Vortex in a relativistic perfect isentropic fluid and Nambu Goto dynamics

By a weak deformation of the cylindrical symmetry of the potential vortex in a relativistic perfect isentropic fluid, we study the possible dynamics of the central line of this vortex. In "stiff" material the Nanbu-Goto equations are obtainedComment: 11 pages, Accepted for publication in Physical Review

Cosmological Evolution of Global Monopoles

We investigate the cosmological evolution of global monopoles in the radiation dominated (RD) and matter dominated (MD) universes by numerically solving field equations of scalar fields. It is shown that the global monopole network relaxes into the scaling regime, unlike the gauge monopole network. The number density of global monopoles is given by $n(t) \simeq (0.43\pm0.07) / t^{3}$ during the RD era and $n(t) \simeq (0.25\pm0.05) / t^{3}$ during the MD era. Thus, we have confirmed that density fluctuations produced by global monopoles become scale invariant and are given by $\delta \rho \sim 7.2(5.0) \sigma^{2} / t^{2}$ during the RD (MD) era, where $\sigma$ is the breaking scale of the symmetry.Comment: 6 pages, 2 figures, to appear in Phys. Rev. D (R

Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud \ud \ud We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions

The development of a short measure of physical function for knee OA KOOS-Physical Function Shortform (KOOS-PS) – an OARSI/OMERACT initiative

SummaryObjectiveTo develop a short measure of physical function for knee osteoarthritis (OA) using multi-national data from individuals with varying degrees of severity of knee OA.MethodsRasch analysis, based on the partial credit model, was conducted on Knee injury and Osteoarthritis Outcome Score and Western Ontario McMaster Universities' Osteoarthritis Index data from individuals with knee OA, ranging from community to pre-total knee replacement samples from five countries. Fit of the data to the Rasch model was evaluated by overall model fit and item-level fit statistics (χ2, size of residual, F-test). Invariance across age, gender and country was evaluated. Unidimensionality was evaluated by factor analysis of residuals. The derived short measure was further tested for fit through re-analyses in individual sub-samples. A nomogram converting raw summed scores to Rasch-derived interval scores was developed.ResultsThirteen data sets were included (n=2145), with an age range of 26–95 years, and a male/female ratio of 1:1.4. The final model included seven of the original 22 items. From easiest to most difficult, the items (logit) were as follows: rising from bed (1.366), putting on socks/stockings (1.109), rising from sitting (0.537), bending to the floor (0.433), twisting/pivoting on injured knee (−0.861), kneeling (−1.292) and squatting (−1.292). Sub-sample analyses confirmed findings.ConclusionBased on the use of accepted Rasch-based measurement methods and the compliment of countries, languages and OA severity represented in this study, our seven item short measure of physical function for knee OA is likely generalizable and widely applicable. This measure has potential for use as the function component in an OA severity scoring system

Vortex phase diagram in trapped Bose-Einstein condensation

The vortex phase diagram in the external rotation frequency versus temperature is calculated for dilute Bose-Einstein condensed gases. It is determined within the Bogoliubov-Popov theory for a finite temperature where the condensate and non-condensate fractions are treated in an equal footing. The temperature dependences of various thermodynamic instability lines for the vortex nucleation are computed to construct the phase diagram. Experiments are proposed to resolve a recent controversy on the vortex creation problem associated with the quantized vortex observation in $^{87}$Rb atom gases.Comment: 11 pages, 8 figure

Collisional-inhomogeneity-induced generation of matter-wave dark solitons

We propose an experimentally relevant protocol for the controlled generation of matter-wave dark solitons in atomic Bose-Einstein condensates (BECs). In particular, using direct numerical simulations, we show that by switching-on a spatially inhomogeneous (step-like) change of the s-wave scattering length, it is possible to generate a controllable number of dark solitons in a quasi-one-dimensional BEC. A similar phenomenology is also found in the two-dimensional setting of "disk-shaped" BECs but, as the solitons are subject to the snaking instability, they decay into vortex structures. A detailed investigation of how the parameters involved affect the emergence and evolution of solitons and vortices is provided.Comment: 8 pages, 5 Figures, Physics Letters A (in press

From Feshbach-Resonance Managed Bose-Einstein Condensates to Anisotropic Universes: Some Applications of the Ermakov-Pinney equation with Time-Dependent Nonlinearity

In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to ``engineer'' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies.Comment: 9 pages, 4 figure

Laser Cooling of Trapped Fermi Gases deeply below the Fermi Temperature

We study the collective Raman cooling of a polarized trapped Fermi gas in the Festina Lente regime, when the heating effects associated with photon reabsorptions are suppressed. We predict that by adjusting the spontaneous Raman emission rates and using appropriately designed anharmonic traps, temperatures of the order of 2.7% of the Fermi temperature can be achieved in 3D.Comment: 4 pages, 3 figures; final versio

Dilatonic current-carrying cosmic strings

We investigate the nature of ordinary cosmic vortices in some scalar-tensor extensions of gravity. We find solutions for which the dilaton field condenses inside the vortex core. These solutions can be interpreted as raising the degeneracy between the eigenvalues of the effective stress-energy tensor, namely the energy per unit length U and the tension T, by picking a privileged spacelike or timelike coordinate direction; in the latter case, a phase frequency threshold occurs that is similar to what is found in ordinary neutral current-carrying cosmic strings. We find that the dilaton contribution for the equation of state, once averaged along the string worldsheet, vanishes, leading to an effective Nambu-Goto behavior of such a string network in cosmology, i.e. on very large scales. It is found also that on small scales, the energy per unit length and tension depend on the string internal coordinates in such a way as to permit the existence of centrifugally supported equilibrium configuration, also known as vortons, whose stability, depending on the very short distance (unknown) physics, can lead to catastrophic consequences on the evolution of the Universe.Comment: 10 pages, ReVTeX, 2 figures, minor typos corrected. This version to appear in Phys. Rev.

The kk-essence scalar field in the context of Supernova Ia Observations

A $k$-essence scalar field model having (non canonical) Lagrangian of the form $L=-V(\phi)F(X)$ where $X=1/2g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ with constant $V(\phi)$ is shown to be consistent with luminosity distance-redshift data observed for type Ia Supernova. For constant $V(\phi)$, $F(X)$ satisfies a scaling relation which is used to set up a differential equation involving the Hubble parameter $H$, the scale factor $a$ and the $k$-essence field $\phi$. $H$ and $a$ are extracted from SNe Ia data and using the differential equation the time dependence of the field $\phi$ is found to be: $\phi(t) \sim \lambda_0 + \lambda_1 t + \lambda_2 t^2$. The constants $\lambda_i$ have been determined. The time dependence is similar to that of the quintessence scalar field (having canonical kinetic energy) responsible for homogeneous inflation. Furthermore, the scaling relation and the obtained time dependence of the field $\phi$ is used to determine the $X$-dependence of the function $F(X)$.Comment: 8 pages, 5 figures, Late