Stability of a vortex in a small trapped Bose-Einstein condensate

A second-order expansion of the Gross-Pitaevskii equation in the interaction parameter determines the thermodynamic critical angular velocity Omega_c for the creation of a vortex in a small axisymmetric condensate. Similarly, a second-order expansion of the Bogoliubov equations determines the (negative) frequency omega_a of the anomalous mode. Although Omega_c = -omega_a through first order, the second-order contributions ensure that the absolute value |omega_a| is always smaller than the critical angular velocity Omega_c. With increasing external rotation Omega, the dynamical instability of the condensate with a vortex disappears at Omega*=|omega_a|, whereas the vortex state becomes energetically stable at the larger value Omega_c. Both second-order contributions depend explicitly on the axial anisotropy of the trap. The appearance of a local minimum of the free energy for a vortex at the center determines the metastable angular velocity Omega_m. A variational calculation yields Omega_m=|\omega_a| to first order (hence Omega_m also coincides with the critical angular velocity Omega_c to this order). Qualitatively, the scenario for the onset of stability in the weak-coupling limit is the same as that found in the strong-coupling (Thomas-Fermi) limit.Comment: 8 pages, RevTe

Design approaches in technology enhanced learning

Design is a critical to the successful development of any interactive learning environment (ILE). Moreover, in technology enhanced learning (TEL), the design process requires input from many diverse areas of expertise. As such, anyone undertaking tool development is required to directly address the design challenge from multiple perspectives. We provide a motivation and rationale for design approaches for learning technologies that draws upon Simon's seminal proposition of Design Science (Simon, 1969). We then review the application of Design Experiments (Brown, 1992) and Design Patterns (Alexander et al., 1977) and argue that a patterns approach has the potential to address many of the critical challenges faced by learning technologists

Stability of rotating states in a weakly-interacting Bose-Einstein condensate

We investigate the lowest state of a rotating, weakly-interacting Bose-Einstein condensate trapped in a harmonic confining potential that is driven by an infinitesimally asymmetric perturbation. Although in an axially-symmetric confining potential the gas has an axially-symmetric single-particle density distribution, we show that in the presence of the small asymmetric perturbation its lowest state is the one given by the mean-field approximation, which is a broken-symmetric state. We also estimate the rate of relaxation of angular momentum when the gas is no longer driven by the asymmetric perturbation and identify two regimes of "slow" and "fast" relaxation. States of certain symmetry are found to be more robust.Comment: 6 pages, RevTe

Is a Trapped One-Dimensional Bose Gas a Luttinger Liquid?

The low-energy fluctuations of a trapped, interacting quasi one-dimensional Bose gas are studied. Our considerations apply to experiments with highly anisotropic traps. We show that under suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically preventing Bose-Einstein condensation. At significantly lower temperatures a finite size gap destroys the Luttinger liquid picture and Bose-Einstein condensation is again possible.Comment: 4 pages (revtex), 1 figure (eps file

Rapidly Rotating Fermions in an Anisotropic Trap

We consider a cold gas of non-interacting fermions in a two dimensional harmonic trap with two different trapping frequencies $\omega_x \leq \omega_y$, and discuss the effect of rotation on the density profile. Depending on the rotation frequency $\Omega$ and the trap anisotropy $\omega_y/\omega_x$, the density profile assumes two qualitatively different shapes. For small anisotropy ($\omega_y/\omega_x \ll \sqrt{1+4 \Omega^2/\omega_x^2}$), the density consists of elliptical plateaus of constant density, corresponding to Landau levels and is well described by a two dimensional local density approximation. For large anisotropy ($\omega_y/\omega_x \gg \sqrt{1+4 \Omega^2/\omega_x^2}$), the density profile is Gaussian in the strong confining direction and semicircular with prominent Friedel oscillations in the weak direction. In this regime, a one dimensional local density approximation is well suited to describe the system. The crossover between the two regimes is smooth where the step structure between the Landau level edges turn into Friedel oscillations. Increasing the temperature causes the step structure or the Friedel oscillations to wash out leaving a Boltzmann gas density profile.Comment: 14 pages, 7 figure

Nail abnormalities identified in an ageing study of 30 inbred mouse strains.

In a large-scale ageing study, 30 inbred mouse strains were systematically screened for histologic evidence of lesions in all organ systems. Ten strains were diagnosed with similar nail abnormalities. The highest frequency was noted in NON/ShiLtJ mice. Lesions identified fell into two main categories: acute to chronic penetration of the third phalangeal bone through the hyponychium with associated inflammation and bone remodelling or metaplasia of the nail matrix and nail bed associated with severe orthokeratotic hyperkeratosis replacing the nail plate. Penetration of the distal phalanx through the hyponychium appeared to be the initiating feature resulting in nail abnormalities. The accompanying acute to subacute inflammatory response was associated with osteolysis of the distal phalanx. Evaluation of young NON/ShiLtJ mice revealed that these lesions were not often found, or affected only one digit. The only other nail unit abnormality identified was sporadic subungual epidermoid inclusion cysts which closely resembled similar lesions in human patients. These abnormalities, being age-related developments, may have contributed to weight loss due to impacts upon feeding and should be a consideration for future research due to the potential to interact with other experimental factors in ageing studies using the affected strains of mice.American Hair Research Society Mentorship Grants (to SL and AM) Ellison Medical Foundation (to JPS) National Institutes of Health (AG025707, for the Shock Aging Center). The Jackson Laboratory Shared Scientific Services were supported in part by a Basic Cancer Center Core Grant from the National Cancer Institute (CA034196)

Safety of trastuzumab emtansine (T-DM1) in patients with HER2-positive advanced breast cancer: Primary results from the KAMILLA study cohort 1

Abstract Background Many patients with metastatic human epidermal growth factor receptor 2 (HER2)-positive breast cancer (BC) are candidates for trastuzumab emtansine (T-DM1) treatment sometime in their disease history. KAMILLA evaluated safety of T-DM1 in patients with previously treated HER2-positive locally advanced or metastatic BC (advanced BC). Methods KAMILLA (NCT01702571) is a single-arm, open-label, international, phase IIIb safety study of patients with HER2-positive advanced BC with progression after prior treatment with chemotherapy and a HER2-directed agent for MBC or within 6 months of completing adjuvant therapy. Patients received T-DM1 (3.6 mg/kg every 3 weeks) until unacceptable toxicity, withdrawal or disease progression. Results Among 2002 treated patients, median age was 55 years (range, 26–88; 373 [18.6%] aged ≥65 years), 1321 (66.0%) received ≥2 prior metastatic treatment lines and 398 (19.9%) had baseline central nervous system metastases. Adverse events (AEs) and serious AEs occurred in 1862 (93.0%) and 427 (21.3%) patients, respectively. Grade ≥3 AEs occurred in 751 (37.5%) patients; the three most common (individual Medical Dictionary for Regulatory Activity terms) were anaemia (3.0%), thrombocytopaenia (2.7%) and fatigue (2.5%). Median progression-free survival (PFS) was 6.9 months (95% confidence interval [CI], 6.0–7.6). Median overall survival (OS) was 27.2 months (95% CI, 25.5–28.7). With increasing lines of prior advanced therapy (0–1 versus 4+), median PFS and OS decreased numerically from 8.3 to 5.6 months and from 31.3 to 22.5 months, respectively. Conclusions KAMILLA is the largest cohort of T-DM1–treated patients studied to date. Results are consistent with prior randomised studies, thereby supporting T-DM1 as safe, tolerable and efficacious treatment for patients with previously treated HER2-positive advanced BC

Adiabaticity Criterion for Moving Vortices in Dilute Bose-Einstein Condensates

Considering a moving vortex line in a dilute atomic Bose-Einstein condensate within time-dependent Hartree-Fock-Bogoliubov-Popov theory, we derive a criterion for the quasiparticle excitations to follow the vortex core rigidly. The assumption of adiabaticity, which is crucial for the validity of the stationary self-consistent theories in describing such time-dependent phenomena, is shown to imply a stringent criterion for the velocity of the vortex line. Furthermore, this condition is shown to be violated in the recent vortex precession experiments.Comment: 4 pages, 1 figur