singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution
versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to
ftp://vela.acs.oakland.edu/pub/berger/u1genfig
Liquid racism and the Danish Prophet Muhammad cartoons
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2010 The Author.This article examines reactions to the October 2005 publication of the Prophet Muhammad cartoons in the Danish newspaper Jyllands-Posten. It does so by using the concept of âliquid racismâ. While the controversy arose because it is considered blasphemous by many Muslims to create images of the Prophet Muhammad, the article argues that the meaning of the cartoons is multidimensional, that their analysis is significantly more complex than most commentators acknowledge, and that this complexity can best be addressed via the concept of liquid racism. The article examines the liquidity of the cartoons in relation to four readings. These see the cartoons as: (1) a criticism of Islamic fundamentalism; (2) blasphemous images; (3) Islamophobic and racist; and (4) satire and a defence of freedom of speech. Finally, the relationship between postmodernity and the rise of fundamentalism is discussed because the cartoons, reactions to them, and Islamic fundamentalism, all contain an important postmodern dimension.ESR
New Studies of the Pulsar Wind Nebula in the Supernova Remnant CTB 80
We investigated the kinematics of the pulsar wind nebula (PWN) associated
with PSR B1951+32 in the old supernova remnant CTB 80 using the Fabry-Perot
interferometer of the 6m Special Astrophysical Observatory telescope. In
addition to the previously known expansion of the system of bright filaments
with a velocity of 100-200km/s, we detected weak high-velocity features in the
H-alpha line at least up to velocities of 400-450km/s. We analyzed the
morphology of the PWN in the H-alpha, [SII], and [OIII] lines using HST data
and discuss its nature. The shape of the central filamentary shell, which is
determined by the emission in the [OIII] line and in the radio continuum, is
shown to be consistent with the bow-shock model for a significant (about 60
degrees) inclination of the pulsar's velocity vector to the plane of the sky.
In this case, the space velocity of the pulsar is twice higher than its
tangential velocity, i.e., it reaches ~500 km/s, and PSR B1951+32 is the first
pulsar whose line-of-sight velocity (of about 400 km/s) has been estimated from
the PWN observations. The shell-like H-alpha-structures outside the bow shock
front in the east and the west may be associated with both the pulsar's jets
and the pulsar-wind breakthrough due to the layered structure of the extended
CTB 80 shell.Comment: to appear in Astronomy Letters, 12 pages, 6 postscript figures, two
in colour; for a version with high resolution figures see
http://www.sao.ru/hq/grb/team/vkom/CTB80_fine.pd
Numerical Approaches to Spacetime Singularities
This Living Review updates a previous version which its itself an update of a
review article. Numerical exploration of the properties of singularities could,
in principle, yield detailed understanding of their nature in physically
realistic cases. Examples of numerical investigations into the formation of
naked singularities, critical behavior in collapse, passage through the Cauchy
horizon, chaos of the Mixmaster singularity, and singularities in spatially
inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev.
Relativity 2002-1 at www.livingreviews.or
Non-exponential Dissipation in a Lossy Elastodynamic Billiard, Comparison with Porter-Thomas and Random Matrix Predictions
We study the dissipation of diffuse ultrasonic energy in a reverberant body
coupled to a waveguide, an analog for a mesoscopic electron in a quantum dot. A
simple model predicts a Porter-Thomas like distribution of level widths and
corresponding nonexponential dissipation, a behavior largely confirmed by
measurements. For the case of fully open channels, however, measurements
deviate from this model to a statistically significant degree. A random matrix
supersymmetric calculation is found to accurately model the observed behaviors
at all coupling strengths.Comment: 4 pages, 8 figures, figures resized, misprints correcte
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