8,414 research outputs found
A volumetric Penrose inequality for conformally flat manifolds
We consider asymptotically flat Riemannian manifolds with nonnegative scalar
curvature that are conformal to , and so that
their boundary is a minimal hypersurface. (Here, is open
bounded with smooth mean-convex boundary.) We prove that the ADM mass of any
such manifold is bounded below by , where is the
Euclidean volume of and is the volume of the Euclidean
unit -ball. This gives a partial proof to a conjecture of Bray and Iga
\cite{brayiga}. Surprisingly, we do not require the boundary to be outermost.Comment: 7 page
Corrections to Scaling in Phase-Ordering Kinetics
The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st
Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
We study the persistence phenomenon in a socio-econo dynamics model using
computer simulations at a finite temperature on hypercubic lattices in
dimensions up to 5. The model includes a ` social\rq local field which contains
the magnetization at time . The nearest neighbour quenched interactions are
drawn from a binary distribution which is a function of the bond concentration,
. The decay of the persistence probability in the model depends on both the
spatial dimension and . We find no evidence of ` blocking\rq in this model.
We also discuss the implications of our results for possible applications in
the social and economic fields. It is suggested that the absence, or otherwise,
of blocking could be used as a criterion to decide on the validity of a given
model in different scenarios.Comment: 11 pages, 4 figure
Self-monitoring for improving control of blood pressue in patients with hypertension
The objective of this review is to determine the effect of SBPM in adults with hypertension on blood pressure control as compared to OBPM or usual care
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
Perturbative Corrections to the Ohta-Jasnow-Kawasaki Theory of Phase-Ordering Dynamics
A perturbation expansion is considered about the Ohta-Jasnow-Kawasaki theory
of phase-ordering dynamics; the non-linear terms neglected in the OJK
calculation are reinstated and treated as a perturbation to the linearised
equation. The first order correction term to the pair correlation function is
calculated in the large-d limit and found to be of order 1/(d^2).Comment: Revtex, 27 pages including 2 figures, submitted to Phys. Rev. E,
references adde
Self Consistent Screening Approximation For Critical Dynamics
We generalise Bray's self-consistent screening approximation to describe the
critical dynamics of the theory. In order to obtain the dynamical
exponent , we have to make an ansatz for the form of the scaling functions,
which fortunately can be much constrained by general arguments. Numerical
values of for , and are obtained using two different
ans\"atze, and differ by a very small amount. In particular, the value of obtained for the 3-d Ising model agrees well with recent
Monte-Carlo simulations.Comment: 21 pages, LaTeX file + 4 (EPS) figure
Replica field theory and renormalization group for the Ising spin glass in an external magnetic field
We use the generic replica symmetric cubic field-theory to study the
transition of short range Ising spin glasses in a magnetic field around the
upper critical dimension, d=6. A novel fixed-point is found, in addition to the
well-known zero magnetic field fixed-point, from the application of the
renormalization group. In the spin glass limit, n going to 0, this fixed-point
governs the critical behaviour of a class of systems characterised by a single
cubic interaction parameter. For this universality class, the spin glass
susceptibility diverges at criticality, whereas the longitudinal mode remains
massive. The third mode, the so-called anomalous one, however, behaves
unusually, having a jump at criticality. The physical consequences of this
unusual behaviour are discussed, and a comparison with the conventional de
Almeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev.
Let
Theory of Suspension Segregation in Partially Filled Horizontal Rotating Cylinders
It is shown that a suspension of particles in a partially-filled, horizontal,
rotating cylinder is linearly unstable towards axial segregation and an
undulation of the free surface at large enough particle concentrations. Relying
on the shear-induced diffusion of particles, concentration-dependent viscosity,
and the existence of a free surface, our theory provides an explanation of the
experiments of Tirumkudulu et al., Phys. Fluids 11, 507-509 (1999); ibid. 12,
1615 (2000).Comment: Accepted for publication in Phys Fluids (Lett) 10 pages, two eps
figure
A Remark on Boundary Effects in Static Vacuum Initial Data sets
Let (M, g) be an asymptotically flat static vacuum initial data set with
non-empty compact boundary. We prove that (M, g) is isometric to a spacelike
slice of a Schwarzschild spacetime under the mere assumption that the boundary
of (M, g) has zero mean curvature, hence generalizing a classic result of
Bunting and Masood-ul-Alam. In the case that the boundary has constant positive
mean curvature and satisfies a stability condition, we derive an upper bound of
the ADM mass of (M, g) in terms of the area and mean curvature of the boundary.
Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit
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