Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review

Energy-Momentum Tensor of Particles Created in an Expanding Universe

We present a general formulation of the time-dependent initial value problem for a quantum scalar field of arbitrary mass and curvature coupling in a FRW cosmological model. We introduce an adiabatic number basis which has the virtue that the divergent parts of the quantum expectation value of the energy-momentum tensor are isolated in the vacuum piece of , and may be removed using adiabatic subtraction. The resulting renormalized is conserved, independent of the cutoff, and has a physically transparent, quasiclassical form in terms of the average number of created adiabatic `particles'. By analyzing the evolution of the adiabatic particle number in de Sitter spacetime we exhibit the time structure of the particle creation process, which can be understood in terms of the time at which different momentum scales enter the horizon. A numerical scheme to compute as a function of time with arbitrary adiabatic initial states (not necessarily de Sitter invariant) is described. For minimally coupled, massless fields, at late times the renormalized goes asymptotically to the de Sitter invariant state previously found by Allen and Folacci, and not to the zero mass limit of the Bunch-Davies vacuum. If the mass m and the curvature coupling xi differ from zero, but satisfy m^2+xi R=0, the energy density and pressure of the scalar field grow linearly in cosmic time demonstrating that, at least in this case, backreaction effects become significant and cannot be neglected in de Sitter spacetime.Comment: 28 pages, Revtex, 11 embedded .ps figure

Density and Pair Correlation Function of Confined Identical Particles: the Bose-Einstein Case

Two basic correlation functions are calculated for a model of $N$ harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case. The dependence of these static response properties on the complete range of the temperature and of the number of particles is obtained. The calculation technique is based on the path integral approach of symmetrized density matrices for identical particles in a parabolic confining well.Comment: 8 pages (REVTEX) + 6 figures (postscript

Attractor states and infrared scaling in de Sitter space

The renormalized expectation value of the energy-momentum tensor for a scalar field with any mass m and curvature coupling xi is studied for an arbitrary homogeneous and isotropic physical initial state in de Sitter spacetime. We prove quite generally that has a fixed point attractor behavior at late times, which depends only on m and xi, for any fourth order adiabatic state that is infrared finite. Specifically, when m^2 + xi R > 0, approaches the Bunch-Davies de Sitter invariant value at late times, independently of the initial state. When m = xi = 0, it approaches instead the de Sitter invariant Allen-Folacci value. When m = 0 and xi \ge 0 we show that this state independent asymptotic value of the energy-momentum tensor is proportional to the conserved geometrical tensor (3)H_{ab}, which is related to the behavior of the quantum effective action of the scalar field under global Weyl rescaling. This relationship serves to generalize the definition of the trace anomaly in the infrared for massless, non-conformal fields. In the case m^2 + xi R = 0, but m and xi separately different from zero, grows linearly with cosmic time at late times. For most values of m and xi in the tachyonic cases, m^2 + xi R grows exponentially at late cosmic times for all physically admissable initial states.Comment: 30 pages, 6 figures, 46 kB tar.gz fil

Development of a Maxwell X-57 High Lift Motor Reference Design

NASA's all-electric X-57 airplane will utilize 14 electric motors, of which 12 are exclusively for lift augmentation during takeoff and landing. This report covers the design and development process taken to create an open reference model representative of the 12 lift augmenting motors. A combined worst case scenario was used as the design point, which represents the simultaneously occurring worst case aspects of thermal, static stress, electromagnetic, and rotor dynamic conditions. This work also highlights the tightly coupled nature of aerospace electric motor design, requiring constant iteration between all disciplines involved. Further adding to the uniqueness is the cooling method, which is limited to nacelle skin forced convection cooling only, no internal air flow is permitted. The stator outer diameter limit of 156.45 mm greatly impacts the degree of coupling between the electromagnetic design with the thermal analysis. The permanent magnet synchronous motor developed here operates between 385 V and 538 V, at a peak current of 50 A. Detailed electromagnetic, thermal, static load, and rotordynamic analysis was completed for this electric motor; all of which are required for a full design. The rotordynamic analysis took into consideration the motor housing which is designed specifically for this motor. The final electric motor has a mass of 2.34 kg, produces 24.1 Nm of torque with a specific power of 5.56 kW/kg, and has an efficiency of 96.61% at the combined worst case design point

A specific amino acid motif of HLA-DRB1 mediates risk and interacts with smoking history in Parkinson's disease.

Parkinson's disease (PD) is a neurodegenerative disease in which genetic risk has been mapped to HLA, but precise allelic associations have been difficult to infer due to limitations in genotyping methodology. Mapping PD risk at highest possible resolution, we performed sequencing of 11 HLA genes in 1,597 PD cases and 1,606 controls. We found that susceptibility to PD can be explained by a specific combination of amino acids at positions 70-74 on the HLA-DRB1 molecule. Previously identified as the primary risk factor in rheumatoid arthritis and referred to as the "shared epitope" (SE), the residues Q/R-K/R-R-A-A at positions 70-74 in combination with valine at position 11 (11-V) is highly protective in PD, while risk is attributable to the identical epitope in the absence of 11-V. Notably, these effects are modified by history of cigarette smoking, with a strong protective effect mediated by a positive history of smoking in combination with the SE and 11-V (P = 10-4; odds ratio, 0.51; 95% confidence interval, 0.36-0.72) and risk attributable to never smoking in combination with the SE without 11-V (P = 0.01; odds ratio, 1.51; 95% confidence interval, 1.08-2.12). The association of specific combinations of amino acids that participate in critical peptide-binding pockets of the HLA class II molecule implicates antigen presentation in PD pathogenesis and provides further support for genetic control of neuroinflammation in disease. The interaction of HLA-DRB1 with smoking history in disease predisposition, along with predicted patterns of peptide binding to HLA, provide a molecular model that explains the unique epidemiology of smoking in PD

Confined Harmonically Interacting Spin-Polarized Fermions in a Magnetic Field: Thermodynamics

We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin polarized fermions in a confiment potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three dimensional model of N harmonically interacting spin polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.Comment: 7 pages REVTEX and 8 postscript figures, accepted in Phys. Rev.

Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions

For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for both static responses. The density and the pair correlation function are evaluated explicitly in the ground state of a confined fermion system with a number of particles ranging from 1 to 220 and filling the Fermi level completely.Comment: 11 REVTEX pages, 3 postscript figures. Accepted for publication in Phys. Rev. E, Vol. 58 (August 1, 1998

Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap

We present a model which predicts the temperature of Bose-Einstein condensation in atomic alkali gases and find excellent agreement with recent experimental observations. A system of bosons confined by a harmonic oscillator potential is not characterized by a critical temperature in the same way as an identical system which is not confined. We discuss the problem of Bose-Einstein condensation in an isotropic harmonic oscillator potential analytically and numerically for a range of parameters of relevance to the study of low temperature gases of alkali metals.Comment: 11 pages latex with two postscript figure

Plasma sTNFR1 and IL8 for prognostic enrichment in sepsis trials: a prospective cohort study.

BackgroundEnrichment strategies improve therapeutic targeting and trial efficiency, but enrichment factors for sepsis trials are lacking. We determined whether concentrations of soluble tumor necrosis factor receptor-1 (sTNFR1), interleukin-8 (IL8), and angiopoietin-2 (Ang2) could identify sepsis patients at higher mortality risk and serve as prognostic enrichment factors.MethodsIn a multicenter prospective cohort study of 400 critically ill septic patients, we derived and validated thresholds for each marker and expressed prognostic enrichment using risk differences (RD) of 30-day mortality as predictive values. We then used decision curve analysis to simulate the prognostic enrichment of each marker and compare different prognostic enrichment strategies.Measurements and main resultsAn admission sTNFR1 concentration > 8861 pg/ml identified patients with increased mortality in both the derivation (RD 21.6%) and validation (RD 17.8%) populations. Among immunocompetent patients, an IL8 concentration > 94 pg/ml identified patients with increased mortality in both the derivation (RD 17.7%) and validation (RD 27.0%) populations. An Ang2 level > 9761 pg/ml identified patients at 21.3% and 12.3% increased risk of mortality in the derivation and validation populations, respectively. Using sTNFR1 or IL8 to select high-risk patients improved clinical trial power and efficiency compared to selecting patients with septic shock. Ang2 did not outperform septic shock as an enrichment factor.ConclusionsThresholds for sTNFR1 and IL8 consistently identified sepsis patients with higher mortality risk and may have utility for prognostic enrichment in sepsis trials