467 research outputs found
Mass transfer efficiency of a tall and low plate free area liquid pulsed sieve-plate extraction column
Acknowledgements The authors would like to acknowledge Chakwal group of industries for funding the project. Ms. Madiha, Ms. Zona, Mr. Sohaib, Mr. Abdullah, Mr. Mudassar, and Mr. Salahuddin also deserve our acknowledgements for their assistance in different ways.Peer reviewedPublisher PD
Extension of Bogoliubov theory to quasi-condensates
We present an extension of the well-known Bogoliubov theory to treat low
dimensional degenerate Bose gases in the limit of weak interactions and low
density fluctuations. We use a density-phase representation and show that a
precise definition of the phase operator requires a space discretisation in
cells of size . We perform a systematic expansion of the Hamiltonian in
terms of two small parameters, the relative density fluctuations inside a cell
and the phase change over a cell. The resulting macroscopic observables can be
computed in one, two and three dimensions with no ultraviolet or infrared
divergence. Furthermore this approach exactly matches Bogoliubov's approach
when there is a true condensate. We give the resulting expressions for the
equation of state of the gas, the ground state energy, the first order and
second order correlations functions of the field. Explicit calculations are
done for homogeneous systems.Comment: 32 pages, 2 figures; typos corrected in revised versio
Kinetic Theory of Collective Excitations and Damping in Bose-Einstein Condensed Gases
We calculate the frequencies and damping rates of the low-lying collective
modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex
nonlinear Schr\"odinger equation to determine the dynamics of the condensate
atoms, and couple it to a Boltzmann equation for the noncondensate atoms. In
this manner we take into account both collisions between
noncondensate-noncondensate and condensate-noncondensate atoms. We solve the
linear response of these equations, using a time-dependent gaussian trial
function for the condensate wave function and a truncated power expansion for
the deviation function of the thermal cloud. As a result, our calculation turns
out to be characterized by two dimensionless parameters proportional to the
noncondensate-noncondensate and condensate-noncondensate mean collision times.
We find in general quite good agreement with experiment, both for the
frequencies and damping of the collective modes.Comment: 10 pages, 8 figure
Exact calculation of the skyrmion lifetime in a ferromagnetic Bose condensate
The tunneling rate of a skyrmion in ferromagnetic spin-1/2 Bose condensates
through an off-centered potential barrier is calculated exactly with the
periodic instanton method. The prefactor is shown to depend on the chemical
potential of the core atoms, at which level the atom tunnels. Our results can
be readily extended to estimate the lifetime of other topological excitations
in the condensate, such as vortices and monopoles.Comment: 16 pages, 4 figures, to appear Phys. Rev.
Excitations of a Bose-Einstein condensate in a one-dimensional optical lattice
We investigate the low-lying excitations of a stack of weakly-coupled
two-dimensional Bose-Einstein condensates that is formed by a one-dimensional
optical lattice. In particular, we calculate the dispersion relations of the
monopole and quadrupole modes, both for the ground state as well as for the
case in which the system contains a vortex along the direction of the lasers
creating the optical lattice. Our variational approach enables us to determine
analytically the dispersion relations for an arbitrary number of atoms in every
two-dimensional condensate and for an arbitrary momentum. We also discuss the
feasibility of experimentally observing our results.Comment: 16 pages, 5 figures, minor changes,accepted for publication in Phys.
Rev.
Vortex lattice formation in a rotating Bose-Einstein condensate
We study the dynamics of vortex lattice formation of a rotating trapped
Bose-Einstein condensate by numerically solving the two-dimensional
Gross-Pitaevskii equation, and find that the condensate undergoes elliptic
deformation, followed by unstable surface-mode excitations before forming a
quantized vortex lattice. The origin of the peculiar surface-mode excitations
is identified to be phase fluctuations at the low-density surface regime. The
obtained dependence of a distortion parameter on time and that on the driving
frequency agree with the recent experiments by Madison {\it et al.} [Phys. Rev.
Lett. {\bf 86}, 4443 (2001)].Comment: 4 pages, 4 figure
Dynamics of a classical gas including dissipative and mean field effects
By means of a scaling ansatz, we investigate an approximated solution of the
Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive
the frequencies and the damping of the collective oscillations of a
harmonically trapped gas and we investigate its expansion after release of the
trap. The method is well suited to studying the collisional effects taking
place in the system and in particular to discussing the crossover between the
hydrodynamic and the collisionless regimes. An explicit link between the
relaxation times relevant for the damping of the collective oscillations and
for the expansion is established.Comment: 4 pages, 1 figur
Evaluation of retinal nerve fibre layer thickness as a possible measure of diabetic retinal neurodegeneration in the EPIC-Norfolk Eye Study
Background/aims: Markers to clinically evaluate structural changes from diabetic retinal neurodegeneration (DRN) have not yet been established. To study the potential role of peripapillary retinal nerve fibre layer (pRNFL) thickness as a marker for DRN, we evaluated the relationship between diabetes, as well as glycaemic control irrespective of diabetes status and pRNFL thickness.
Methods: Leveraging data from a population-based cohort, we used general linear mixed models (GLMMs) with a random intercept for patient and eye to assess the association between pRNFL thickness (measured using GDx) and demographic, systemic and ocular parameters after adjusting for typical scan score. GLMMs were also used to determine: (1) the relationship between: (A) glycated haemoglobin (HbA1c) irrespective of diabetes diagnosis and pRNFL thickness, (B) diabetes and pRNFL thickness and (2) which quadrants of pRNFL may be affected in participants with diabetes and in relation to HbA1c.
Results: 7076 participants were included. After controlling for covariates, inferior pRNFL thickness was 0.94 ”m lower (95% CI â1.28 ”m to â0.60 ”m), superior pRNFL thickness was 0.83 ”m lower (95% CI â1.17 ”m to â0.49 ”m) and temporal pRNFL thickness was 1.33 ”m higher (95% CI 0.99 ”m to 1.67 ”m) per unit increase in HbA1c. Nasal pRNFL thickness was not significantly associated with HbA1c (p=0.23). Similar trends were noted when diabetes was used as the predictor.
Conclusion: Superior and inferior pRNFL was significantly thinner among those with higher HbA1c levels and/or diabetes, representing areas of the pRNFL that may be most affected by diabetes
Axisymmetric versus Non-axisymmetric Vortices in Spinor Bose-Einstein Condensates
The structure and stability of various vortices in F=1 spinor Bose-Einstein
condensates are investigated by solving the extended Gross-Pitaevskii equation
under rotation. We perform an extensive search for stable vortices, considering
both axisymmetric and non-axisymmetric vortices and covering a wide range of
ferromagnetic and antiferromagnetic interactions. The topological defect called
Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for ferromagnetic
case. The phase diagram is established in a plane of external rotation Omega vs
total magnetization M by comparing the free energies of possible vortices. It
is shown that there are qualitative differences between axisymmetric and
non-axisymmetric vortices which are manifested in the Omega- and M-dependences.Comment: 9 pages, 9 figure
The transverse breathing mode of an elongated Bose-Einstein condensate
We study experimentally the transverse monopole mode of an elongated rubidium
condensate. Due to the scaling invariance of the non-linear Schr\"odinger
(Gross-Pitaevski) equation, the oscillation is monochromatic and sinusoidal at
short times, even under strong excitation. For ultra-low temperatures, the
quality factor can exceed 2000, where and
are the mode angular frequency and damping rate. This value is much
larger than any previously reported for other eigenmodes of a condensate. We
also present the temperature variation of and .Comment: 4 pages, 4 figures, submitted to PR
- âŠ