322 research outputs found
Spectral responses in granular compaction
The slow compaction of a gently tapped granular packing is reminiscent of the
low-temperature dynamics of structural and spin glasses. Here, I probe the
dynamical spectrum of granular compaction by measuring a complex
(frequency-dependent) volumetric susceptibility . While the
packing density displays glass-like slow relaxations (aging) and
history-dependence (memory) at low tapping amplitudes, the susceptibility
displays very weak aging effects, and its spectrum shows no
sign of a rapidly growing timescale. These features place in
sharp contrast to its dielectric and magnetic counterparts in structural and
spin glasses; instead, bears close similarities to the complex
specific heat of spin glasses. This, I suggest, indicates the glass-like
dynamics in granular compaction are governed by statistically rare relaxation
processes that become increasingly separated in timescale from the typical
relaxations of the system. Finally, I examine the effect of finite system size
on the spectrum of compaction dynamics. Starting from the ansatz that low
frequency processes correspond to large scale particle rearrangements, I
suggest the observed finite size effects are consistent with the suppression of
large-scale collective rearrangements in small systems.Comment: 18 pages, 17 figures. Submitted to PR
Non-universality of compact support probability distributions in random matrix theory
The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials V(M)=M2p. Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their nonuniversality
Correlations between eigenvalues of large random matrices with independent entries
We derive the connected correlation functions for eigenvalues of large
Hermitian random matrices with independently distributed elements using both a
diagrammatic and a renormalization group (RG) inspired approach. With the
diagrammatic method we obtain a general form for the one, two and three-point
connected Green function for this class of ensembles when matrix elements are
identically distributed, and then discuss the derivation of higher order
functions by the same approach. Using the RG approach we re-derive the one and
two-point Green functions and show they are unchanged by choosing certain
ensembles with non-identically distributed elements. Throughout, we compare the
Green functions we obtain to those from the class of ensembles with unitary
invariant distributions and discuss universality in both ensemble classes.Comment: 23 pages, RevTex, hard figures available from [email protected]
Double sign reversal of the vortex Hall effect in YBa2Cu3O7-delta thin films in the strong pinning limit of low magnetic fields
Measurements of the Hall effect and the resistivity in twinned
YBa2Cu3O7-delta thin films in magnetic fields B oriented parallel to the
crystallographic c-axis and to the twin boundaries reveal a double sign
reversal of the Hall coefficient for B below 1 T. In high transport current
densities, or with B tilted off the twin boundaries by 5 degrees, the second
sign reversal vanishes. The power-law scaling of the Hall conductivity to the
longitudinal conductivity in the mixed state is strongly modified in the regime
of the second sign reversal. Our observations are interpreted as strong,
disorder-type dependent vortex pinning and confirm that the Hall conductivity
in high temperature superconductors is not independent of pinning.Comment: 4 pages, 4 figure
The Maximal Denumerant of a Numerical Semigroup
Given a numerical semigroup S = and n in S, we
consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >=
0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over
all such factorizations of n. We provide an algorithm for computing the maximum
number of maximal factorizations possible for an element in S, which is called
the maximal denumerant of S. We also consider various cases that have
connections to the Cohen-Macualay and Gorenstein properties of associated
graded rings for which this algorithm simplifies.Comment: 13 Page
"Single Ring Theorem" and the Disk-Annulus Phase Transition
Recently, an analytic method was developed to study in the large limit
non-hermitean random matrices that are drawn from a large class of circularly
symmetric non-Gaussian probability distributions, thus extending the existing
Gaussian non-hermitean literature. One obtains an explicit algebraic equation
for the integrated density of eigenvalues from which the Green's function and
averaged density of eigenvalues could be calculated in a simple manner. Thus,
that formalism may be thought of as the non-hermitean analog of the method due
to Br\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian
random matrices. A somewhat surprising result is the so called "Single Ring"
theorem, namely, that the domain of the eigenvalue distribution in the complex
plane is either a disk or an annulus. In this paper we extend previous results
and provide simple new explicit expressions for the radii of the eigenvalue
distiobution and for the value of the eigenvalue density at the edges of the
eigenvalue distribution of the non-hermitean matrix in terms of moments of the
eigenvalue distribution of the associated hermitean matrix. We then present
several numerical verifications of the previously obtained analytic results for
the quartic ensemble and its phase transition from a disk shaped eigenvalue
distribution to an annular distribution. Finally, we demonstrate numerically
the "Single Ring" theorem for the sextic potential, namely, the potential of
lowest degree for which the "Single Ring" theorem has non-trivial consequences.Comment: latex, 5 eps figures, 41 page
Continuous Lidocaine Infusions to Manage OpioidâRefractory Pain in a Series of Cancer Patients in a Pediatric Hospital
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134501/1/pbc25870.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134501/2/pbc25870_am.pd
Vibration-induced "thermally activated" jamming transition in granular media
The quasi-static frequency response of a granular medium is measured by a
forced torsion oscillator method, with forcing frequency in the range
Hz to 5 Hz, while weak vibrations at high-frequency , in the
range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of
vibration, , is below the fluidization limit. A loss factor peak is
observed in the oscillator response as a function of or . In a
plot of against , the position of the peak follows an
Arrhenius-like behaviour over four orders of magnitude in . The data can
be described as a stochastic hopping process involving a probability factor
with a -dependent characteristic
vibration intensity. A -independent description is given by
, with an intrinsic characteristic time, and
, n=0.5-0.6, an empirical control parameter with
unit of time. is seen as the effective average time during which the
perturbed grains can undergo structural rearrangement. The loss factor peak
appears as a crossover in the dynamic behaviour of the vibrated granular
system, which, at the time-scale , is solid-like at low , and
the oscillator is jammed into the granular material, and is fluid-like at high
, where the oscillator can slide viscously.Comment: Final version to appear in PR
Aging in humid granular media
Aging behavior is an important effect in the friction properties of solid
surfaces. In this paper we investigate the temporal evolution of the static
properties of a granular medium by studying the aging over time of the maximum
stability angle of submillimetric glass beads. We report the effect of several
parameters on these aging properties, such as the wear on the beads, the stress
during the resting period, and the humidity content of the atmosphere. Aging
effects in an ethanol atmosphere are also studied. These experimental results
are discussed at the end of the paper.Comment: 7 pages, 9 figure
Melting of Flux Lines in an Alternating Parallel Current
We use a Langevin equation to examine the dynamics and fluctuations of a flux
line (FL) in the presence of an {\it alternating longitudinal current}
. The magnus and dissipative forces are equated to those
resulting from line tension, confinement in a harmonic cage by neighboring FLs,
parallel current, and noise. The resulting mean-square FL fluctuations are
calculated {\it exactly}, and a Lindemann criterion is then used to obtain a
nonequilibrium `phase diagram' as a function of the magnitude and frequency of
. For zero frequency, the melting temperature of the
mixed phase (a lattice, or the putative "Bose" or "Bragg Glass") vanishes at a
limiting current. However, for any finite frequency, there is a non-zero
melting temperature.Comment: 5 pages, 1 figur
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