20,349 research outputs found
Quantum Numbers for Excitations of Bose-Einstein Condensates in 1D Optical Lattices
The excitation spectrum and the band structure of a Bose-Einstein condensate
in a periodic potential are investigated. Analyses within full 3D systems,
finite 1D systems, and ideal periodic 1D systems are compared. We find two
branches of excitations in the spectra of the finite 1D model. The band
structures for the first and (part of) the second band are compared between a
finite 1D and the fully periodic 1D systems, utilizing a new definition of a
effective wavenumber and a phase-slip number. The upper and lower edges of the
first gap coincide well between the two cases. The remaining difference is
explained by the existence of the two branches due to the finite-size effect.Comment: 5 pages, 9 figure
Radio Afterglows of Gamma-Ray Bursts and Hypernovae at High Redshift, and their Potential for 21-cm Absorption Studies
We investigate the radio afterglows of gamma-ray bursts (GRBs) and hypernovae
(HNe) at high redshifts and quantify their detectability, as well as their
potential usefulness for 21 cm absorption line studies of the intergalactic
medium (IGM) and intervening structures. We examine several sets of source and
environment model parameters that are physically plausible at high redshifts.
The radio afterglows of GRBs would be detectable out to z ~ 30, while the
energetic HNe could be detectable out to z ~ 20 even by the current Very Large
Array (VLA). We find that the 21 cm absorption line due to the diffuse neutral
IGM is difficult to detect even by the proposed Square Kilometer Array (SKA),
except for highly energetic sources. We also find that the 21 cm line due to
collapsed gas clouds with high optical depth may be detected on rare occasions.Comment: 36 pages, 12 figures, 1 table, accepted for publication in Ap
A λ = 1.3 Millimeter Aperture Synthesis Molecular Line Survey of Orion Kleinmann-Low
We present a 1".3 spatial resolution interferometric spectral line survey of the core of the Orion molecular cloud, obtained with the OVRO millimeter array. Covering 4 GHz bandwidth in total, the survey contains ~100 emission lines from 18 chemical species. The spatial distributions of a number of molecules point to source I near the IRc2 complex as the dominant energy source in the region but do not rule out the presence of additional lower luminosity objects. At arcsecond resolution, the offsets between dust emission and various molecular tracers suggest that the spectacular "hot core" emission in the Orion core arises via the heating and ablation of material from the surfaces of very high density clumps located ≳500 AU from source I and traced by the dust emission. We find no evidence for a strong internal heating source within the hot core condensation(s)
A Co-moving Coordinate System for Relativistic Hydrodynamics
The equations of relativistic hydrodynamics are transformed so that steps
forward in time preserves local simultaneity. In these variables, the
space-time coordinates of neighboring points on the mesh are simultaneous
according to co-moving observers. Aside from the time step varying as a
function of the location on the mesh, the local velocity gradient and the local
density then evolve according to non-relativistic equations of motion. Analytic
solutions are found for two one-dimensional cases with constant speed of sound.
One solution has a Gaussian density profile when mapped into the new
coordinates. That solution is analyzed for the effects of longitudinal
acceleration in relativistic heavy ion collisions at RHIC, especially in
regards to two-particle correlation measurements of the longitudinal size
The Hubbard model on a complete graph: Exact Analytical results
We derive the analytical expression of the ground state of the Hubbard model
with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation
The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case () as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004
Saddles in the energy landscape: extensivity and thermodynamic formalism
We formally extend the energy landscape approach for the thermodynamics of
liquids to account for saddle points. By considering the extensive nature of
macroscopic potential energies, we derive the scaling behavior of saddles with
system size, as well as several approximations for the properties of low-order
saddles (i.e., those with only a few unstable directions). We then cast the
canonical partition function in a saddle-explicit form and develop, for the
first time, a rigorous energy landscape approach capable of reproducing trends
observed in simulations, in particular the temperature dependence of the energy
and fractional order of sampled saddles.Comment: 4 pages, 1 figur
Recommended from our members
Can hypnotic suggestibility be measured online?
Hypnosis and hypnotic suggestions are gradually gaining popularity within the consciousness community as established tools for the experimental manipulation of illusions of involuntariness, hallucinations and delusions. However, hypnosis is still far from being a widespread instrument; a crucial hindrance to taking it up is the amount of time needed to invest in identifying people high and low in responsiveness to suggestion. In this study, we introduced an online assessment of hypnotic response and estimated the extent to which the scores and psychometric properties of an online screening differ from an offline one. We propose that the online screening of hypnotic response is viable as it reduces the level of responsiveness only by a slight extent. The application of online screening may prompt researchers to run large-scale studies with more heterogeneous samples, which would help researchers to overcome some of the issues underlying the current replication crisis in psychology
Cross-Correlation Studies between CMB Temperature Anisotropies and 21 cm Fluctuations
During the transition from a neutral to a fully reionized universe,
scattering of cosmic microwave background (CMB) photons via free-electrons
leads to a new anisotropy contribution to the temperature distribution. If the
reionization process is inhomogeneous and patchy, the era of reionization is
also visible via brightness temperature fluctuations in the redshifted 21 cm
line emission from neutral Hydrogen. Since regions containing electrons and
neutral Hydrogen are expected to trace the same underlying density field, the
two are (anti) correlated and this is expected to be reflected in the
anisotropy maps via a correlation between arcminute-scale CMB temperature and
the 21 cm background. In terms of the angular cross-power spectrum,
unfortunately, this correlation is insignificant due to a geometric
cancellation associated with second order CMB anisotropies. The same
cross-correlation between ionized and neutral regions, however, can be studied
using a bispectrum involving large scale velocity field of ionized regions from
the Doppler effect, arcminute scale CMB anisotropies during reionization, and
the 21 cm background. While the geometric cancellation is partly avoided, the
signal-to-noise ratio related to this bispectrum is reduced due to the large
cosmic variance related to velocity fluctuations traced by the Doppler effect.
Unless the velocity field during reionization can be independently established,
it is unlikely that the correlation information related to the relative
distribution of ionized electrons and regions containing neutral Hydrogen can
be obtained with a combined study involving CMB and 21 cm fluctuations.Comment: 10 pages, 3 figure
Thermophoresis of Brownian particles driven by coloured noise
The Brownian motion of microscopic particles is driven by the collisions with
the molecules of the surrounding fluid. The noise associated with these
collisions is not white, but coloured due, e.g., to the presence of
hydrodynamic memory. The noise characteristic time scale is typically of the
same order as the time over which the particle's kinetic energy is lost due to
friction (inertial time scale). We demonstrate theoretically that, in the
presence of a temperature gradient, the interplay between these two
characteristic time scales can have measurable consequences on the particle
long-time behaviour. Using homogenization theory, we analyse the infinitesimal
generator of the stochastic differential equation describing the system in the
limit where the two characteristic times are taken to zero; from this
generator, we derive the thermophoretic transport coefficient, which, we find,
can vary in both magnitude and sign, as observed in experiments. Furthermore,
studying the long-term stationary particle distribution, we show that particles
can accumulate towards the colder (positive thermophoresis) or the warmer
(negative thermophoresis) regions depending on the dependence of their physical
parameters and, in particular, their mobility on the temperature.Comment: 9 pages, 4 figure
- …