Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma

Energy Conversion Alternatives Study (ECAS), Westinghouse phase 1. Volume 12: Fuel cells

A parametric assessment of four fuel cell power systems -- based on phosphoric acid, potassium hydroxide, molten carbonate, and stabilized zirconia -- has shown that the most important parameters for electricity-cost reduction and/or efficiency improvement standpoints are fuel cell useful life and power density, use of a waste-heat recovery system, and fuel type. Typical capital costs, overall energy efficiencies (based on the heating value of the coal used to produce the power plant fuel), and electricity costs are: phosphoric acid $350-450/kWe, 24-29$450-700/kWe, 26-31%, and 12.8 to 16.9 mills/MJ (46 to 61 mills/kWh); molten carbonate $480-650/kWe, 32-46$420-950/kWe, 26-53%, and 9.7 to 16.9 mills/MJ (35 to 61 mills/kWh). Three types of fuel cell power plants -- solid electrolytic with steam bottoming, molten carbonate with steam bottoming, and solid electrolyte with an integrated coal gasifier -- are recommended for further study

Spontaneous curvature cancellation in forced thin sheets

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container. We show that this feature is independent of thickness of the sheet, the supporting radius and the amount of deflection. Several variants of developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets.Comment: 13 pages, 12 figures, revtex

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit

Differential peripheral B cell phenotype in patients with primary Sjögren’s syndrome (pSS) compared to secondary Sjögren’s syndrome associated with systemic lupus erythematosus (SS/SLE)

Introduction: Peripheral B-cell abnormalities, a feature of both systemic lupus erythematosus (SLE) and primary Sjogren’s syndrome (pSS), are implicated in the pathogenesis of both diseases and correlate with disease activity. This study aims to investigate how the defective B-cell phenotype in pSS patients compares to patients with SS and SLE (SS/SLE), and whether abnormalities in B-cell phenotype could be related to differential B-cell lipid-raft expression and B-cell activating factor (BAFF) receptor function in patients with pSS and SLE and secondary SS (SS/SLE). Methods: Blood samples and clinical and laboratory parameters from 32 patients with pSS and SS/SLE and 13 age/sex matched HC were obtained. We used flow-cytometry to perform B-cell immunophenotyping and analysed lipid-raft expression (marker of B-cell activation). In vitro cultures were also used to assess lipid-raft expression in response to BAFF. Results: Patients with SS/SLE had a significantly decreased Bm1 and Bm5 and increased Bm2 populations compared to HC (p=0.031, p=0.035 and p=0.01, respectively), and increased Bm2 compared to pSS (p=0.027). Bm1-cells were decreased in both pSS and SS/SLE patients compared to HC (p=0.028 and p= 0.031, respectively). Both age and disease duration correlated strongly with Bm2’ cells in SS/SLE patients (r=0.9572, p= 0.0428), and the immunosuppressive treatment correlated negatively with the number of circulating Bm2 and Bm2’ cell in pSS (r = -0.54, p=0.01 and r = -0.56, p=0.008, respectively). B-cells from patients with pSS had a significant increase in lipid-raft expression compared to HC (p=0.01) and patients with SS/SLE (p<0.05). Lipid-raft levels correlated with BAFF-receptor expression in HC and SS/SLE B-cells (p=0.17, r=0.694) but not in pSS patients. Both disease activity score (ESSDAI) and IgG level correlated positively with lipid rafts expression in B cells from patients with pSS (r = 0.79, p=0.004 and r =0.53, p=0.04, respectively). Conclusion: Patients with SS/SLE had more significant B-cell abnormalities compared to HC and pSS, detectable even in a small number of patients. Also the relationship between lipid-raft and BAFF-receptor expression was altered between pSS and SS/SLE patients, and correlated with the disease activity and IgG levels in pSS group, suggesting that therapies targeting BAFF might be particularly successful in the SS/SLE sub-group of patients

Waveless Approximation Theories of Gravity

The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory

Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic