1,938 research outputs found
Passive Scalar: Scaling Exponents and Realizability
An isotropic passive scalar field advected by a rapidly-varying velocity
field is studied. The tail of the probability distribution for
the difference in across an inertial-range distance is found
to be Gaussian. Scaling exponents of moments of increase as
or faster at large order , if a mean dissipation conditioned on is
a nondecreasing function of . The computed numerically
under the so-called linear ansatz is found to be realizable. Some classes of
gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4
pages) with 2 postscript figures. Send email to [email protected]
Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes
The dynamics of relativistic stars and black holes are often studied in terms
of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with
different effective potentials . In this paper we present a systematic
study of the relation between the structure of the QNM's of the KG equation and
the form of . In particular, we determine the requirements on in
order for the QNM's to form complete sets, and discuss in what sense they form
complete sets. Among other implications, this study opens up the possibility of
using QNM expansions to analyse the behavior of waves in relativistic systems,
even for systems whose QNM's do {\it not} form a complete set. For such
systems, we show that a complete set of QNM's can often be obtained by
introducing an infinitesimal change in the effective potential
Structural brain imaging studies offer clues about the effects of the shared genetic etiology among neuropsychiatric disorders
Malalties; GenèticaEnfermedades; GenéticaDiseases; GeneticsGenomewide association studies have found significant genetic correlations among many neuropsychiatric disorders. In contrast, we know much less about the degree to which structural brain alterations are similar among disorders and, if so, the degree to which such similarities have a genetic etiology. From the Enhancing Neuroimaging Genetics through Meta-Analysis (ENIGMA) consortium, we acquired standardized mean differences (SMDs) in regional brain volume and cortical thickness between cases and controls. We had data on 41 brain regions for: attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder (ASD), bipolar disorder (BD), epilepsy, major depressive disorder (MDD), obsessive compulsive disorder (OCD), and schizophrenia (SCZ). These data had been derived from 24,360 patients and 37,425 controls. The SMDs were significantly correlated between SCZ and BD, OCD, MDD, and ASD. MDD was positively correlated with BD and OCD. BD was positively correlated with OCD and negatively correlated with ADHD. These pairwise correlations among disorders were correlated with the corresponding pairwise correlations among disorders derived from genomewide association studies (r = 0.494). Our results show substantial similarities in sMRI phenotypes among neuropsychiatric disorders and suggest that these similarities are accounted for, in part, by corresponding similarities in common genetic variant architectures
Radiative falloff in Einstein-Straus spacetime
The Einstein-Straus spacetime describes a nonrotating black hole immersed in
a matter-dominated cosmology. It is constructed by scooping out a spherical
ball of the dust and replacing it with a vacuum region containing a black hole
of the same mass. The metric is smooth at the boundary, which is comoving with
the rest of the universe. We study the evolution of a massless scalar field in
the Einstein-Straus spacetime, with a special emphasis on its late-time
behavior. This is done by numerically integrating the scalar wave equation in a
double-null coordinate system that covers both portions (vacuum and dust) of
the spacetime. We show that the field's evolution is governed mostly by the
strong concentration of curvature near the black hole, and the discontinuity in
the dust's mass density at the boundary; these give rise to a rather complex
behavior at late times. Contrary to what it would do in an asymptotically-flat
spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure
Local spin density in two-dimensional electron gas with hexagonal boundary
The intrinsic spin-Hall effect in hexagon-shaped samples is investigated. To
take into account the spin-orbit couplings and to fit the hexagon edges, we
derive the triangular version of the tight-binding model for the linear Rashba
[Sov. Phys. Solid State 2, 1109 (1960)] and Dresselhaus [Phys. Rev. 100, 580
(1955)] [001] Hamiltonians, which allow direct application of the
Landauer-Keldysh non-equilibrium Green function formalism to calculating the
local spin density within the hexagonal sample. Focusing on the out-of-plane
component of spin, we obtain the geometry-dependent spin-Hall accumulation
patterns, which are sensitive to not only the sample size, the spin-orbit
coupling strength, the bias strength, but also the lead configurations.
Contrary to the rectangular samples, the accumulation pattern can be very
different in our hexagonal samples. Our present work provides a fundamental
description of the geometry effect on the intrinsic spin-Hall effect, taking
the hexagon as the specific case. Moreover, broken spin-Hall symmetry due to
the coexistence of the Rashba and Dresselhaus couplings is also discussed. Upon
exchanging the two coupling strengths, the accumulation pattern is reversed,
confirming the earlier predicted sign change in spin-Hall conductivity.Comment: 7 pages, 4 figure
Unconventional Gravitational Excitation of a Schwarzschild Black Hole
Besides the well-known quasinormal modes, the gravitational spectrum of a
Schwarzschild black hole also has a continuum part on the negative imaginary
frequency axis. The latter is studied numerically for quadrupole waves. The
results show unexpected striking behavior near the algebraically special
frequency . This reveals a pair of unconventional damped modes very
near , confirmed analytically.Comment: REVTeX4, 4pp, 6 EPS figure files. N.B.: "Alec" is my first, and
"Maassen van den Brink" my family name. v2: better pole placement in Fig. 1.
v3: fixed Refs. [9,20]. v4: added context on "area quantum" research; trimmed
one Fig.; textual clarification
Radiative Falloff in Neutron Star Spacetimes
We systematically study late-time tails of scalar waves propagating in
neutron star spacetimes. We consider uniform density neutron stars, for which
the background spacetime is analytic and the compaction of the star can be
varied continously between the Newtonian limit 2M/R << 1 and the relativistic
Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off
neutron stars of different compactions 2M/R and find that a Newtonian, an
intermediate, and a highly relativistic regime can be clearly distinguished. In
the highly relativistic regime, the reflected signal is dominated by
quasi-periodic peaks, which originate from the wave packet bouncing back and
forth between the center of the star and the maximum of the background
curvature potential at R ~ 3 M. Between these peaks, the field decays according
to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between
the center and the maximum or the curvature potential grows without bound, so
that the first peak arrives only at infinitely late time. The modes of neutron
stars can therefore no longer be excited in the ultra-relativistic limit, and
it is in this sense that the late-time radiative decay from neutron stars
looses all its features and gives rise to power-law tails reminiscent of
Schwarzschild black holes.Comment: 10 pages, 7 figures, to appear in PR
Quasi-Normal Mode Expansion for Linearized Waves in Gravitational Systems
The quasinormal modes (QNM's) of gravitational systems modeled by the
Klein-Gordon equation with effective potentials are studied in analogy to the
QNM's of optical cavities. Conditions are given for the QNM's to form a
complete set, i.e., for the Green's function to be expressible as a sum over
QNM's, answering a conjecture by Price and Husain [Phys. Rev. Lett. {\bf 68},
1973 (1992)]. In the cases where the QNM sum is divergent, procedures for
regularization are given. The crucial condition for completeness is the
existence of spatial discontinuities in the system, e.g., the discontinuity at
the stellar surface in the model of Price and Husain.Comment: 12 pages, WUGRAV-94-
Perturbative Approach to the Quasinormal Modes of Dirty Black Holes
Using a recently developed perturbation theory for uasinormal modes (QNM's),
we evaluate the shifts in the real and imaginary parts of the QNM frequencies
due to a quasi-static perturbation of the black hole spacetime. We show the
perturbed QNM spectrum of a black hole can have interesting features using a
simple model based on the scalar wave equation.Comment: Published in PR
Waves in Schwarzschild spacetimes: How strong can imprints of the spacetime curvature be
Misprints corrected, two references added. To appear in the Phys. Rev. D
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