10,143 research outputs found
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
Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport
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, Îł2, 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
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