898 research outputs found
Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data
We establish necessary conditions for the appearance of both apparent
horizons and singularities in the initial data of spherically symmetric general
relativity when spacetime is foliated extrinsically. When the dominant energy
condition is satisfied these conditions assume a particularly simple form. Let
be the maximum value of the energy density and the radial
measure of its support. If is bounded from above by some
numerical constant, the initial data cannot possess an apparent horizon. This
constant does not depend sensitively on the gauge. An analogous inequality is
obtained for singularities with some larger constant. The derivation exploits
Poincar\'e type inequalities to bound integrals over certain spatial scalars. A
novel approach to the construction of analogous necessary conditions for
general initial data is suggested.Comment: 15 pages, revtex, to appear in Phys. Rev.
Force dipoles and stable local defects on fluid vesicles
An exact description is provided of an almost spherical fluid vesicle with a
fixed area and a fixed enclosed volume locally deformed by external normal
forces bringing two nearby points on the surface together symmetrically. The
conformal invariance of the two-dimensional bending energy is used to identify
the distribution of energy as well as the stress established in the vesicle.
While these states are local minima of the energy, this energy is degenerate;
there is a zero mode in the energy fluctuation spectrum, associated with area
and volume preserving conformal transformations, which breaks the symmetry
between the two points. The volume constraint fixes the distance , measured
along the surface, between the two points; if it is relaxed, a second zero mode
appears, reflecting the independence of the energy on ; in the absence of
this constraint a pathway opens for the membrane to slip out of the defect.
Logarithmic curvature singularities in the surface geometry at the points of
contact signal the presence of external forces. The magnitude of these forces
varies inversely with and so diverges as the points merge; the
corresponding torques vanish in these defects. The geometry behaves near each
of the singularities as a biharmonic monopole, in the region between them as a
surface of constant mean curvature, and in distant regions as a biharmonic
quadrupole. Comparison of the distribution of stress with the quadratic
approximation in the height functions points to shortcomings of the latter
representation. Radial tension is accompanied by lateral compression, both near
the singularities and far away, with a crossover from tension to compression
occurring in the region between them.Comment: 26 pages, 10 figure
The Jang equation, apparent horizons, and the Penrose inequality
The Jang equation in the spherically symmetric case reduces to a first order
equation. This permits an easy analysis of the role apparent horizons play in
the (non)existence of solutions. We demonstrate that the proposed derivation of
the Penrose inequality based on the Jang equation cannot work in the
spherically symmetric case. Thus it is fruitless to apply this method, as it
stands, to the general case. We show also that those analytic criteria for the
formation of horizons that are based on the use of the Jang equation are of
limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte
Axially symmetric membranes with polar tethers
Axially symmetric equilibrium configurations of the conformally invariant
Willmore energy are shown to satisfy an equation that is two orders lower in
derivatives of the embedding functions than the equilibrium shape equation, not
one as would be expected on the basis of axial symmetry. Modulo a translation
along the axis, this equation involves a single free parameter c.If c\ne 0, a
geometry with spherical topology will possess curvature singularities at its
poles. The physical origin of the singularity is identified by examining the
Noether charge associated with the translational invariance of the energy; it
is consistent with an external axial force acting at the poles. A one-parameter
family of exact solutions displaying a discocyte to stomatocyte transition is
described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon
equation for the shape of axi-symmetric membrane
Helfrich-Canham bending energy as a constrained non-linear sigma model
The Helfrich-Canham bending energy is identified with a non-linear sigma
model for a unit vector. The identification, however, is dependent on one
additional constraint: that the unit vector be constrained to lie orthogonal to
the surface. The presence of this constraint adds a source to the divergence of
the stress tensor for this vector so that it is not conserved. The stress
tensor which is conserved is identified and its conservation shown to reproduce
the correct shape equation.Comment: 5 page
Chern-Simons theory and three-dimensional surfaces
There are two natural Chern-Simons theories associated with the embedding of
a three-dimensional surface in Euclidean space; one is constructed using the
induced metric connection -- it involves only the intrinsic geometry, the other
is extrinsic and uses the connection associated with the gauging of normal
rotations. As such, the two theories appear to describe very different aspects
of the surface geometry. Remarkably, at a classical level, they are equivalent.
In particular, it will be shown that their stress tensors differ only by a null
contribution. Their Euler-Lagrange equations provide identical constraints on
the normal curvature. A new identity for the Cotton tensor is associated with
the triviality of the Chern-Simons theory for embedded hypersurfaces implied by
this equivalence. The corresponding null surface stress capturing this
information will be constructed explicitly.Comment: 10 pages, unnecessary details removed, typos fixed, references adde
Geometry of Deformations of Relativistic Membranes
A kinematical description of infinitesimal deformations of the worldsheet
spanned in spacetime by a relativistic membrane is presented. This provides a
framework for obtaining both the classical equations of motion and the
equations describing infinitesimal deformations about solutions of these
equations when the action describing the dynamics of this membrane is
constructed using {\it any} local geometrical worldsheet scalars. As examples,
we consider a Nambu membrane, and an action quadratic in the extrinsic
curvature of the worldsheet.Comment: 20 pages, Plain Tex, sign errors corrected, many new references
added. To appear in Physical Review
Impact of maximum back-EMF limits on the performance characteristics of interior permanent magnet synchronous machines
Interior permanent magnet (IPM) synchronous machines are vulnerable to uncontrolled generator (UCG) faults at high speed that can damage the inverter. One approach to reducing this risk is to impose limits on the maximum machine back-EMF voltage at top speed. This paper presents the results of a comparative design study that clarifies the nature and extent of the penalties imposed on the IPM machine metrics and performance characteristics as a result of imposing progressively tighter values of back-EMF voltage limits. As an alternative to limiting back-EMF and penalizing machine designs, this paper also investigates the effectiveness of the system-side protection approach to the same UCG fault problem.Seok-hee Han, Thomas M. Jahns, Metin Aydin, Mustafa K. Guven, Wen L. Soon
Synthesis of Novel 6-(4-Substituted piperazine-1-yl)-9(b-D-ribofuranosyl) purine Derivatives, Which Lead to Senescence-Induced Cell Death in liver Cancer Cells
Cataloged from PDF version of article.Novel purine ribonucleoside analogues (9-13) containing a 4-substituted piperazine in the substituent at N-6 were synthesized and evaluated for their cytotoxicity on Huh7, HepG2, FOCUS, Mahlavu liver, MCF7 breast, and HCT116 colon carcinoma cell lines. The purine nucleoside analogues were analyzed initially by an anticancer drug-screening method based on a sulforhodamine B assay. Two nucleoside derivatives with promising cytotoxic activities (11 and 12) were further analyzed on the hepatoma cells. The N-6-(4-Trifluoromethylphenyl)piperazine analogue 11 displayed the best antitumor activity, with IC50 values between 5.2 and 9.2 mu M. Similar to previously described nucleoside analogues, compound 11 also interferes with cellular ATP reserves, possibly through influencing cellular kinase activities. Furthermore, the novel nucleoside analogue 11 was shown to induce senescence-associated cell death, as demonstrated by the SA beta-gal assay. The senescence-dependent cytotoxic effect of 11 was also confirmed through phosphorylation of the Rb protein by p15(INK4b) overexpression in the presence of this compound
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