158 research outputs found
Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
The two-dimensional one-component plasma (2dOCP) is a system of mobile
particles of the same charge on a surface with a neutralising background.
The Boltzmann factor of the 2dOCP at temperature can be expressed as a
Vandermonde determinant to the power . Recent advances in
the theory of symmetric and anti-symmetric Jack polymonials provide an
efficient way to expand this power of the Vandermonde in their monomial basis,
allowing the computation of several thermodynamic and structural properties of
the 2dOCP for values up to 14 and equal to 4, 6 and 8. In this
work, we explore two applications of this formalism to study the moments of the
pair correlation function of the 2dOCP on a sphere, and the distribution of
radial linear statistics of the 2dOCP in the plane
Two-dimensional one-component plasma on a Flamm's paraboloid
We study the classical non-relativistic two-dimensional one-component plasma
at Coulomb coupling Gamma=2 on the Riemannian surface known as Flamm's
paraboloid which is obtained from the spatial part of the Schwarzschild metric.
At this special value of the coupling constant, the statistical mechanics of
the system are exactly solvable analytically. The Helmholtz free energy
asymptotic expansion for the large system has been found. The density of the
plasma, in the thermodynamic limit, has been carefully studied in various
situations
Critical behavior of Josephson-junction arrays at f=1/2
The critical behavior of frustrated Josephson-junction arrays at flux
quantum per plaquette is considered. Results from Monte Carlo simulations and
transfer matrix computations support the identification of the critical
behavior of the square and triangular classical arrays and the one-dimensional
quantum ladder with the universality class of the XY-Ising model. In the
quantum ladder, the transition can happen either as a simultaneous ordering of
the and order parameters or in two separate stages, depending on
the ratio between interchain and intrachain Josephson couplings. For the
classical arrays, weak random plaquette disorder acts like a random field and
positional disorder as random bonds on the variables. Increasing
positional disorder decouples the and variables leading to the
same critical behavior as for integer .Comment: 9 pages, Latex, workshop on JJA, to appear in Physica
Glassy Vortex State in a Two-Dimensional Disordered XY-Model
The two-dimensional XY-model with random phase-shifts on bonds is studied.
The analysis is based on a renormalization group for the replicated system. The
model is shown to have an ordered phase with quasi long-range order. This
ordered phase consists of a glass-like region at lower temperatures and of a
non-glassy region at higher temperatures. The transition from the disordered
phase into the ordered phase is not reentrant and is of a new universality
class at zero temperature. In contrast to previous approaches the disorder
strength is found to be renormalized to larger values. Several correlation
functions are calculated for the ordered phase. They allow to identify not only
the transition into the glassy phase but also an additional crossover line,
where the disconnected vortex correlation changes its behavior on large scales
non-analytically. The renormalization group approach yields the glassy features
without a breaking of replica symmetry.Comment: latex 12 pages with 3 figures, using epsf.sty and multicol.st
Asynchronous food-web pathways could buffer the response of Serengeti predators to El Niño southern oscillation
Understanding how entire ecosystems maintain stability in the face of climatic and human disturbance is one of the most fundamental challenges in ecology. Theory suggests that a crucial factor determining the degree of ecosystem stability is simply the degree of synchrony with which different species in ecological food webs respond to environmental stochasticity. Ecosystems in which all food-web pathways are affected similarly by external disturbance should amplify variability in top carnivore abundance over time due to population interactions, whereas ecosystems in which a large fraction of pathways are nonresponsive or even inversely responsive to external disturbance will have more constant levels of abundance at upper trophic levels. To test the mechanism underlying this hypothesis, we used over half a century of demographic data for multiple species in the Serengeti (Tanzania) ecosystem to measure the degree of synchrony to variation imposed by an external environmental driver, the El Niño Southern Oscillation (ENSO). ENSO effects were mediated largely via changes in dry-season vs. wet-season rainfall and consequent changes in vegetation availability, propagating via bottom-up effects to higher levels of the Serengeti food web to influence herbivores, predators and parasites. Some species in the Serengeti food web responded to the influence of ENSO in opposite ways, whereas other species were insensitive to variation in ENSO. Although far from conclusive, our results suggest that a diffuse mixture of herbivore responses could help buffer top carnivores, such as Serengeti lions, from variability in climate. Future global climate changes that favor some pathways over others, however, could alter the effectiveness of such processes in the future
Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz-Thouless Critical Exponent
We present an exact derivation for the asymptotic large distance behavior of
the spin two-point correlation function in the XY-model. This allows for the
exact obtainment of the critical exponent at the Kosterlitz-Thouless
transition that occurs in this model and in the 2D neutral Coulomb gas and
which has been previously obtained by scaling arguments. In order to do that,
we use the language of sine-Gordon theory to obtain a Coulomb Gas description
of the XY-model spin correlation function, which becomes identified with the
soliton correlator of that theory. Using a representation in terms of bipolar
coordinates we obtain an exact expression for the asymptotic large distance
behavior of the relevant correlator at , which corresponds to the
Kosterlitz-Thouless transition. The result is obtained by approaching this
point from the plasma (high-temperature) phase of the gas. The vortex
correlator of the XY-model is also obtained using the same procedure.Comment: To appear in J. Stat. Phys., 11 page
Stochastic processes and conformal invariance
We discuss a one-dimensional model of a fluctuating interface with a dynamic
exponent . The events that occur are adsorption, which is local, and
desorption which is non-local and may take place over regions of the order of
the system size. In the thermodynamic limit, the time dependence of the system
is given by characters of the conformal field theory of percolation. This
implies in a rigorous way a connection between CFT and stochastic processes.
The finite-size scaling behavior of the average height, interface width and
other observables are obtained. The avalanches produced during desorption are
analyzed and we show that the probability distribution of the avalanche sizes
obeys finite-size scaling with new critical exponents.Comment: 4 pages, 6 figures, revtex4. v2: change of title and minor
correction
Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
Feeding ecology of five commercial shark species of the Celtic Sea through stable isotope and trace metal analysis
In order to trace their feeding habits, stable carbon and nitrogen isotope ratios (delta(15)N and delta(13)C), as well as trace metal concentrations (Zn, Cd, Fe, Cu, Se and Hg) were analysed in the tissues of five commercial shark species from the Celtic Sea: the tope shark Galeorhinus galeus, the black-mouthed catshark Galeus melastomus, the starry smooth hound Mustelus asterias, the spiny dogfish Squalus acanthias and the lesser-spotted dogfish Scyliorhinus canicula. Our results were compared to previously described stomach contents and isotopic composition of potential preys. Isotopic ratio delta(15)N suggested that tope sharks fed at a higher trophic level (16.7 parts per thousand in the muscle) than the other species, reflecting its piscivorous diet. The lower values of spiny dogfish (11.6 parts per thousand in the muscle) might be explained, amongst other things, by either its migratory behaviour or its preference for preys from lower trophic levels. Cd and Hg were correlated with isotopic ratios delta(13)C and delta(15)N, and were shown to be diet-related whereas Zn, Fe and Cu seemed much more linked to species-specific metabolism. Although this multidisciplinary approach is revealed as a useful tool for the study of shark ecology, the lack of known trophic fractionation suggests that isotopic data be compared to traditional diet analyses. (c) 2005 Elsevier Ltd. All rights reserved.Peer reviewe
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