4,844 research outputs found
On principal hook length partitions and durfee sizes in skew characters
In this paper we construct for a given arbitrary skew diagram A all
partitions nu with maximal principal hook lengths among all partitions with the
character [nu] appearing in the skew character [A]. Furthermore we show that
these are also partitions with minimal Durfee size. This we use to give the
maximal Durfee size for [nu] appearing in [A] for the cases when A decays into
two partitions and for some special cases of A. Also this gives conditions for
two skew diagrams to represent the same skew character.Comment: 13 pages, minor changes from v1 to v2 as suggested by the referee, to
appear in Annals. Com
Equality of multiplicity free skew characters
In this paper we show that two skew diagrams lambda/mu and alpha/beta can
represent the same multiplicity free skew character [lambda/mu]=[alpha/beta]
only in the the trivial cases when lambda/mu and alpha/beta are the same up to
translation or rotation or if lambda=alpha is a staircase partition
lambda=(l,l-1,...,2,1) and lambda/mu and alpha/beta are conjugate of each
other.Comment: 16 pages, changes from v1 to v2: corrected the proof of Theorem 3.5
and some typos, changes from v2 to v3: minor layout change, enumeration
changed, to appear in J. Algebraic Combi
Energy flows in vibrated granular media
We study vibrated granular media, investigating each of the three components
of the energy flow: particle-particle dissipation, energy input at the
vibrating wall, and particle-wall dissipation. Energy dissipated by
interparticle collisions is well estimated by existing theories when the
granular material is dilute, and these theories are extended to include
rotational kinetic energy. When the granular material is dense, the observed
particle-particle dissipation rate decreases to as little as 2/5 of the
theoretical prediction. We observe that the rate of energy input is the weight
of the granular material times an average vibration velocity times a function
of the ratio of particle to vibration velocity. `Particle-wall' dissipation has
been neglected in all theories up to now, but can play an important role when
the granular material is dilute. The ratio between gravitational potential
energy and kinetic energy can vary by as much as a factor of 3. Previous
simulations and experiments have shown that E ~ V^delta, with delta=2 for
dilute granular material, and delta ~ 1.5 for dense granular material. We
relate this change in exponent to the departure of particle-particle
dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR
Temperature scaling in a dense vibro-fluidised granular material
The leading order "temperature" of a dense two dimensional granular material
fluidised by external vibrations is determined. An asymptotic solution is
obtained where the particles are considered to be elastic in the leading
approximation. The velocity distribution is a Maxwell-Boltzmann distribution in
the leading approximation. The density profile is determined by solving the
momentum balance equation in the vertical direction, where the relation between
the pressure and density is provided by the virial equation of state. The
predictions of the present analysis show good agreement with simulation results
at higher densities where theories for a dilute vibrated granular material,
with the pressure-density relation provided by the ideal gas law, are in error.
The theory also predicts the scaling relations of the total dissipation in the
bed reported by McNamara and Luding (PRE v 58, p 813).Comment: ReVTeX (psfrag), 5 pages, 5 figures, Submitted to PR
Relation between Stochastic Resonance and Synchronization of Passages in a Double-Well System
We calculate, numerically, the residence times (and their distribution) of a
Brownian particle in a two-well system under the action of a periodic,
saw-tooth type, external field. We define hysteresis in the system. The
hysteresis loop area is shown to be a good measure of synchronization of
passages from one well to the other. We establish connection between this
stochastic synchronization and stochastic resonance in the system.Comment: To appear in PRE May 1997, figures available on reques
Sand as Maxwell's demon
We consider a dilute gas of granular material inside a box, kept in a
stationary state by shaking. A wall separates the box into two identical
compartments, save for a small hole at some finite height . As the gas is
cooled, a second order phase transition occurs, in which the particles
preferentially occupy one side of the box. We develop a quantitative theory of
this clustering phenomenon and find good agreement with numerical simulations
Self-diffusion in granular gases
The coefficient of self-diffusion for a homogeneously cooling granular gas
changes significantly if the impact-velocity dependence of the restitution
coefficient is taken into account. For the case of a constant
the particles spread logarithmically slow with time, whereas the
velocity dependent coefficient yields a power law time-dependence. The impact
of the difference in these time dependences on the properties of a freely
cooling granular gas is discussed.Comment: 6 pages, no figure
O-6 Optical Property Degradation of the Hubble Space Telescope's Wide Field Camera-2 Pick Off Mirror
Degradation in the performance of optical components can be greatly affected by exposure to the space environment. Many factors can contribute to such degradation including surface contaminants; outgassing; vacuum, UV, and atomic oxygen exposure; temperature cycling; or combinations of parameters. In-situ observations give important clues to degradation processes, but there are relatively few opportunities to correlate those observations with post-flight ground analyses. The return of instruments from the Hubble Space Telescope (HST) after its final servicing mission in May 2009 provided such an opportunity. Among the instruments returned from HST was the Wide-Field Planetary Camera-2 (WFPC-2), which had been exposed to the space environment for 16 years. This work focuses on the identifying the sources of degradation in the performance of the Pick-off mirror (POM) from WFPC-2. Techniques including surface reflectivity measurements, spectroscopic ellipsometry, FTIR (and ATR-FTIR) analyses, SEM/EDS, X-ray photoelectron spectroscopy (XPS) with and without ion milling, and wet and dry physical surface sampling were performed. Destructive and contact analyses took place only after completion of the non-destructive measurements. Spectroscopic ellipsometry was then repeated to determine the extent of contaminant removal by the destructive techniques, providing insight into the nature and extent of polymerization of the contaminant layer
Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems
The statistics of transitions between the metastable states of a periodically
driven bistable Brownian oscillator are investigated on the basis of a
two-state description by means of a master equation with time-dependent rates.
The results are compared with extensive numerical simulations of the Langevin
equation for a sinusoidal driving force. Very good agreement is achieved both
for the counting statistics of the number of transitions and the residence time
distribution of the process in either state. The counting statistics
corroborate in a consistent way the interpretation of stochastic resonance as a
synchronisation phenomenon for a properly defined generalized Rice phase.Comment: 15 pages, 9 figure
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