781 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.
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
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
Spinor representation of surfaces and complex stresses on membranes and interfaces
Variational principles are developed within the framework of a spinor
representation of the surface geometry to examine the equilibrium properties of
a membrane or interface. This is a far-reaching generalization of the
Weierstrass-Enneper representation for minimal surfaces, introduced by
mathematicians in the nineties, permitting the relaxation of the vanishing mean
curvature constraint. In this representation the surface geometry is described
by a spinor field, satisfying a two-dimensional Dirac equation, coupled through
a potential associated with the mean curvature. As an application, the
mesoscopic model for a fluid membrane as a surface described by the
Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit
construction is provided of the conserved complex-valued stress tensor
characterizing this surface.Comment: 17 page
Guided and magnetic self-assembly of tunable magnetoceptive gels
Self-assembly of components into complex functional patterns at microscale is common in nature, and used increasingly in numerous disciplines such as optoelectronics, microfabrication, sensors, tissue engineering and computation. Here, we describe the use of stable radicals to guide the self-assembly of magnetically tunable gels, which we call ‘magnetoceptive’ materials at the scale of hundreds of microns to a millimeter, each can be programmed by shape and composition, into heterogeneous complex structures. Using paramagnetism of free radicals as a driving mechanism, complex heterogeneous structures are built in the magnetic field generated by permanent magnets. The overall magnetic signature of final structure is erased via an antioxidant vitamin E, subsequent to guided self-assembly. We demonstrate unique capabilities of radicals and antioxidants in fabrication of soft systems with heterogeneity in material properties, such as porosity, elastic modulus and mass density; then in bottom-up tissue engineering and finally, levitational and selective assembly of microcomponents
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