Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with L(2) whereas the size of the largest cluster grows with ln L(2). The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model-Axelrod's model-we found that these opinion domains are unstable to the effect of a thermal-like noise.

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J, and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices, and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

Ultrasensitive thermal lens spectroscopy of water

A recently developed dual-beam configuration that optimizes the thermal lens technique has been used to obtain the absorption spectrum of pure water from 350 to 528 nm. Our results indicate the minimum linear absorption coefficient smaller than 2 X 10(-5) cm(-1) between 360 and 400 nm. This value is lower than previous literature data, and it is blueshifted. Absorption coefficients as small as 2 X 10(-7) cm(-1) can be measured for water using 1 W of excitation power. A detection limit of similar to 6 X 10(-9) cm(-1) (P=1 W) for CCl(4) was estimated, which represents, to the best of our knowledge, the highest sensitivity obtained in small absorption measurements in liquids. (C) 2009 Optical Society of America

Kondo screening regimes of a quantum dot with a single Mn ion

We study the Kondo and transport properties of a quantum dot with a single magnetic Mn ion connected to metallic leads. By employing a numerical renormalization group technique we show that depending on the value of ferromagnetic coupling strength between the local electronic spin and the magnetic moment of the Mn, two distinct Kondo regimes exist. In the weak-coupling limit, the system can be found in a completely screened Kondo state describing a local magnetic moment decoupled from the rest of the system. In contrast, in the strong-coupling regime the quantum dot spin and the local magnetic moment form a single large-spin entity partially Kondo screened. A crossover between these two regimes can be suitably tuned by varying the tunnel coupling between the quantum dot and the leads. The model investigated here is also suitable to study magnetic molecules adsorbed on a metallic surface. The rich phenomenology of these systems is reflected in the conductance across the system.

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

Exceptional times for the dynamical discrete web

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter tau. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed tau. In this paper, we study the existence of exceptional (random) values of tau where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of such exceptional tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by Haggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in the DyDW is rather different from the situation for the dynamical random walks of Benjamini, Haggstrom, Peres and Steif. For example, we prove that the walk from the origin S(0)(tau) violates the law of the iterated logarithm (LIL) on a set of tau of Hausdorff dimension one. We also discuss how these and other results should extend to the dynamical Brownian web, the natural scaling limit of the DyDW. (C) 2009 Elsevier B.V. All rights reserved.

A PHASE TRANSITION FOR COMPETITION INTERFACES

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle theta of the cone: for theta >= 180 degrees, the direction is deterministic, while for theta < 180 degrees, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.

GEVREY SOLVABILITY AND GEVREY REGULARITY IN DIFFERENTIAL COMPLEXES ASSOCIATED TO LOCALLY INTEGRABLE STRUCTURES

In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, Gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition. As a consequence we obtain the proof of the Gevrey solvability for a first order linear PDE with real-analytic coefficients satisfying the Nirenberg-Treves condition (P).

An oracle approach for interaction neighborhood estimation in random fields

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

Cloud point extraction to avoid interferences by structured background on nickel determination in plant materials by FAAS

An analytical procedure based on microwave-assisted digestion with diluted acid and a double cloud point extraction is proposed for nickel determination in plant materials by flame atomic absorption spectrometry. Extraction in micellar medium was successfully applied for sample clean up, aiming to remove organic species containing phosphorous that caused spectral interferences by structured background attributed to the formation of PO species in the flame. Cloud point extraction of nickel complexes formed with 1,2-thiazolylazo-2-naphthol was explored for pre-concentration, with enrichment factor estimated as 30, detection limit of 5 mu g L(-1) (99.7% confidence level) and linear response up to 80 mu g L(-1). The accuracy of the procedure was evaluated by nickel determinations in reference materials and the results agreed with the certified values at the 95% confidence level.

Quantification of some nonsteroidal anti-inflammatory drugs as reducing agents of Cu(II)/4,4 '-dicarboxy-2,2 '-biquinoline complexes in cationic micellar medium

A simple method was developed for spectrophotometric determination of some nonsteroidal anti-inflammatory drugs (meloxicam, piroxicam and tenoxicam) based on the reduction of copper(II) in buffered solution (pH 7.0) and micellar medium containing 4,4'-dicarboxy-2,2'-buffered solution (pH 7.0) and micellar medium containing 4,4'-dicarboxy-2,2'-biquinoline acid. The-biquinoline acid. The absorbance values at 558 nm, characteristic of the formed Cu(I)/4,4'-dicarboxy-2,2'-biquinoline complexes, are linear with the concentrations (5.7-40 mmol L(-1), n = 5) of these oxicams (meloxicam r = 0.998; piroxicam and tenoxicam r = 0.999). The limit of detection values, in mmol L(-1), calculated for meloxicam (2.7), piroxicam (1.2) and tenoxicam (1.3) was obtained with 99% confidence level and the relative standard deviations for meloxicam (3.1%), piroxicam (5.1%) and tenoxicam (1.2%) were calculated using a 25 mmol L(-1) solution (n = 7). Mean recovery values for meloxicam, piroxicam and tenoxicam forms were 100 +/- 6.9, 98.6 +/- 3.6 and 99.4 +/- 2.5%, respectively. The conditional potential of Cu(II)/Cu(I) in complex medium of 7.5 mmol L(-1) BCA was determined to be 629 +/- 11 mV vs. NHE.

On the template synthesis of nanostructured inorganic/organic hybrid films

Prussian Blue has been introduced as a mediator to achieve stable, sensitive, reproducible, and interference-free biosensors. However, Na(+), Li(+), H(+), and all group II cations are capable to block the activity of Prussian Blue and, because Na(+) can be found in most human fluids, Prussian Blue analogs have already been developed to overcome this problem. These analogs, such as copper hexacyanoferrate, have also been introduced in a conducting polypyrrole matrix to create hybrid materials (copper hexacyanoferrate/polypyrrole, CuHCNFe/Ppy) with improved mechanical and electrochemical characteristics. Nowadays, the challenges in amperometric enzymatic biosensors consist of improving the enzyme immobilization and in making the chemical signal transduction more efficient. The incorporation of nanostructured materials in biosensors can optimize both steps and a nanostructured hybrid CuHCNFe/Ppy mediator has been developed using a template of colloidal polystyrene particles. The nanostructured material has achieved sensitivities 7.6 times higher than the bulk film during H(2)O(2) detection and it has also presented better results in other analytical parameters such as time response and detection limit. Besides, the nanostructured mediator was successfully applied at glucose biosensing in electrolytes containing Prussian Blue blocking cations. (C) 2008 The Electrochemical Society.

Continuous monitoring of ascorbate transport through neuroblastoma cells with a ruthenium oxide hexacyanoferrate modified microelectrode

The uptake of ascorbate by neuroblastoma cells using a ruthenium oxide hexacyanoferrate (RuOHCF)-modified carbon fiber disc (CFD) microelectrode (r = 14.5 mu m) was investigated. By use of the proposed electrochemical sensor the amperometric determination of ascorbate was performed at 0.0 V in minimum essential medium (MEM, pH = 7.2) with a limit of detection of 25 mu mol L(-1). Under the optimum experimental conditions, no interference from MEM constituents and reduced glutathione (used to prevent the oxidation of ascorbate during the experiments) was noticed. The stability of the RuOHCF-modified electrode response was studied by measuring the sensitivity over an extended period of time (120 h), a decrease of around 10% being noticed at the end of the experiment. The rate of ascorbate uptake by control human neuroblastoma SH-SY5Y cells, and cells transfected with wild-type Cu,Zn-superoxide dismutase (SOD WT) or with a mutant typical of familial amyotrophic lateral sclerosis (SOD G93A), was in agreement with the level of oxidative stress in these cells. The usefulness of the RuOHCF-modified microelectrode for in vivo monitoring of ascorbate inside neuroblastoma cells was also demonstrated.