5,200 research outputs found
The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow
We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix
Caustics of Compensated Spherical Lens Models
We consider compensated spherical lens models and the caustic surfaces they
create in the past light cone. Examination of cusp and crossover angles
associated with particular source and lens redshifts gives explicit lensing
models that confirm previous claims that area distances can differ by
substantial factors from angular diameter distances even when averaged over
large angular scales. `Shrinking' in apparent sizes occurs, typically by a
factor of 3 for a single spherical lens, on the scale of the cusp caused by the
lens; summing over many lenses will still leave a residual effect.Comment: 21 pages, 5 ps figures, eps
Toward Empirical Constraints on the Global Redshifted 21 cm Brightness Temperature During the Epoch of Reionization
Preliminary results are presented from a simple, single-antenna experiment
designed to measure the all-sky radio spectrum between 100 and 200 MHz. The
system used an internal comparison-switching scheme to reduce non-smooth
instrumental contaminants in the measured spectrum to 75 mK. From the
observations, we place an initial upper limit of 450 mK on the relative
brightness temperature of the redshifted 21 cm contribution to the spectrum due
to neutral hydrogen in the intergalactic medium (IGM) during the epoch of
reionization, assuming a rapid transition to a fully ionized IGM at a redshift
of 8. With refinement, this technique should be able to distinguish between
slow and fast reionization scenarios. To constrain the duration of reionization
to dz > 2, the systematic residuals in the measured spectrum must be reduced to
3 mK.Comment: Submitted to ApJ. 9 pages including 6 figure
The optimal cloning of quantum coherent states is non-Gaussian
We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.Comment: 4 pages, 2 figures, revtex; changed title, extended list of authors,
included optical implementation of optimal clone
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Whole-cortex mapping of common genetic influences on depression and a social deficits dimension
Social processes are associated with depression, particularly understanding and responding to others, deficits in which can manifest as callousness/unemotionality (CU). Thus, CU may reflect some of the genetic risk to depression. Further, this vulnerability likely reflects the neurological substrates of depression, presenting biomarkers to capture genetic vulnerability of depression severity. However, heritability varies within brain regions, so a high-resolution genetic perspective is needed. We developed a toolbox that maps genetic and environmental associations between brain and behavior at high resolution. We used this toolbox to estimate brain areas that are genetically associated with both depressive symptoms and CU in a sample of 258 same-sex twin pairs from the Colorado Longitudinal Twin Study (LTS). We then overlapped the two maps to generate coordinates that allow for tests of downstream effects of genes influencing our clusters. Genetic variance influencing cortical thickness in the right dorsal lateral prefrontal cortex (DLFPC) sulci and gyri, ventral posterior cingulate cortex (PCC), pre-somatic motor cortex (PreSMA), medial precuneus, left occipital-temporal junction (OTJ), parietal-temporal junction (PTJ), ventral somatosensory cortex (vSMA), and medial and lateral precuneus were genetically associated with both depression and CU. Split-half replication found support for both DLPFC clusters. Meta-analytic term search identified "theory of mind", "inhibit", and "pain" as likely functions. Gene and transcript mapping/enrichment analyses implicated calcium channels. CU reflects genetic vulnerability to depression that likely involves executive and social functioning in a distributed process across the cortex. This approach works to unify neuroimaging, neuroinformatics, and genetics to discover pathways to psychiatric vulnerability.</p
Decoherence produces coherent states: an explicit proof for harmonic chains
We study the behavior of infinite systems of coupled harmonic oscillators as
t->infinity, and generalize the Central Limit Theorem (CLT) to show that their
reduced Wigner distributions become Gaussian under quite general conditions.
This shows that generalized coherent states tend to be produced naturally. A
sufficient condition for this to happen is shown to be that the spectral
function is analytic and nonlinear. For a rectangular lattice of coupled
oscillators, the nonlinearity requirement means that waves must be dispersive,
so that localized wave-packets become suppressed. Virtually all harmonic
heat-bath models in the literature satisfy this constraint, and we have good
reason to believe that coherent states and their generalizations are not merely
a useful analytical tool, but that nature is indeed full of them. Standard
proofs of the CLT rely heavily on the fact that probability densities are
non-negative. Although the CLT generally fails if the probability densities are
allowed to take negative values, we show that a CLT does indeed hold for a
special class of such functions. We find that, intriguingly, nature has
arranged things so that all Wigner functions belong to this class.Comment: Final published version. 17 pages, Plain TeX, no figures. Online at
http://astro.berkeley.edu/~max/gaussians.html (faster from the US), from
http://www.mpa-garching.mpg.de/~max/gaussians.html (faster from Europe) or
from [email protected]
The stability of cosmological scaling solutions
We study the stability of cosmological scaling solutions within the class of
spatially homogeneous cosmological models with a perfect fluid subject to the
equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant
satisfying 0 < gamma < 2) and a scalar field with an exponential potential. The
scaling solutions, which are spatially flat isotropic models in which the
scalar field energy density tracks that of the perfect fluid, are of physical
interest. For example, in these models a significant fraction of the current
energy density of the Universe may be contained in the scalar field whose
dynamical effects mimic cold dark matter. It is known that the scaling
solutions are late-time attractors (i.e., stable) in the subclass of flat
isotropic models. We find that the scaling solutions are stable (to shear and
curvature perturbations) in generic anisotropic Bianchi models when gamma <
2/3. However, when gamma > 2/3, and particularly for realistic matter with
gamma >= 1, the scaling solutions are unstable; essentially they are unstable
to curvature perturbations, although they are stable to shear perturbations. We
briefly discuss the physical consequences of these results.Comment: AMSTeX, 7 pages, re-submitted to Phys Rev Let
One-dimensional relativistic dissipative system with constant force and its quantization
For a relativistic particle under a constant force and a linear velocity
dissipation force, a constant of motion is found. Problems are shown for
getting the Hamiltoninan of this system. Thus, the quantization of this system
is carried out through the constant of motion and using the quantization of the
velocity variable. The dissipative relativistic quantum bouncer is outlined
within this quantization approach.Comment: 11 pages, no figure
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