727 research outputs found
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
We argue that the freezing transition scenario, previously explored in the
statistical mechanics of 1/f-noise random energy models, also determines the
value distribution of the maximum of the modulus of the characteristic
polynomials of large N x N random unitary (CUE) matrices. We postulate that our
results extend to the extreme values taken by the Riemann zeta-function zeta(s)
over sections of the critical line s=1/2+it of constant length and present the
results of numerical computations in support. Our main purpose is to draw
attention to possible connections between the statistical mechanics of random
energy landscapes, random matrix theory, and the theory of the Riemann zeta
function.Comment: published version with a few misprints corrected and references adde
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
Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble
The paper studies the spectral properties of large Wigner, band and sample
covariance random matrices with heavy tails of the marginal distributions of
matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at
Giens, France on September 13-17, 200
Sub-gap conductance in ferromagnetic-superconducting mesoscopic structures
We study the sub-gap conductance of a ferromagnetic mesoscopic region
attached to a ferromagnetic and a superconducting electrode by means of tunnel
junctions. In the absence of the exchange field, the ratio of the two tunnel junction resistances determines the behaviour of
the sub-gap conductance which possesses a zero-bias peak for and for
a peak at finite voltage. We show that the inclusion of the exchange
field leads to a peak splitting for , while it shifts the zero-bias
anomaly to finite voltages for .Comment: 5 pages revte
Last passage percolation and traveling fronts
We consider a system of N particles with a stochastic dynamics introduced by
Brunet and Derrida. The particles can be interpreted as last passage times in
directed percolation on {1,...,N} of mean-field type. The particles remain
grouped and move like a traveling wave, subject to discretization and driven by
a random noise. As N increases, we obtain estimates for the speed of the front
and its profile, for different laws of the driving noise. The Gumbel
distribution plays a central role for the particle jumps, and we show that the
scaling limit is a L\'evy process in this case. The case of bounded jumps
yields a completely different behavior
Extreme values and fat tails of multifractal fluctuations
In this paper we discuss the problem of the estimation of extreme event
occurrence probability for data drawn from some multifractal process. We also
study the heavy (power-law) tail behavior of probability density function
associated with such data. We show that because of strong correlations,
standard extreme value approach is not valid and classical tail exponent
estimators should be interpreted cautiously. Extreme statistics associated with
multifractal random processes turn out to be characterized by non
self-averaging properties. Our considerations rely upon some analogy between
random multiplicative cascades and the physics of disordered systems and also
on recent mathematical results about the so-called multifractal formalism.
Applied to financial time series, our findings allow us to propose an unified
framemork that accounts for the observed multiscaling properties of return
fluctuations, the volatility clustering phenomenon and the observed ``inverse
cubic law'' of the return pdf tails
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
Anaerobic Carbon Monoxide Dehydrogenase Diversity in the Homoacetogenic Hindgut Microbial Communities of Lower Termites and the Wood Roach
Anaerobic carbon monoxide dehydrogenase (CODH) is a key enzyme in the Wood-Ljungdahl (acetyl-CoA) pathway for acetogenesis performed by homoacetogenic bacteria. Acetate generated by gut bacteria via the acetyl-CoA pathway provides considerable nutrition to wood-feeding dictyopteran insects making CODH important to the obligate mutualism occurring between termites and their hindgut microbiota. To investigate CODH diversity in insect gut communities, we developed the first degenerate primers designed to amplify cooS genes, which encode the catalytic (β) subunit of anaerobic CODH enzyme complexes. These primers target over 68 million combinations of potential forward and reverse cooS primer-binding sequences. We used the primers to identify cooS genes in bacterial isolates from the hindgut of a phylogenetically lower termite and to sample cooS diversity present in a variety of insect hindgut microbial communities including those of three phylogenetically-lower termites, Zootermopsis nevadensis, Reticulitermes hesperus, and Incisitermes minor, a wood-feeding cockroach, Cryptocercus punctulatus, and an omnivorous cockroach, Periplaneta americana. In total, we sequenced and analyzed 151 different cooS genes. These genes encode proteins that group within one of three highly divergent CODH phylogenetic clades. Each insect gut community contained CODH variants from all three of these clades. The patterns of CODH diversity in these communities likely reflect differences in enzyme or physiological function, and suggest that a diversity of microbial species participate in homoacetogenesis in these communities
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Evaluating the structure and magnitude of the ash plume during the initial phase of the 2010 Eyjafjallajökull eruption using lidar observations and NAME simulations
The Eyjafjallajökull volcano in Iceland erupted explosively on 14 April 2010, emitting a plume of ash into the atmosphere. The ash was transported from Iceland toward Europe where mostly cloud-free skies allowed ground-based lidars at Chilbolton in England and Leipzig in Germany to estimate the mass concentration in the ash cloud as it passed overhead. The UK Met Office's Numerical Atmospheric-dispersion Modeling Environment (NAME) has been used to simulate the evolution of the ash cloud from the Eyjafjallajökull volcano during the initial phase of the ash emissions, 14–16 April 2010. NAME captures the timing and sloped structure of the ash layer observed over Leipzig, close to the central axis of the ash cloud. Relatively small errors in the ash cloud position, probably caused by the cumulative effect of errors in the driving meteorology en route, result in a timing error at distances far from the central axis of the ash cloud. Taking the timing error into account, NAME is able to capture the sloped ash layer over the UK. Comparison of the lidar observations and NAME simulations has allowed an estimation of the plume height time series to be made. It is necessary to include in the model input the large variations in plume height in order to accurately predict the ash cloud structure at long range. Quantitative comparison with the mass concentrations at Leipzig and Chilbolton suggest that around 3% of the total emitted mass is transported as far as these sites by small (<100 μm diameter) ash particles
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
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