554 research outputs found
Gravitational Chern-Simons Lagrangians and black hole entropy
We analyze the problem of defining the black hole entropy when Chern-Simons
terms are present in the action. Extending previous works, we define a general
procedure, valid in any odd dimensions both for purely gravitational CS terms
and for mixed gauge-gravitational ones. The final formula is very similar to
Wald's original formula valid for covariant actions, with a significant
modification. Notwithstanding an apparent violation of covariance we argue that
the entropy formula is indeed covariant.Comment: 39 page
Variational formulation of ideal fluid flows according to gauge principle
On the basis of the gauge principle of field theory, a new variational
formulation is presented for flows of an ideal fluid. The fluid is defined
thermodynamically by mass density and entropy density, and its flow fields are
characterized by symmetries of translation and rotation. The rotational
transformations are regarded as gauge transformations as well as the
translational ones. In addition to the Lagrangians representing the translation
symmetry, a structure of rotation symmetry is equipped with a Lagrangian
including the vorticity and a vector potential bilinearly. Euler's
equation of motion is derived from variations according to the action
principle. In addition, the equations of continuity and entropy are derived
from the variations. Equations of conserved currents are deduced as the Noether
theorem in the space of Lagrangian coordinate \ba. Without , the
action principle results in the Clebsch solution with vanishing helicity. The
Lagrangian yields non-vanishing vorticity and provides a source
term of non-vanishing helicity. The vorticity equation is derived as an
equation of the gauge field, and the characterizes topology of the
field. The present formulation is comprehensive and provides a consistent basis
for a unique transformation between the Lagrangian \ba space and the Eulerian
\bx space. In contrast, with translation symmetry alone, there is an
arbitrariness in the ransformation between these spaces.Comment: 34 pages, Fluid Dynamics Research (2008), accepted on 1st Dec. 200
Quantum Cosmology for a Quadratic Theory of Gravity
For pure fourth order () quantum cosmology the
Wheeler-DeWitt equation is solved exactly for the closed homogeneous and
isotropic model. It is shown that by imposing as boundary condition that at the origin of the universe the wave functions behave as suggested by
Vilenkin.Comment: 13 pages, latex,no figure
Conformal Covariantization of Moyal-Lax Operators
A covariant approach to the conformal property associated with Moyal-Lax
operators is given. By identifying the conformal covariance with the second
Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the
primary fields of one-parameter deformation of classical -algebras.Comment: 13 pages, Revtex, no figures, v.2: typos corrected, references added
and conclusion modifie
Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences
The conserved densities of hydrodynamic type system in Riemann invariants
satisfy a system of linear second order partial differential equations. For
linear systems of this type Darboux introduced Laplace transformations,
generalising the classical transformations in the scalar case. It is
demonstrated that Laplace transformations can be pulled back to the
transformations of the corresponding hydrodynamic type systems. We discuss
periodic Laplace sequences of with the emphasize on the simplest nontrivial
case of period 2. For 3-component systems in Riemann invariants a complete
discription of closed quadruples is proposed. They turn to be related to a
special quadratic reduction of the (2+1)-dimensional 3-wave system which can be
reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of
the Lame and rotation coefficients Laplace transformations have a natural
interpretation as the symmetries of the Dirac operator, associated with the
(2+1)-dimensional n-wave system. The 2-component Laplace transformations can be
interpreted also as the symmetries of the (2+1)-dimensional integrable
equations of Davey-Stewartson type. Laplace transformations of hydrodynamic
type systems originate from a canonical geometric correspondence between
systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late
Topological transversals to a family of convex sets
Let be a family of compact convex sets in . We say
that has a \emph{topological -transversal of index }
(, ) if there are, homologically, as many transversal
-planes to as -planes containing a fixed -plane in
.
Clearly, if has a -transversal plane, then
has a topological -transversal of index for and . The converse is not true in general.
We prove that for a family of compact convex sets in
a topological -transversal of index implies an
ordinary -transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences
Pain in patients with equal radiographic grades of osteoarthritis in both knees: the value of gray scale ultrasound
SummaryObjectivesTo investigate the association of ultrasound (US) features with pain and the functional scores in patients with equal radiographic grades of osteoarthritis (OA) in both knees.MethodsFifty-six consecutive patients with knee OA: 85 symptomatic knees (81 knees with medial pain) and 27 asymptomatic knees, and 10 healthy patients without knee OA as a control were enrolled. US was done by two ultrasonographers blinded to patient diagnoses. US features were semiquantitatively scored (0–3) when appropriate.ResultsIn the OA group, common US findings were marginal osteophyte, suprapatellar synovitis, suprapatellar effusion (SPE), medial meniscus protrusion, medial compartment synovitis (MCS), lateral compartment synovitis, and Baker's cyst. Only SPE and MCS were significantly associated with knee pain. Visual analog pain scale (VAS) scores on motion were positively linearly associated with SPE and MCS (P < 0.01). Only MCS was degree-dependently associated with VAS scores at rest, the Western Ontario and McMaster Universities pain subscale, and the presence of medial knee pain (P < 0.01) after adjustments for age, gender, body mass index (BMI), radiographic grade, and other US features. In the control group, no US features were associated with knee pain.ConclusionsUS inflammation features, including SPE and MCS, were positively linearly associated with knee pain in motion. MCS was also degree-dependently associated with pain at rest and the presence of medial knee pain. These findings show that synovitis was one important predictive factor of pain. Further studies to confirm the association of US features and pain are warranted
Kernel Formula Approach to the Universal Whitham Hierarchy
We derive the dispersionless Hirota equations of the universal Whitham
hierarchy from the kernel formula approach proposed by Carroll and Kodama.
Besides, we also verify the associativity equations in this hierarchy from the
dispersionless Hirota equations and give a realization of the associative
algebra with structure constants expressed in terms of the residue formulas.Comment: 18 page
Materials with Colossal Dielectric Constant: Do They Exist?
Experimental evidence is provided that colossal dielectric constants, epsilon
>= 1000, sometimes reported to exist in a broad temperature range, can often be
explained by Maxwell-Wagner type contributions of depletion layers at the
interface between sample and contacts, or at grain boundaries. We demonstrate
this on a variety of different materials. We speculate that the largest
intrinsic dielectric constant observed so far in non-ferroelectric materials is
of order 100.Comment: 3 figure
Spinor formulation of topologically massive gravity
In the framework of real 2-component spinors in three dimensional space-time
we present a description of topologically massive gravity (TMG) in terms of
differential forms with triad scalar coefficients. This is essentially a real
version of the Newman-Penrose formalism in general relativity. A triad
formulation of TMG was considered earlier by Hall, Morgan and Perjes, however,
due to an unfortunate choice of signature some of the spinors underlying the
Hall-Morgan-Perjes formalism are real, while others are pure imaginary. We
obtain the basic geometrical identities as well as the TMG field equations
including a cosmological constant for the appropriate signature. As an
application of this formalism we discuss the Bianchi Type exact
solutions of TMG and point out that they are parallelizable manifolds. We also
consider various re-identifications of these homogeneous spaces that result in
black hole solutions of TMG.Comment: An expanded version of paper published in Classical and Quantum
Gravity 12 (1995) 291
- …