99,199 research outputs found
Some recent developments in quantization of fractal measures
We give an overview on the quantization problem for fractal measures,
including some related results and methods which have been developed in the
last decades. Based on the work of Graf and Luschgy, we propose a three-step
procedure to estimate the quantization errors. We survey some recent progress,
which makes use of this procedure, including the quantization for self-affine
measures, Markov-type measures on graph-directed fractals, and product measures
on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page
Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results
Various astronomical observations have been consistently making a strong case
for the existence of a component of dark energy with negative pressure in the
universe. It is now necessary to take the dark energy component(s) into account
in gravitational lensing statistics and other cosmological tests. By using the
comoving distance we derive analytic but simple expressions for the optical
depth of multiple image, the expected value of image separation and the
probability distribution of image separation caused by an assemble of singular
isothermal spheres in general FRW cosmological models with dark energy
component(s). We also present the kinematical and dynamical properties of these
kinds of cosmological models and calculate the age of the universe and the
distance measures, which are often used in classical cosmological tests. In
some cases we are able to give formulae that are simpler than those found
elsewhere in the literature, which could make the cosmological tests for dark
energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil
Numerical simulations of negative-index refraction in wedge-shaped metamaterials
A wedge-shaped structure made of split-ring resonators (SRR) and wires is
numerically simulated to evaluate its refraction behavior. Four frequency
bands, namely, the stop band, left-handed band, ultralow-index band, and
positive-index band, are distinguished according to the refracted field
distributions. Negative phase velocity inside the wedge is demonstrated in the
left-handed band and the Snell's law is conformed in terms of its refraction
behaviors in different frequency bands. Our results confirmed that negative
index of refraction indeed exists in such a composite metamaterial and also
provided a convincing support to the results of previous Snell's law
experiments.Comment: 18 pages, 6 figure
Gravitational Lensing Statistics as a Probe of Dark Energy
By using the comoving distance, we derive an analytic expression for the
optical depth of gravitational lensing, which depends on the redshift to the
source and the cosmological model characterized by the cosmic mass density
parameter , the dark energy density parameter and its
equation of state . It is shown that, the larger the
dark energy density is and the more negative its pressure is, the higher the
gravitational lensing probability is. This fact can provide an independent
constraint for dark energy.Comment: 9 pages, 2 figure
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