Generating vortex rings in Bose-Einstein condensates in the line-source approximation

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the rotational of the superfluid velocity field is different from zero only on a circumference of given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.Comment: Accepted for publication in Phys. Rev.

Matter wave solitons at finite temperatures

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and $N$-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature.Comment: 6 pages, 2 figures, submitted to the Proceedings of QFS '0

1D model for the dynamics and expansion of elongated Bose-Einstein condensates

We present a 1D effective model for the evolution of a cigar-shaped Bose-Einstein condensate in time dependent potentials whose radial component is harmonic. We apply this model to investigate the dynamics and expansion of condensates in 1D optical lattices, by comparing our predictions with recent experimental data and theoretical results. We also discuss negative-mass effects which could be probed during the expansion of a condensate moving in an optical lattice.Comment: RevTeX4, 8 pages, 10 figures, extended and revised versio

Scalar Solitons on the Fuzzy Sphere

We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. These solutions are rotationally symmetric about an axis and have no allowed deformations. Solitons that describe multiple lumps on the fuzzy sphere can also be constructed but they are not stable.Comment: 24 pages, 2 figures, typo corrected and stylistic changes. v3: reference adde

Titanium alloy microstructure fingerprint plots from in-process machining

Titanium alloy components require several machining stages of forged billets which are supplied in a range of annealing conditions. Generally, the machining performance is influenced by the heat treatment and changes in billet microstructures are often overlooked by tool manufacturers and machinists. Due to the non-linear strain path during primary forging, titanium alloy billets are anisotropic in nature and require ex-situ non-destructive evaluation (NDE) during the manufacturing stages to ensure excellent service performance, particularly in safety-critical aerospace components. In this study, the local analysis of the fluctuations presented in the force response during face-turning operations is directly linked to the billet heat treatment condition and presented as microstructure fingerprint plots. The evolution of cutting forces in four different billet conditions of the alpha + beta titanium alloy Ti–6Al–2Sn–4Zr–6Mo (Ti-6246) was measured. The magnitude and fluctuations in force were directly correlated to microstructural features derived from the heat treatments. In addition, local spatial high-resolution synchronization of the cutting forces was used to determine the effects of microstructure from the heterogeneous upstream forging process and subsequent heat treatment. These rapidly produced microstructure fingerprint plots are an important development step for providing manufacturers with an in-process machining NDE method: this will help to qualify material upstream prior to expensive secondary forging or finish machining stages

Tool for automatic macrozone characterization from EBSD data sets of titanium alloys

Microtexture heterogeneities are commonly found in titanium forgings because of the thermomechanical processing. Also known as macrozones, these regions can reach millimetres in length, with grains sharing a similar crystallographic orientation leading to less resistance to crack propagation. Since the link between macrozones and the reduction of cold-dwell-fatigue performance on rotative components in gas turbine engines was established, efforts have been put into macrozone definition and characterization. The electron backscatter diffraction (EBSD) technique, widely used for texture analysis, allows for a qualitative macrozone characterization; however, further processing is required to define the boundaries and disorientation spread of each macrozone. Current approaches often use c-axis misorientation criteria, but this can sometimes lead to a large disorientation spread within a macrozone. This article describes the development and application of a computational tool implemented in MATLAB for automatic macrozone identification from EBSD data sets on the basis of a more conservative approach where both the c-axis tilting and rotation are considered. The tool allows for detection of macrozones according to the disorientation angle and density-fraction criteria. The clustering efficiency is validated by pole-figure plots, and the effects of the key parameters defining the macrozone clustering (disorientation and fraction) are discussed. In addition, this tool was successfully applied to both fully equiaxed and bimodal microstructures of titanium forgings

Solitons, solitonic vortices, and vortex rings in a confined Bose-Einstein condensate

Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional solitary waves such as axisymmetric vortex rings and non-axisymmetric solitonic vortices. We calculate the profiles of the above structures and examine their dependence on the velocity of propagation along a cylindrical trap. At sufficiently high velocity, both the vortex ring and the solitonic vortex transform into an axisymmetric soliton. We also calculate the energy-momentum dispersions and show that a Lieb-type mode appears in the excitation spectrum for all particle densities.Comment: RevTeX 9 pages, 9 figure

The effect of forging texture and machining parameters on the fatigue performance of titanium alloy disc components

The Mechanisms of fatigue failure in Ti-6Al-2Sn-4Zr-6Mo forged discs are investigated: the effects of forging and machining operations on fatigue are decoupled. A four-point bend fatigue testing approach enabled the crack initiation and propagation characteristics to be studied at multiple locations around the disc periphery. Fatigue performance variation (of ~60%) at different positions, and crack initiation and propagation behaviour were linked to the heterogeneous crystallographic texture - developed during upstream forging. Downstream machining processes were found to increase fatigue life, regardless of the cutting speed. However, circumferential fatigue heterogeneity, inherent from the forging stage was still evident even after machining

Bogoliubov sound speed in periodically modulated Bose-Einstein condensates

We study the Bogoliubov excitations of a Bose-condensed gas in an optical lattice. Of primary interest is the long wavelength phonon dispersion for both current-free and current-carrying condensates. We obtain the dispersion relation by carrying out a systematic expansion of the Bogoliubov equations in powers of the phonon wave vector. Our result for the current-carrying case agrees with the one recently obtained by means of a hydrodynamic theory.Comment: 16 pages, no figure

Nonlinear waves in a cylindrical Bose-Einstein condensate

We present a complete calculation of solitary waves propagating in a steady state with constant velocity v along a cigar-shaped Bose-Einstein trap approximated as infinitely-long cylindrical. For sufficiently weak couplings (densities) the main features of the calculated solitons could be captured by effective one-dimensional (1D) models. However, for stronger couplings of practical interest, the relevant solitary waves are found to be hybrids of quasi-1D solitons and 3D vortex rings. An interesting hierarchy of vortex rings occurs as the effective coupling constant is increased through a sequence of critical values. The energy-momentum dispersion of the above structures is shown to exhibit characteristics similar to a mode proposed sometime ago by Lieb within a strictly 1D model, as well as some rotonlike features.Comment: 10 pages, 12 figure