1,959 research outputs found
Intermittency on catalysts
The present paper provides an overview of results obtained in four recent
papers by the authors. These papers address the problem of intermittency for
the Parabolic Anderson Model in a \emph{time-dependent random medium},
describing the evolution of a ``reactant'' in the presence of a ``catalyst''.
Three examples of catalysts are considered: (1) independent simple random
walks; (2) symmetric exclusion process; (3) symmetric voter model. The focus is
on the annealed Lyapunov exponents, i.e., the exponential growth rates of the
successive moments of the reactant. It turns out that these exponents exhibit
an interesting dependence on the dimension and on the diffusion constant.Comment: 11 pages, invited paper to appear in a Festschrift in honour of
Heinrich von Weizs\"acker, on the occasion of his 60th birthday, to be
published by Cambridge University Pres
Intermittency on catalysts: three-dimensional simple symmetric exclusion
We continue our study of intermittency for the parabolic Anderson model
in a space-time random medium
, where is a positive diffusion constant, is the lattice
Laplacian on , , and is a simple symmetric exclusion
process on in Bernoulli equilibrium. This model describes the evolution
of a \emph{reactant} under the influence of a \emph{catalyst} .
In G\"artner, den Hollander and Maillard (2007) we investigated the behavior
of the annealed Lyapunov exponents, i.e., the exponential growth rates as
of the successive moments of the solution . This led to an
almost complete picture of intermittency as a function of and . In
the present paper we finish our study by focussing on the asymptotics of the
Lyaponov exponents as in the \emph{critical} dimension ,
which was left open in G\"artner, den Hollander and Maillard (2007) and which
is the most challenging. We show that, interestingly, this asymptotics is
characterized not only by a \emph{Green} term, as in , but also by a
\emph{polaron} term. The presence of the latter implies intermittency of
\emph{all} orders above a finite threshold for .Comment: 38 page
Intermittency on catalysts: Voter model
In this paper we study intermittency for the parabolic Anderson equation
with
, where is
the diffusion constant, is the discrete Laplacian,
is the coupling constant, and
is a space--time random medium.
The solution of this equation describes the evolution of a ``reactant''
under the influence of a ``catalyst'' . We focus on the case where
is the voter model with opinions 0 and 1 that are updated according to a random
walk transition kernel, starting from either the Bernoulli measure
or the equilibrium measure , where is the density of
1's. We consider the annealed Lyapunov exponents, that is, the exponential
growth rates of the successive moments of . We show that if the random walk
transition kernel has zero mean and finite variance, then these exponents are
trivial for , but display an interesting dependence on the
diffusion constant for , with qualitatively different
behavior in different dimensions. In earlier work we considered the case where
is a field of independent simple random walks in a Poisson equilibrium,
respectively, a symmetric exclusion process in a Bernoulli equilibrium, which
are both reversible dynamics. In the present work a main obstacle is the
nonreversibility of the voter model dynamics, since this precludes the
application of spectral techniques. The duality with coalescing random walks is
key to our analysis, and leads to a representation formula for the Lyapunov
exponents that allows for the application of large deviation estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOP535 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model
We study birational transformations of the projective space originating from
lattice statistical mechanics, specifically from various chiral Potts models.
Associating these models to \emph{stable patterns} and \emph{signed-patterns},
we give general results which allow us to find \emph{all} chiral -state
spin-edge Potts models when the number of states is a prime or the square
of a prime, as well as several -dependent family of models. We also prove
the absence of monocolor stable signed-pattern with more than four states. This
demonstrates a conjecture about cyclic Hadamard matrices in a particular case.
The birational transformations associated to these lattice spin-edge models
show complexity reduction. In particular we recover a one-parameter family of
integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the
results into two sections : results pertaining to Physics and results
pertaining to Mathematic
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
New Results on the Helium Stars in the Galactic Center Using BEAR Spectro-Imagery
Integral field spectroscopy of the central parsec of the Galactic Center was obtained at 2.06 microns using BEAR, an imaging Fourier Transform Spectrometer, at a spectral resolution of 74 km/s. Sixteen stars were confirmed as helium stars by detecting the He I 2.058 microns line in emission, providing a homogeneous set of fully resolved line profiles. These observations allow us to discard some of the earlier detections of such stars in the central cluster and to add three new stars. The sources detected in the BEAR data were compared with adaptive optics images in the K band to determine whether the emission was due to single stars. Two sub-classes of almost equal number are clearly identified from the width of their line profiles, and from the brightness of their continuum. Most of the emission lines show a P Cygni profile. From these results, we propose that the latter group is formed of stars in or near the LBV phase, and the other one of stars at the WR stage. The division into two groups is also shown by their spatial distribution, with the narrow-line stars in a compact central cluster (IRS 16) and the other group distributed at the periphery of the central cluster of hot stars. In the same data cube, streamers of interstellar helium gas are also detected. The helium emission traces the densest parts of the SgrA West Mini-Spiral. Several helium stars have a radial velocity comparable to the velocity of the interstellar gas in which they are embedded. In the final discussion, all these findings are examined to present a possible scenario for the formation of very massive stars in the exceptional conditions of the vicinity of the central Black Hole
Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices
A conjecture is given for the exact location of the multicritical point in
the phase diagram of the +/- J Ising model on the triangular lattice. The
result p_c=0.8358058 agrees well with a recent numerical estimate. From this
value, it is possible to derive a comparable conjecture for the exact location
of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in
excellent agreement with a numerical study. The method is a variant of duality
transformation to relate the triangular lattice directly with its dual
triangular lattice without recourse to the hexagonal lattice, in conjunction
with the replica method.Comment: 9 pages, 1 figure; Minor corrections in notatio
Comparison of the efficacy of natural-based and synthetic biocides to disinfect silicone and stainless steel surfaces
New biocidal solutions are needed to combat effectively the evolution of microbes developing antibiotic resistance while having a low or no environmental toxicity impact. This work aims to assess the efficacy of commonly used biocides and natural-based compounds on the disinfection of silicone and stainless steel (SS) surfaces seeded with different Staphylococcus aureus strains. Minimum inhibitory concentration was determined for synthetic (benzalkonium chloride-BAC, glutaraldehyde-GTA, ortho-phthalaldehyde-OPA and peracetic acid-PAA) and natural-based (cuminaldehyde-CUM), eugenol-EUG and indole-3-carbinol-I3C) biocides by the microdilution method. The efficacy of selected biocides at MIC, 10ĂMIC and 5500 mg/L (representative in-use concentration) on the disinfection of sessile S. aureus on silicone and SS was assessed by viable counting. Silicone surfaces were harder to disinfect than SS. GTA, OPA and PAA yielded complete CFU reduction of sessile cells for all test concentrations as well as BAC at 10ĂMIC and 5500 mg/L. CUM was the least efficient compound. EUG was efficient for SS disinfection, regardless of strains and concentrations tested. I3C at 10ĂMIC and 5500 mg/L was able to cause total CFU reduction of silicone and SS deposited bacteria. Although not so efficient as synthetic compounds, the natural-based biocides are promising to be used in disinfectant formulations, particularly I3C and EUG
On the complexity of some birational transformations
Using three different approaches, we analyze the complexity of various
birational maps constructed from simple operations (inversions) on square
matrices of arbitrary size. The first approach consists in the study of the
images of lines, and relies mainly on univariate polynomial algebra, the second
approach is a singularity analysis, and the third method is more numerical,
using integer arithmetics. Each method has its own domain of application, but
they give corroborating results, and lead us to a conjecture on the complexity
of a class of maps constructed from matrix inversions
Multicritical Points of Potts Spin Glasses on the Triangular Lattice
We predict the locations of several multicritical points of the Potts spin
glass model on the triangular lattice. In particular, continuous multicritical
lines, which consist of multicritical points, are obtained for two types of
two-state Potts (i.e., Ising) spin glasses with two- and three-body
interactions on the triangular lattice. These results provide us with numerous
examples to further verify the validity of the conjecture, which has succeeded
in deriving highly precise locations of multicritical points for several spin
glass models. The technique, called the direct triangular duality, a variant of
the ordinary duality transformation, directly relates the triangular lattice
with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure
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