743 research outputs found
Vibration characteristics of 1/8-scale dynamic models of the space-shuttle solid-rocket boosters
Vibration tests and analyses of six 1/8 scale models of the space shuttle solid rocket boosters are reported. Natural vibration frequencies and mode shapes were obtained for these aluminum shell models having internal solid fuel configurations corresponding to launch, midburn (maximum dynamic pressure), and near endburn (burnout) flight conditions. Test results for longitudinal, torsional, bending, and shell vibration frequencies are compared with analytical predictions derived from thin shell theory and from finite element plate and beam theory. The lowest analytical longitudinal, torsional, bending, and shell vibration frequencies were within + or - 10 percent of experimental values. The effects of damping and asymmetric end skirts on natural vibration frequency were also considered. The analytical frequencies of an idealized full scale space shuttle solid rocket boosted structure are computed with and without internal pressure and are compared with the 1/8 scale model results
On The Misuse Of Confidence Intervals For Two Means In Testing For The Significance Of The Difference Between The Means
Comparing individual confidence intervals of two population means is an incorrect procedure for determining the statistical significance of the difference between the means. We show conditions where confidence intervals for the means from two independent samples overlap and the difference between the means is in fact significant
Extreme value statistics and return intervals in long-range correlated uniform deviates
We study extremal statistics and return intervals in stationary long-range
correlated sequences for which the underlying probability density function is
bounded and uniform. The extremal statistics we consider e.g., maximum relative
to minimum are such that the reference point from which the maximum is measured
is itself a random quantity. We analytically calculate the limiting
distributions for independent and identically distributed random variables, and
use these as a reference point for correlated cases. The distributions are
different from that of the maximum itself i.e., a Weibull distribution,
reflecting the fact that the distribution of the reference point either
dominates over or convolves with the distribution of the maximum. The
functional form of the limiting distributions is unaffected by correlations,
although the convergence is slower. We show that our findings can be directly
generalized to a wide class of stochastic processes. We also analyze return
interval distributions, and compare them to recent conjectures of their
functional form
Countable Random Sets: Uniqueness in Law and Constructiveness
The first part of this article deals with theorems on uniqueness in law for
\sigma-finite and constructive countable random sets, which in contrast to the
usual assumptions may have points of accumulation. We discuss and compare two
approaches on uniqueness theorems: First, the study of generators for
\sigma-fields used in this context and, secondly, the analysis of hitting
functions. The last section of this paper deals with the notion of
constructiveness. We will prove a measurable selection theorem and a
decomposition theorem for constructive countable random sets, and study
constructive countable random sets with independent increments.Comment: Published in Journal of Theoretical Probability
(http://www.springerlink.com/content/0894-9840/). The final publication is
available at http://www.springerlink.co
Extreme value laws in dynamical systems under physical observables
Extreme value theory for chaotic dynamical systems is a rapidly expanding
area of research. Given a system and a real function (observable) defined on
its phase space, extreme value theory studies the limit probabilistic laws
obeyed by large values attained by the observable along orbits of the system.
Based on this theory, the so-called block maximum method is often used in
applications for statistical prediction of large value occurrences. In this
method, one performs inference for the parameters of the Generalised Extreme
Value (GEV) distribution, using maxima over blocks of regularly sampled
observations along an orbit of the system. The observables studied so far in
the theory are expressed as functions of the distance with respect to a point,
which is assumed to be a density point of the system's invariant measure.
However, this is not the structure of the observables typically encountered in
physical applications, such as windspeed or vorticity in atmospheric models. In
this paper we consider extreme value limit laws for observables which are not
functions of the distance from a density point of the dynamical system. In such
cases, the limit laws are no longer determined by the functional form of the
observable and the dimension of the invariant measure: they also depend on the
specific geometry of the underlying attractor and of the observable's level
sets. We present a collection of analytical and numerical results, starting
with a toral hyperbolic automorphism as a simple template to illustrate the
main ideas. We then formulate our main results for a uniformly hyperbolic
system, the solenoid map. We also discuss non-uniformly hyperbolic examples of
maps (H\'enon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models).
Our purpose is to outline the main ideas and to highlight several serious
problems found in the numerical estimation of the limit laws
Considerations in the determination of orientational order parameters from X-ray scattering experiments
An assessment of the data processing and analysis methods used to obtain the second- and fourth-rank orientational order parameters of liquid crystals from X-ray scattering experiments has been carried out, using experimental data from four extensively studied alkyl-cyanobiphenyls and calculated data generated from two general types of theoretical orientational distribution function. The application of a background subtraction and two different baseline correction methods to the scattering profiles is assessed, along with three different methods to analyse the processed data. The choice of baseline correction method is shown to have a significant effect: an offset to zero overestimates the order parameters from the experimental and calculated data sets, particularly for lower order parameters arising from broad distributions, whereas an offset to a value estimated from regions of low scattering intensity provides experimental values close to those reported from other experimental techniques. By contrast, the three different analysis methods are shown generally to result in relatively small absolute differences between the order parameters. We outline a straightforward general approach to experimental X-ray scattering data processing and analysis for uniaxial phases that results in order parameters that match well with those reported using other experimental techniques
The global picture of self-similar and not self-similar decay in Burgers Turbulence
This paper continue earlier investigations on the decay of Burgers turbulence
in one dimension from Gaussian random initial conditions of the power-law
spectral type . Depending on the power , different
characteristic regions are distinguished. The main focus of this paper is to
delineate the regions in wave-number and time in which self-similarity
can (and cannot) be observed, taking into account small- and large-
cutoffs. The evolution of the spectrum can be inferred using physical arguments
describing the competition between the initial spectrum and the new frequencies
generated by the dynamics. For large wavenumbers, we always have
region, associated to the shocks. When is less than one, the large-scale
part of the spectrum is preserved in time and the global evolution is
self-similar, so that scaling arguments perfectly predict the behavior in time
of the energy and of the integral scale. If is larger than two, the
spectrum tends for long times to a universal scaling form independent of the
initial conditions, with universal behavior at small wavenumbers. In the
interval the leading behaviour is self-similar, independent of and
with universal behavior at small wavenumber. When , the spectrum
has three scaling regions : first, a region at very small \ms1 with
a time-independent constant, second, a region at intermediate
wavenumbers, finally, the usual region. In the remaining interval,
the small- cutoff dominates, and also plays no role. We find also
(numerically) the subleading term in the evolution of the spectrum
in the interval . High-resolution numerical simulations have been
performed confirming both scaling predictions and analytical asymptotic theory.Comment: 14 pages, 19 figure
Structure and Dynamics of Superconducting NaxCoO(2) Hydrate and Its Unhydrated Analog
Neutron scattering has been used to investigate the crystal structure and
lattice dynamics of superconducting Na0.3CoO2 1.4(H/D)2O, and the parent
Na0.3CoO2 material. The structure of Na0.3CoO2 consists of alternate layers of
CoO2 and Na and is the same as the structure at higher Na concentrations. For
the superconductor, the water forms two additional layers between the Na and
CoO2, increasing the c-axis lattice parameter of the hexagonal P63/mmc space
group from 11.16 A to 19.5 A. The Na ions are found to occupy a different
configuration from the parent compound, while the water forms a structure that
replicates the structure of ice. Both types of sites are only partially
occupied. The CoO2 layer in these structures is robust, on the other hand, and
we find a strong inverse correlation between the CoO2 layer thickness and the
superconducting transition temperature (TC increases with decreasing
thickness). The phonon density-of-states for Na0.3CoO2 exhibits distinct
acoustic and optic bands, with a high-energy cutoff of ~100 meV. The lattice
dynamical scattering for the superconductor is dominated by the hydrogen modes,
with librational and bending modes that are quite similar to ice, supporting
the structural model that the water intercalates and forms ice-like layers in
the superconductor.Comment: 14 pages, 7 figures, Phys. Rev. B (in press). Minor changes + two
figures removed as requested by refere
Low-temperature specific heat and thermal conductivity of glycerol
We have measured the thermal conductivity of glassy glycerol between 1.5 K
and 100 K, as well as the specific heat of both glassy and crystalline phases
of glycerol between 0.5 K and 25 K. We discuss both low-temperature properties
of this typical molecular glass in terms of the soft-potential model. Our
finding of an excellent agreement between its predictions and experimental data
for these two independent measurements constitutes a robust proof of the
capabilities of the soft-potential model to account for the low-temperature
properties of glasses in a wide temperature range.Comment: 4 pages, 3 figures. To be published in Phys. Rev. B (2002
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