6,914 research outputs found
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
We study synchronization properties of general uncoupled limit-cycle
oscillators driven by common and independent Gaussian white noises. Using phase
reduction and averaging methods, we analytically derive the stationary
distribution of the phase difference between oscillators for weak noise
intensity. We demonstrate that in addition to synchronization, clustering, or
more generally coherence, always results from arbitrary initial conditions,
irrespective of the details of the oscillators.Comment: 6 pages, 2 figure
Can Gravitational Waves Prevent Inflation?
To investigate the cosmic no hair conjecture, we analyze numerically
1-dimensional plane symmetrical inhomogeneities due to gravitational waves in
vacuum spacetimes with a positive cosmological constant. Assuming periodic
gravitational pulse waves initially, we study the time evolution of those waves
and the nature of their collisions. As measures of inhomogeneity on each
hypersurface, we use the 3-dimensional Riemann invariant and the electric and magnetic parts of
the Weyl tensor. We find a temporal growth of the curvature in the waves'
collision region, but the overall expansion of the universe later overcomes
this effect. No singularity appears and the result is a ``no hair" de Sitter
spacetime. The waves we study have amplitudes between and widths between ,
where , the horizon scale of de Sitter spacetime. This
supports the cosmic no hair conjecture.Comment: LaTeX, 11 pages, 3 figures are available on request <To
[email protected] (Hisa-aki SHINKAI)>, WU-AP/29/9
Clinical application of somatosensory amplification in psychosomatic medicine
Many patients with somatoform disorders are frequently encountered in psychosomatic clinics as well as in primary care clinics. To assess such patients objectively, the concept of somatosensory amplification may be useful. Somatosensory amplification refers to the tendency to experience a somatic sensation as intense, noxious, and disturbing. It may have a role in a variety of medical conditions characterized by somatic symptoms that are disproportionate to demonstrable organ pathology. It may also explain some of the variability in somatic symptomatology found among different patients with the same serious medical disorder. It has been assessed with a self-report questionnaire, the Somatosensory Amplification Scale. This instrument was developed in a clinical setting in the U.S., and the reliability and validity of the Japanese and Turkish versions have been confirmed as well
Two Boosted Black Holes in Asymptotically de Sitter Space-Time - Relation between Mass and Apparent Horizon Formation -
We study the apparent horizon for two boosted black holes in the
asymptotically de Sitter space-time by solving the initial data on a space with
punctures. We show that the apparent horizon enclosing both black holes is not
formed if the conserved mass of the system (Abbott-Deser mass) is larger than a
critical mass. The black hole with too large AD mass therefore cannot be formed
in the asymptotically de Sitter space-time even though each black hole has any
inward momentum. We also discuss the dynamical meaning of AD mass by examining
the electric part of the Weyl tensor (the tidal force) for various initial
data.Comment: 15 pages, accepted for publication in PR
(Semi)classical limit of the Hartree equation with harmonic potential
Nonlinear Schrodinger Equations (NLS) of the Hartree type occur in the
modeling of quantum semiconductor devices. Their "semiclassical" limit of
vanishing (scaled) Planck constant is both a mathematical challenge and
practically relevant when coupling quantum models to classical models.
With the aim of describing the semi-classical limit of the 3D
Schrodinger--Poisson system with an additional harmonic potential, we study
some semi-classical limits of the Hartree equation with harmonic potential in
space dimension n>1. The harmonic potential is confining, and causes focusing
periodically in time. We prove asymptotics in several cases, showing different
possible nonlinear phenomena according to the interplay of the size of the
initial data and the power of the Hartree potential. In the case of the 3D
Schrodinger-Poisson system with harmonic potential, we can only give a formal
computation since the need of modified scattering operators for this long range
scattering case goes beyond current theory. We also deal with the case of an
additional "local" nonlinearity given by a power of the local density - a model
that is relevant when incorporating the Pauli principle in the simplest model
given by the "Schrodinger-Poisson-X equation". Further we discuss the
connection of our WKB based analysis to the Wigner function approach to
semiclassical limits.Comment: 26 page
Independent Component Analysis of Spatiotemporal Chaos
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear
oscillators are analyzed using independent component analysis (ICA). For
diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth
amplitude patterns, ICA extracts localized one-humped basis vectors that
reflect the characteristic hole structures of the system, and for nonlocally
coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns,
ICA extracts localized basis vectors with characteristic gap structures.
Statistics of the decomposed signals also provide insight into the complex
dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.
Langevin Analysis of Eternal Inflation
It has been widely claimed that inflation is generically eternal to the
future, even in models where the inflaton potential monotonically increases
away from its minimum. The idea is that quantum fluctuations allow the field to
jump uphill, thereby continually revitalizing the inflationary process in some
regions. In this paper we investigate a simple model of this process,
pertaining to inflation with a quartic potential, in which analytic progress
may be made. We calculate several quantities of interest, such as the expected
number of inflationary efolds, first without and then with various selection
effects. With no additional weighting, the stochastic noise has little impact
on the total number of inflationary efoldings even if the inflaton starts with
a Planckian energy density. A "rolling" volume factor, i.e. weighting in
proportion to the volume at that time, also leads to a monotonically decreasing
Hubble constant and hence no eternal inflation. We show how stronger selection
effects including a constraint on the initial and final states and weighting
with the final volume factor can lead to a picture similar to that usually
associated with eternal inflation.Comment: 22 pages, 2 figure
Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials
The object of the present study is the integrated density of states of a
quantum particle in multi-dimensional Euclidean space which is characterized by
a Schr\"odinger operator with a constant magnetic field and a random potential
which may be unbounded from above and from below. For an ergodic random
potential satisfying a simple moment condition, we give a detailed proof that
the infinite-volume limits of spatial eigenvalue concentrations of
finite-volume operators with different boundary conditions exist almost surely.
Since all these limits are shown to coincide with the expectation of the trace
of the spatially localized spectral family of the infinite-volume operator, the
integrated density of states is almost surely non-random and independent of the
chosen boundary condition. Our proof of the independence of the boundary
condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and
T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal.
{\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first
version of math-ph/0010013. For a revised version of the second part, see
math-ph/0105046. To appear in Reviews in Mathematical Physic
Dynamical renormalization group methods in theory of eternal inflation
Dynamics of eternal inflation on the landscape admits description in terms of
the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one
correspondence with vacuum dynamics equations. On those sectors of the
landscape, where transport properties of the probability measure for eternal
inflation are important, renormalization group fixed points of the MSR
effective action determine late time behavior of the probability measure. I
argue that these RG fixed points may be relevant for the solution of the gauge
invariance problem for eternal inflation.Comment: 11 pages; invited mini-review for Grav.Cos
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