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W Figueiredo

Publications and source records attributed to W Figueiredo.

At least 19 recordsLinked to original sources
PubMed2006

Three-dimensional square water in the presence of an external electric field.

In this work we study a tridimensional statistical model for the hydrogen-bond (HB) network formed in liquid water in the presence of an external electric field. This model is analogous to the so-called square water, whose ground state gives a good estimate for the residual entropy of the ice. In our case, each water molecule occupies one site of a cubic lattice, and no hole is allowed. The hydrogen atoms of water molecules are disposed at the lines connecting nearest-neighbor sites, in a way that each water can be found in 15 different states. We say that there is a hydrogen bond between two neighboring molecules when only one hydrogen is in the line connecting both molecules. Through Monte Carlo simulations with Metropolis and entropic sampling algorithms, and by exact calculations for small lattices, we determined the dependence of the number of molecules aligned to the field and the number of hydrogen bonds per molecule as a function of temperature and the intensity of the external field. The results for both approaches showed that, different of the two-dimensional case, there is no maximum in the number of HBs as a function of the electric field. However, we observed nonmonotonic behaviors as a function of the temperature of the quantities of interest. We also found the dependence of the entropy on the external electric field at very low temperatures. In this case, the entropy vanishes for the value of the external field for which the contributions to the total energy coming from the HBs and the field become the same.

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PubMed2004

Short-time dynamics for the spin-3/2 Blume-Capel model.

We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dynamic critical exponents for the generalized two-dimensional Blume-Capel model of spin-3/2. We showed that the critical behavior at the second-order phase-transition line between the paramagnetic and ferromagnetic phases is in the same universality class of the two-dimensional Ising model. However, at the double critical end point, which is present in the phase diagram of the model, the critical exponent beta , associated to the order parameter, is different from that of the Ising model.

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PubMed2004

A trimer model for water.

A statistical model for water is studied, where the molecules are represented by trimers in a triangular lattice. Each atom of a water molecule occupies a single site on the lattice, and the HOH bond angle is assumed to be 120 degrees. The molecules can interact via three different potentials: the excluded volume interaction, which prevents two molecules from occupying the same atom site, an attractive potential between any two nearest-neighbor atoms belonging to different molecules (the van der Waals interaction), and the hydrogen bond interaction, which occurs only for a particular orientation and displacement of a pair of molecules. The model is investigated by means of Monte Carlo simulations in the canonical and grand canonical ensembles. The Metropolis and the entropic sampling algorithms are used to obtain the thermodynamics of the system. We find that the entropic sampling prescription is the most efficient algorithm of them, providing information about the entropy and free energy of the system in a straightforward way. The curves for the polarization, number of hydrogen bonds, specific heat, and cumulant of energy were obtained as a function of the temperature and total concentration. In addition, the entropy of the noninteracting version of the model is compared to that of the angular trimers in a square lattice and triangles in a triangular lattice.

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PubMed2004

Growth model with a finite number of orientations on a linear substrate.

The aim of this work is to present a simple model for studying the texture formation during the electrodeposition process. Monte Carlo simulations are used to describe the formation of the deposits, and the scaling concepts are employed to characterize their growth and roughness properties. In this model particles are randomly deposited with an orientation chosen from a discrete set of possible directions. The final orientation of the deposited particle is determined by its interaction with the first neighboring particles and by the temperature of the substrate. Particle interactions are chosen according to the q-state ferromagnetic Potts model Hamiltonian. Simulations were performed on (1+1) dimensions, and for several values of temperature and substrate size. The results of the simulations lead to different behaviors for the model at low and high temperatures. At high temperatures, the scaling exponent beta=0.5 was found, which characterizes a pure random deposition model. However, at low temperatures, we observed that after a given time interval, particles start orienting in a fixed direction and the interface width saturates just during a time window. Suddenly, a fluctuation makes the interface width increase again, that is, we never observed a full saturation. On the other hand, at zero temperature, the system reaches an absorbing state with all the layers occupied by particles oriented in the same direction. At zero temperature we found z=1.90, alpha=1.80, and beta=0.99 for the dynamic, roughness, and growth exponents, respectively. The scaling exponents are consistent with a self-affine behavior of the model and they are in agreement with the well known Family-Vicsek scaling relation.

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PubMed2004

Fast and slow degrees of freedom coupling two different reservoirs.

We considered a Hamiltonian system that can be described by two generalized variables. One of them relaxes quickly when the system is in contact with a heat bath at fixed temperature, while the second one, the slow variable, mimics the interaction of the system with another heat bath at a lower temperature. The coupling between these variables leads to an energy flow between the heat baths. Allahverdyan and Nieuwenhuizen [Phys. Rev. E 62, 845 (2000)] proposed a formalism to deal with such problem and calculated the steady states of the system and some related properties as entropy production, energy dissipation, etc. In this work we applied the formalism to a coupled system of ideal gases and also to an ideal gas interacting with a harmonic oscillator. If the temperatures of the heat baths are not too close, the Onsager relations do not apply.

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PubMed2002

Effect of the subsurface oxygen diffusion on the Ziff-Gulari-Barshad catalytic reaction model.

We study a version of the Ziff-Gulari-Barshad model where we include the diffusion of oxygen atoms between the uppermost layer and the subsurface. When a CO molecule impinges the surface, it occupies a single site, while the O2 molecule needs two neighboring sites to be adsorbed. The oxidation of the CO molecule occurs only at the top layer, and this happens whenever a CO molecule is nearest neighbor of an O atom. Through the pair mean-field approximation we determine the phase diagram of the model for different values of the diffusion rate of oxygen atoms between the subsurface and the top layer. The diagram exhibits a continuous line that separates regions displaying O-poisoned and non-O-poisoned states. We show that above a critical value of the diffusion rate of oxygen atoms from the subsurface to the top layer, there is no more oxygen poisoning for any nonzero value of the diffusion rate from the top layer to the subsurface. This behavior is also verified in Monte Carlo simulations.

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PubMed2001

Higher-order moments at the critical point of the Ziff-Gulari-Barshad model.

We studied the continuous phase transition between the active and the absorbing state of the Ziff-Gulari-Barshad (ZGB) model. Through Monte Carlo simulations we determined all the moments of the order parameter up to fourth order and their ratios at the critical point. We show that the ratios we found are in agreement with those of the contact and pair contact processes in two dimensions, which give support to the idea that the ZGB model is in the directed percolation universality class in (2+1) dimensions.

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PubMed2001

Critical dynamics of the Baxter-Wu model.

The short-time behavior of the Baxter-Wu model is investigated through the relaxation of the order parameter at the critical temperature. We considered Monte Carlo simulations for this model on a triangular lattice, and we studied relaxation starting from the fourfold-degenerate ground state. Using the short-time scaling formalism we found the static critical exponents beta and nu of the model and the corresponding dynamical critical exponent z. The values of the static exponents we find agree with the exact ones. To the best of our knowledge, this is the first determination of the dynamical critical exponent of the Baxter-Wu model.

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PubMed2000

Competitive reactions among three monomers over a catalytic surface

We studied in this work a three-monomer reaction model on one- and two-dimensional lattices. We have taken different reactivity rates among pairs of monomers and the reaction between two selected monomers was forbidden. We have employed the mean field and the pair approximation to decouple the equations of motion for the densities of single and pairs of monomers. We found the stationary states and the phase diagram of the model. We have shown that, in two dimensions and within the pair approximation, there is a first-order transition line between active and poisoned steady states.

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PubMed2000

Mixed-spin ising model with one- and two-spin competing dynamics

In this work we found the stationary states of a kinetic Ising model, with two different types of spins: sigma=1/2 and S=1. We divided the spins into two interpenetrating sublattices, and found the time evolution for the probability of the states of the system. We employed two transition rates which compete between themselves: one, associated with the Glauber process, which describes the relaxation of the system through one-spin flips; the other, related to the simultaneous flipping of pairs of neighboring spins, simulates an input of energy into the system. Using the dynamical pair approximation, we determined the equations of motion for the sublattice magnetizations, and also for the correlation function between first neighbors. We found the phase diagram for the stationary states of the model, and we showed that it exhibits two continuous transition lines: one line between the ferrimagnetic and paramagnetic phases, and the other between the paramagnetic and antiferrimagnetic phases.

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PubMed2000

Short-time dynamics of a metamagnetic model

We studied a layered metamagnetic Ising model with competing ferromagnetic and antiferromagnetic interactions on a square lattice. The model is formed of ferromagnetic chains coupled by an antiferromagnetic interaction. Using Monte Carlo simulations we have determined the phase diagram of the model, which exhibits a tricritical point. By exploring the short-time scaling dynamics, we have found the dynamic and static critical exponents along the continuous transition line between the antiferromagnetic and paramagnetic phases.

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PubMed2000

Ziff-gulari-barshad model with random distribution of inert sites

A random distribution of inert sites is introduced in the Ziff-Gulari-Barshad model to study the phase transitions between active and poisoned states. The adsorption of CO and O2 molecules is not possible at the position of the inert sites. This model is investigated in the site and pair approximations, as well as through Monte Carlo simulations. We determine the mean coverages of the elements as a function of the dilution and show that the continuous transition between the active and O-poisoned states is slightly affected by moderate values of dilution in the pair approximation and in the simulations. On the other hand, from the analysis of the hysteresis curves, the transition between the active and CO-poisoned states changes from first order to continuous as one increases the concentration of inactive sites. The observed transition in the site and pair approximations is always of first-order nature. We also found the lines of transition and spinodal points as a function of the concentration of inert sites. Finally, the production rate of CO2 is calculated as a function of the dilution of sites.

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PubMed2000

Spin-1 aggregation model in one dimension

We studied a simple model of aggregation in one dimension that resembles the self-assembly of amphiphiles in an aqueous solution. We mapped the water and amphiphilic molecules by Ising spin variables for S=1. The zero component of spin represents the water molecules, while the remaining components (+/-1) account for the amphiphilic molecules. We defined an aggregate in one dimension by a set of spin components (+/-1) placed between two zero spin components. There is no difference between up and down components of the spins inside the aggregates. In this way what really matters is the square of the spin component. The grand-canonical partition function and the probability of formation of different aggregate sizes were calculated by the transfer matrix method. We have shown that for any value of the chemical potential and temperature, the system does not exhibit the typical aggregate size distribution which is observed in micellar solutions at low concentrations. The distribution curve for the aggregate size does not show the minimum and the maximum as a function of the concentration which is the signature of the appearance of micelles. We can say that this one-dimensional model does not present any phase transition nor a transition from the micellar to nonmicellar state.

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PubMed1999

Monte Carlo simulation of an antiferromagnetic Ising model at two competing temperatures.

We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.

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PubMed1999

Theory of the NO+CO surface-reaction model.

We derive a pair approximation (PA) for the NO+CO model with instantaneous reactions. For both the triangular and square lattices, the PA, derived here using a simpler approach, yields a phase diagram with an active state for CO-fractions y in the interval y(1)<y<y(2), with a continuous (discontinuous) phase transition to a poisoned state at y(1) (y(2)). This is in qualitative agreement with simulation for the triangular lattice, where our theory gives a rather accurate prediction for y(2). To obtain the correct phase diagram for the square lattice, i.e., no active stationary state, we reformulate the PA using sublattices. The (formerly) active regime is then replaced by a poisoned state with broken symmetry (unequal sublattice coverages), as observed recently by Kortlüke et al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in which the active state persists, although reduced in extent, we report here the qualitatively correct theory of the NO+CO model on the square lattice. Surface diffusion of nitrogen can lead to an active state in this case. In one dimension, the PA predicts that diffusion is required for the existence of an active state.

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PubMed1999

Competitive dynamics in a three-dimensional Ising model.

We consider a three-dimensional ferromagnetic Ising model on a cubic lattice in contact with a heat bath at temperature T. The states of the system evolve in time according to two stochastic processes: the one-spin-flip Glauber dynamics where the order parameter is not conserved, and the two-spin-exchange Kawasaki kinetics, which conserves the order parameter. The former process mimics an input of energy into the system. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model, and the corresponding critical exponents. Similarly to the observed for the related two-dimensional ferromagnetic Ising model, the phase diagram obtained exhibits the phenomenon of self-organization. Although the stationary states are mainly ferromagnetic at low temperatures, an antiferromagnetic phase appears for extremely high values of the flux of energy. Unlike the ferromagnetic case, the region of the phase diagram occupied by the antiferromagnetic phase is now larger. The determined critical exponents for this nonequilibrium model are in agreement with the well-known accepted values for the three-dimensional equilibrium Ising model.

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