23,099 research outputs found
Using the statistic to test for missed levels in mixed sequence neutron resonance data
The statistic is studied as a tool to detect missing levels in
the neutron resonance data where 2 sequences are present. These systems are
problematic because there is no level repulsion, and the resonances can be too
close to resolve. is a measure of the fluctuations in the number
of levels in an interval of length on the energy axis. The method used is
tested on ensembles of mixed Gaussian Orthogonal Ensemble (GOE) spectra, with a
known fraction of levels () randomly depleted, and can accurately return
. The accuracy of the method as a function of spectrum size is established.
The method is used on neutron resonance data for 11 isotopes with either s-wave
neutrons on odd-A, or p-wave neutrons on even-A. The method compares favorably
with a maximum likelihood method applied to the level spacing distribution.
Nuclear Data Ensembles were made from 20 isotopes in total, and their
statistic are discussed in the context of Random Matrix Theory.Comment: 22 pages, 12 figures, 4 table
Calculation of some determinants using the s-shifted factorial
Several determinants with gamma functions as elements are evaluated. This
kind of determinants are encountered in the computation of the probability
density of the determinant of random matrices. The s-shifted factorial is
defined as a generalization for non-negative integers of the power function,
the rising factorial (or Pochammer's symbol) and the falling factorial. It is a
special case of polynomial sequence of the binomial type studied in
combinatorics theory. In terms of the gamma function, an extension is defined
for negative integers and even complex values. Properties, mainly composition
laws and binomial formulae, are given. They are used to evaluate families of
generalized Vandermonde determinants with s-shifted factorials as elements,
instead of power functions.Comment: 25 pages; added section 5 for some examples of application
Application of the Trace Formula in Pseudointegrable Systems
We apply periodic-orbit theory to calculate the integrated density of states
from the periodic orbits of pseudointegrable polygon and barrier
billiards. We show that the results agree so well with the results obtained
from direct diagonalization of the Schr\"odinger equation, that about the first
100 eigenvalues can be obtained directly from the periodic-orbit calculations
in good accuracy.Comment: 5 Pages, 4 Figures, submitted to Phys. Rev.
Probability density of determinants of random matrices
In this brief paper the probability density of a random real, complex and
quaternion determinant is rederived using singular values. The behaviour of
suitably rescaled random determinants is studied in the limit of infinite order
of the matrices
Periodic orbit theory and spectral rigidity in pseudointegrable systems
We calculate numerically the periodic orbits of pseudointegrable systems of
low genus numbers that arise from rectangular systems with one or two
salient corners. From the periodic orbits, we calculate the spectral rigidity
using semiclassical quantum mechanics with reaching up to
quite large values. We find that the diagonal approximation is applicable when
averaging over a suitable energy interval. Comparing systems of various shapes
we find that our results agree well with calculated directly from
the eigenvalues by spectral statistics. Therefore, additional terms as e.g.
diffraction terms seem to be small in the case of the systems investigated in
this work. By reducing the size of the corners, the spectral statistics of our
pseudointegrable systems approaches the one of an integrable system, whereas
very large differences between integrable and pseudointegrable systems occur,
when the salient corners are large. Both types of behavior can be well
understood by the properties of the periodic orbits in the system
Energy correlations for a random matrix model of disordered bosons
Linearizing the Heisenberg equations of motion around the ground state of an
interacting quantum many-body system, one gets a time-evolution generator in
the positive cone of a real symplectic Lie algebra. The presence of disorder in
the physical system determines a probability measure with support on this cone.
The present paper analyzes a discrete family of such measures of exponential
type, and does so in an attempt to capture, by a simple random matrix model,
some generic statistical features of the characteristic frequencies of
disordered bosonic quasi-particle systems. The level correlation functions of
the said measures are shown to be those of a determinantal process, and the
kernel of the process is expressed as a sum of bi-orthogonal polynomials. While
the correlations in the bulk scaling limit are in accord with sine-kernel or
GUE universality, at the low-frequency end of the spectrum an unusual type of
scaling behavior is found.Comment: 20 pages, 3 figures, references adde
Sensitivity of the structure of untripped mixing layers to small changes in initial conditions
An experimental study was conducted concerning the influence of small changes in initial conditions on the near- and far-field evolution of the three-dimensional structure of a plan mixing layer. A two-stream mixing layer with a velocity ratio of 0.6 was generated with the initial boundary layers on the splitter plate laminar and was nominally two-dimensional. The initial conditions were changed slightly by interchanging the high- and low-speed sides of the wind tunnel, while maintaining the same velocities, and hence velocity ratio. This resulted in small changes in the initial boundary layer properties, and the perturbations present in the boundary layers were interchanged between the high- and low-speed sides for the two cases. The results indicate that, even with this relatively minor change in initial conditions, the near-field regions of the two cases differ significantly. The peak Reynolds stress levels in the near-field differ by up to 100 percent, and this is attributed to a difference in the location of the initial spanwise vortex roll-up. In addition, the positions and shapes of the individual streamwise vortical structures differ for the two cases, although the overall structures differ for the two cases, although the overall qualitative description of these structures is comparable. The subsequent reorganization and decay of the streamwise vortical structures is very similar for the two cases. As a result, in the far field, both mixing layers achieve similar structure, yielding comparable growth rates, Reynolds stress, distribution, and spectral content
A 3-component laser-Doppler velocimeter data acquisition and reduction system
A laser doppler velocimeter capable of measuring all three components of velocity simultaneously in low-speed flows is described. All the mean velocities, Reynolds stresses, and higher-order products can be evaluated. The approach followed is to split one of the two colors used in a 2-D system, thus creating a third set of beams which is then focused in the flow from an off-axis direction. The third velocity component is computed from the known geometry of the system. The laser optical hardware and the data acquisition electronics are described in detail. In addition, full operating procedures and listings of the software (written in BASIC and ASSEMBLY languages) are also included. Some typical measurements obtained with this system in a vortex/mixing layer interaction are presented and compared directly to those obtained with a cross-wire system
Competition and cooperation:aspects of dynamics in sandpiles
In this article, we review some of our approaches to granular dynamics, now
well known to consist of both fast and slow relaxational processes. In the
first case, grains typically compete with each other, while in the second, they
cooperate. A typical result of {\it cooperation} is the formation of stable
bridges, signatures of spatiotemporal inhomogeneities; we review their
geometrical characteristics and compare theoretical results with those of
independent simulations. {\it Cooperative} excitations due to local density
fluctuations are also responsible for relaxation at the angle of repose; the
{\it competition} between these fluctuations and external driving forces, can,
on the other hand, result in a (rare) collapse of the sandpile to the
horizontal. Both these features are present in a theory reviewed here. An arena
where the effects of cooperation versus competition are felt most keenly is
granular compaction; we review here a random graph model, where three-spin
interactions are used to model compaction under tapping. The compaction curve
shows distinct regions where 'fast' and 'slow' dynamics apply, separated by
what we have called the {\it single-particle relaxation threshold}. In the
final section of this paper, we explore the effect of shape -- jagged vs.
regular -- on the compaction of packings near their jamming limit. One of our
major results is an entropic landscape that, while microscopically rough,
manifests {\it Edwards' flatness} at a macroscopic level. Another major result
is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction
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