51,025 research outputs found
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
High-frequency Light Reflector via Low-frequency Light Control
We show that the momentum of light can be reversed via the atomic coherence
created by another light with one or two orders of magnitude lower frequency.
Both the backward retrieval of single photons from a timed Dicke state and the
reflection of continuous waves by high-order photonic band gaps are analysed.
The required control field strength scales linearly with the nonlinearity
order, which is explained by the dynamics of superradiance lattices.
Experiments are proposed with Rb atoms and Be ions. This holds
promise for light-controllable X-ray reflectors.Comment: 5 pages, 5 figure
Robustness of predator-prey models for confinement regime transitions in fusion plasmas
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as ārobustnessā for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas
Analysis of some localized boundary-domain integral equations for transmission problems with variable coefficients
This is the post-print version of the Article. The official published version can be found at the links below - Copyright @ 2011 BirkhƤuser Boston.Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.This research was supported by the EPSRC grant EP/H020497/1: āMathematical analysis of Localized Boundary-Domain Integral
Equations for Variable-Coefficient Boundary Value Problemsā and partly by the Georgian Technical University grant in the case of the third author
Superradiance Lattice
We show that the timed Dicke states of a collection of three-level atoms can
form a tight-binding lattice in momentum space. This lattice, coined the
superradiance lattice (SL), can be constructed based on electromagnetically
induced transparency (EIT). For a one-dimensional SL, we need the coupling
field of the EIT system to be a standing wave. The detuning between the two
components of the standing wave introduces an effective uniform force in
momentum space. The quantum lattice dynamics, such as Bloch oscillations,
Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be
observed in the SL. The two-dimensional SL provides a flexible platform for
Dirac physics in graphene. The SL can be extended to three and higher
dimensions where no analogous real space lattices exist with new physics
waiting to be explored.Comment: 6pages, 4 figure
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