On a Localized Riemannian Penrose Inequality

Consider a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary is the disjoint union of two pieces: the horizon boundary and the outer boundary, where the horizon boundary consists of the unique closed minimal surfaces in the manifold and the outer boundary is metrically a round sphere. We obtain an inequality relating the area of the horizon boundary to the area and the total mean curvature of the outer boundary. Such a manifold may be thought as a region, surrounding the outermost apparent horizons of black holes, in a time-symmetric slice of a space-time in the context of general relativity. The inequality we establish has close ties with the Riemannian Penrose Inequality, proved by Huisken and Ilmanen, and by Bray.Comment: 16 page

On the volume functional of compact manifolds with boundary with constant scalar curvature

We study the volume functional on the space of constant scalar curvature metrics with a prescribed boundary metric. We derive a sufficient and necessary condition for a metric to be a critical point, and show that the only domains in space forms, on which the standard metrics are critical points, are geodesic balls. In the zero scalar curvature case, assuming the boundary can be isometrically embedded in the Euclidean space as a compact strictly convex hypersurface, we show that the volume of a critical point is always no less than the Euclidean volume bounded by the isometric embedding of the boundary, and the two volumes are equal if and only if the critical point is isometric to a standard Euclidean ball. We also derive a second variation formula and apply it to show that, on Euclidean balls and ''small'' hyperbolic and spherical balls in dimensions 3 to 5, the standard space form metrics are indeed saddle points for the volume functional

Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain

Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic ground state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. The internal magnon structure of classical spin waves is resolved by performing the semi-classical quantisation using the Riemann-Hilbert problem approach. We present an expression for the overlap of two semi-classical eigenstates and discuss how correlation functions at the semi-classical level arise from classical phase-space averaging.Comment: 61 pages, 14 figure

Reduced Magnetization and Loss In Ag-Mg Sheathed Bi2212 wires: Systematics With Sample Twist Pitch and Length

Suppression of magnetization and effective filament diameter (deff) with twisting was investigated for a series of recent Bi2212 strands manufactured by Oxford Superconducting Technologies. We measured magnetization as a function of field (out to 14 T), at 5.1 K, of twisted and non-twisted 37 x 18 double restack design strands. The samples were helical coils 5-6 mm in height and approximately 5 mm in diameter. The strand diameter was 0.8 mm. The magnetization of samples having twist pitches of 25.4, 12.7, and 6.35 mm were examined and compared to non-twisted samples of the same filament configuration. The critical state model was used to extract the 12 T deff from magnetization data for comparison. Twisting the samples reduced deff by a factor of 1.5 to 3. The deff was shown to increase both with L and Lp. Mathematical expressions, based upon the anisotropic continuum model, were fit to the data, and a parameter, γ2, which quantifies the electrical connectivity perpendicular to the filament axis, was extracted. The bundle-to-bundle connectivity along the radial axis was found to be approximately 0.2%. The deff was substantially reduced with Lp. In addition, the importance of understanding sample length dependence for quantitative measurements is discussed.This work was supported by the U.S. Department of Energy, Office of Science, Division of High Energy Physics, under Grant DE-SC0010312 and DE-SC0011721In this work we measured the suppression of magnetization and deff with twisting for an OST manufactured 0.8 mm 37 x 18 Bi2212 strand. Magnetization and deff values were suppressed by factors of 1.5-3, making deff and magnetization 1.5-3 times smaller for twisted samples as compared to nontwisted samples. This effect was further systemized and quantified by looking at the dependence of deff on Lp, and also the dependence of deff on L. A model was applied which described the linear dependence on both L and Lp, and extracted a value for the connectivity parameter 2; a value of only 0.2% was found between the subelements. We conclude that (1) loss, magnetization, and deff are suppressed by sample twisting, (2) it is possible to quantify this effect by a parameter 2, and (3) it is important to have long samples (L >> Lp, and also L > Lcrit) to obtain results most relevant to application

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We have promoted a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw's particles with the same chirality which spectrum is a vacuum-like one. As another conflictive result we have proved that a Wess-Zumino term used in the literature consists of the scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system.Comment: 6 pages, Revtex. Final version to appear in Physical Review

Loss of Bladder Epithelium Induced by Cytolytic Mast Cell Granules

Programmed death and shedding of epithelial cells is a powerful defense mechanism to reduce bacterial burden during infection but this activity cannot be indiscriminate because of the critical barrier function of the epithelium. We report that during cystitis, shedding of infected bladder epithelial cells (BECs) was preceded by the recruitment of mast cells (MCs) directly underneath the superficial epithelium where they docked and extruded their granules. MCs were responding to interleukin-1β (IL-1β) secreted by BECs after inflammasome and caspase-1 signaling. Upon uptake of granule-associated chymase (mouse MC protease 4 [mMCPT4]), BECs underwent caspase-1-associated cytolysis and exfoliation. Thus, infected epithelial cells require a specific cue for cytolysis from recruited sentinel inflammatory cells before shedding

The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page