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M L Lyra

Publications and source records attributed to M L Lyra.

12 recordsLinked to original sources
PubMed2006

Parallel and orthogonal stimulus in ultradiluted neural networks.

Extending a model due to Derrida, Gardner, and Zippelius, we have studied the recognition ability of an extreme and asymmetrically diluted version of the Hopfield model for associative memory by including the effect of a stimulus in the dynamics of the system. We obtain exact results for the dynamic evolution of the average network superposition. The stimulus field was considered as proportional to the overlapping of the state of the system with a particular stimulated pattern. Two situations were analyzed, namely, the external stimulus acting on the initialization pattern (parallel stimulus) and the external stimulus acting on a pattern orthogonal to the initialization one (orthogonal stimulus). In both cases, we obtained the complete phase diagram in the parameter space composed of the stimulus field, thermal noise, and network capacity. Our results show that the system improves its recognition ability for parallel stimulus. For orthogonal stimulus two recognition phases emerge with the system locking at the initialization or stimulated pattern. We confront our analytical results with numerical simulations for the noiseless case T = 0.

Action Potentials↗
PubMed2006

Temperature dependence of the Casimir-like force in free-standing smectic films.

The thermal Casimir-like force in free-standing liquid crystal films close to the smectic-A-nematic transition temperature is computed using a quadratic functional approach. In the framework of a microscopic mean-field model of free-standing smectic-A films, the temperature dependence of the order parameter profiles is computed and later used to estimate the elastic coupling variability in the vicinity of first- and second-order bulk smectic-A-nematic phase transitions. The strong nonuniformity of the coupling constant profiles promotes a significant increase of the fluctuation-induced force over three orders of magnitude, especially in thin films. This result reinforces the possible predominance of the thermal Casimir force as compared to the standard van der Waals interaction in thin smectic-A liquid crystal films.

Journal Article↗
PubMed2005

Fractality of largest clusters and the percolation transition in power-law diluted chains.

Relying on the fractal character of the largest clusters at criticality, we employ a finite-size scaling analysis to obtain an accurate phase-diagram of the percolation transition in chains with bond concentration decaying as a power-law on the form 1/ r(1+sigma) . For the particular case of sigma=1, no percolation transition is observed to occur at a finite dilution, in contrast with the finite temperature Kosterlitz-Thouless transition exhibited in Ising and Potts chains with inverse square-law couplings. The fractal dimension of the critical percolation cluster is found to follow distinct dependencies on the decay exponent being numerically fitted by d(f) =0.35+4sigma/5 for 0<sigma<1/2 and d(f) = (1+sigma) /2 for 1/2<sigma<1 . We also compute average mass ratios of the two largest clusters at criticality.

Journal Article↗
PubMed2005

Nucleotide correlations and electronic transport of DNA sequences.

We use a tight-binding formulation to investigate the transmissivity and wave-packet dynamics of sequences of single-strand DNA molecules made up from the nucleotides guanine G , adenine A , cytosine C , and thymine T . In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare the results for the genomic DNA sequence with those of two artificial sequences: (i) the Rudin-Shapiro one, which has long-range correlations; (ii) a random sequence, which is a kind of prototype of a short-range correlated system, presented here with the same first-neighbor pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the persistence of resonances of finite segments. On the other hand, the wave-packet dynamics seems to be mostly influenced by the short-range correlations.

Base Sequence↗
PubMed2004

Field-driven crossover from attractive-to-repulsive Casimir-like force in smectic films.

External fields have a profound effect on the fluctuations of strongly correlated fluids, such as a liquid crystal. Within a harmonic functional integral approach, we compute the fluctuation-induced force between the surfaces of a smectic liquid-crystal film under the presence of an ordering field. In particular, we show that for asymmetrically anchored films, the thermal Casimir interaction energy can be collapsed into a universal form crossing over from a repulsive to an attractive interaction as the film thickness is increased. We discuss the possible relevance of this field effect in nematic-smectic wetting transitions.

Journal Article↗
PubMed2003

Bloch-like oscillations in a one-dimensional lattice with long-range correlated disorder.

We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum S(k) approximately 1/k(alpha) with alpha>0. de Moura and Lyra [Phys. Rev. Lett. 81, 3735 (1998)]] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided alpha>2. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.

Journal Article↗
PubMed2002

Largest and second largest cluster statistics at the percolation threshold of hypercubic lattices.

We investigate the scale invariance of the average ratio between the masses of the largest and second largest clusters at percolation. We employ a finite size scaling method to estimate percolation thresholds based on the simulations of relatively small lattices, and report on estimates for p(c) in hypercubic lattices with d=2-7, in full agreement with the best literature estimates. Also, we find the critical mass ratio to be strongly dependent on the boundary conditions, decreasing with the lattice dimension. Further, we compute several relevant mass distribution functions associated with the two largest clusters, which approach to limiting distributions for d>6. Finally, we discuss the main relevant features of the mass distributions in light of the relative role played by the spanning and nonspanning clusters.

Journal Article↗
PubMed2002

Surface effects on the amplitude of fluctuation-induced interactions in smectic films.

Within a quadratic functional integral approach, we investigate the role played by surface terms in the fluctuation-induced surface-surface interaction of free standing smectic liquid crystals. We show that the typical 1/l decay of the Casimir-type contribution to the free energy of a film with thickness l is replaced by a faster 1/l3 decay at a characteristic surface tension. An intermediate 1/l2 decay can also take place for specific surface parameters with unlike boundary conditions. In all the investigated cases, a repulsive long-range force appears only for mixed boundary conditions with strong anchoring at one surface and weak anchoring at the opposite one. Further, the amplitude of the thermal Casimir energy, besides being influenced by the applied surface tension, depicts a nonmonotonic dependence on the coupling between the outermost film layers, reflecting a crossover between strong and weak anchoring regimes.

Journal Article↗
PubMed2002

Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies.

An important application involving two-species reaction-diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms. We investigate the general problem of how the encounter rate depends on whether organisms move in Lévy or Brownian random walks. By simulating a limiting generalized searcher-target model (e.g., predator-prey, mating partner, pollinator-flower), we find that Lévy walks confer a significant advantage for increasing encounter rates when the searcher is larger or moves rapidly relative to the target, and when the target density is low.

Algorithms↗
PubMed2001

Critical behavior of a one-dimensional diffusive epidemic process.

We investigate the critical behavior of a one-dimensional diffusive epidemic propagation process by means of a Monte Carlo procedure. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants D(A) and D(B), respectively. According to a Wilson renormalization calculation, the system presents a second-order phase transition between a steady reactive state and a vacuum state, with distinct universality classes for the cases D(A)=D(B) and D(A) D(B). In this work we perform a finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension d=1. Our results show no signature of a first-order transition in the case of D(A)>D(B). A finite size scaling typical of second-order phase transitions fits well the data from all three regimes. We found that the correlation exponent nu=2 as predicted by field-theoretical arguments. Estimates for beta/nu are given for all relevant regimes.

Journal Article↗