Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Deducing Receptor Signaling Parameters from In Vivo Analysis: LuxN/AI-1 Quorum Sensing in Vibrio harveyi

SummaryQuorum sensing, a process of bacterial cell-cell communication, relies on production, detection, and response to autoinducer signaling molecules. LuxN, a nine-transmembrane domain protein from Vibrio harveyi, is the founding example of membrane-bound receptors for acyl-homoserine lactone (AHL) autoinducers. We used mutagenesis and suppressor analyses to identify the AHL-binding domain of LuxN and discovered LuxN mutants that confer both decreased and increased AHL sensitivity. Our analysis of dose-response curves of multiple LuxN mutants pins these inverse phenotypes on quantifiable opposing shifts in the free-energy bias of LuxN for occupying its kinase and phosphatase states. To understand receptor activation and to characterize the pathway signaling parameters, we exploited a strong LuxN antagonist, one of fifteen small-molecule antagonists we identified. We find that quorum-sensing-mediated communication can be manipulated positively and negatively to control bacterial behavior and, more broadly, that signaling parameters can be deduced from in vivo data

The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

The problem of finding the exact energies and configurations for the Frenkel-Kontorova model consisting of particles in one dimension connected to their nearest-neighbors by springs and placed in a periodic potential consisting of segments from parabolas of identical (positive) curvature but arbitrary height and spacing, is reduced to that of minimizing a certain convex function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6 Postscript figures, accepted by Phys. Rev.

Mean-Field Analysis and Monte Carlo Study of an Interacting Two-Species Catalytic Surface Reaction Model

We study the phase diagram and critical behavior of an interacting one dimensional two species monomer-monomer catalytic surface reaction model with a reactive phase as well as two equivalent adsorbing phase where one of the species saturates the system. A mean field analysis including correlations up to triplets of sites fails to reproduce the phase diagram found by Monte Carlo simulations. The three phases coexist at a bicritical point whose critical behavior is described by the even branching annihilating random walk universality class. This work confirms the hypothesis that the conservation modulo 2 of the domain walls under the dynamics at the bicritical point is the essential feature in producing critical behavior different from directed percolation. The interfacial fluctuations show the same universal behavior seen at the bicritical point in a three-species model, supporting the conjecture that these fluctuations are a new universal characteristic of the model.Comment: 11 pages using RevTeX, plus 4 Postscript figures. Uses psfig.st

Isotropic Transverse XY Chain with Energy- and Magnetization Currents

The ground-state correlations are investigated for an isotropic transverse XY chain which is constrained to carry either a current of magnetization J_M or a current of energy J_E. We find that the effect of nonzero J_M on the large-distance decay of correlations is twofold: i) oscillations are introduced and ii) the amplitude of the power law decay increases with increasing current. The effect of energy current is more complex. Generically, correlations in current carrying states are found to decay faster than in the J_E=0 states, contrary to expectations that correlations are increased by the presence of currents. However, increasing the current, one reaches a special line where the correlations become comparable to those of the J_E=0 states. On this line, the symmetry of the ground state is enhanced and the transverse magnetization vanishes. Further increase of the current destroys the extra symmetry but the transverse magnetization remains at the high-symmetry, zero value.Comment: 7 pages, RevTex, 4 PostScript figure

Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $\Theta = 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys. Rev.

TERMINOLOGIA DESCRITIVA PARA ANÁLISE SENSORIAL DE TOMATE DE MESA

Foi desenvolvida através da metodologia da análise descritiva quantitativa (ADQ) a terminologia para análise sensorial de tomate de mesa convencional e orgânico, (Lycopersicon esculentum Mill.). Foramselecionados e treinados os julgadores e, emconsenso, a equipe escolheu os descritores, suas definições e a ficha de avaliação das amostras. Dezoito termos descritores foram definidos, levando em consideração os defeitos apontados pelos produtores orgânicos, legislação em vigor do produto e as características sensoriais relevantes observadas pelos julgadores. A ficha de avaliação foi elaborada para determinar a intensidade de cada descritor que foi medida através de escala não estruturada de nove centímetros, com os termos ancorados em seus extremos. DESCRIPTIVE TERMINOLOGY FOR THE SENSORY ANALYSIS OF TOMATO FOR FRESH CONSUMPTION Abstract Using the quantitative descriptive analysis (QDA) methodology, the terms for the sensory assessment of conventional and organic tomato (Lycopersicon esculentum Mill.) for fresh consumption were established. The panelists were selected and trained, and together the group built up the descriptors, their definition and the sample evaluation card. Eighteen descriptors were defined based on the defects pointed out by organic producers, the legislation for tomatoes and the relevant sensory characteristics pointed out by the panelists. The evaluation fiche was used to determine the intensity of each descriptor who was evaluated using a 9 cm unstructured line scale with anchor points

Experiments in vortex avalanches

Avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. It can be also found in vortex matter when a type II superconductor is externally driven, for example, by increasing the magnetic field. Vortex avalanches associated with thermal instabilities can be an undesirable effect for applications, but "dynamically driven" avalanches emerging from the competition between intervortex interactions and quenched disorder constitute an interesting scenario to test theoretical ideas related with non-equilibrium dynamics. However, differently from the equilibrium phases of vortex matter in type II superconductors, the study of the corresponding dynamical phases - in which avalanches can play a role - is still in its infancy. In this paper we critically review relevant experiments performed in the last decade or so, emphasizing the ability of different experimental techniques to establish the nature and statistical properties of the observed avalanche behavior.Comment: To be published in Reviews of Modern Physics April 2004. 17 page

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.Comment: 15 pages, 4 figure

Directed avalanche processes with underlying interface dynamics

We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower dimension. In our specific case, the interface growth dynamics belongs to the Kardar-Parisi-Zhang (KPZ) universality class. We formulate relations between the critical exponents of the various avalanche distributions and those of the roughness of the growing interface. The nonlinear nature of the underlying KPZ dynamics provides a nontrivial test of such generic exponent relations. The numerical values of the avalanche exponents are close to the conventional KPZ values, but differ sufficiently to warrant a detailed study of whether avalanche correlated Monte Carlo sampling changes the scaling exponents of KPZ interfaces. We demonstrate that the exponents remain unchanged, but that the traces left on the surface by previous avalanches give rise to unusually strong finite-size corrections to scaling. This type of slow convergence seems intrinsic to avalanche dynamics.Comment: 13 pages, 13 figure