Multiphase flow in the vascular system of wood: From microscopic exploration to 3-D Lattice Boltzmann experiments

This paper provides insights into liquid free water dynamics in wood vessels based on Lattice Boltzmann experiments. The anatomy of real wood samples was reconstructed from systematic 3-D analyses of the vessel contours derived from successive microscopic images. This virtual vascular system was then used to supply fluid-solid boundary conditions to a two-phase Lattice Boltzmann scheme and investigate capillary invasion of this hydrophilic porous medium. Behavior of the liquid phase was strongly dependent on anatomical features, especially vessel bifurcations and reconnections. Various parameters were examined in numerical experiments with ideal vessel bifurcations, to clarify our interpretation of these features. (c) 2010 Elsevier Ltd. All rights reserved.

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

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.

Pentoxifylline modifies three-dimensional collagen lattice model contraction and expression of collagen types I and III by human fibroblasts derived from post-burn hypertrophic scars and from normal skin

Fibroblasts are thought to be partially responsible for the persisting contractile forces that result in burn contractures. Using a monolayer cell culture and fibroblast populated collagen lattice (FPCL) three-dimensional model we subjected hypertrophic scar and non-cicatricial fibroblasts to the antifibrogenic agent pentoxifylline (PTF - 1 mg/mL) in order to reduce proliferation, collagen types I and III synthesis and model contraction. Fibroblasts were isolated from post-burn hypertrophic scars (HSHF) and non-scarred skin (NHF). Cells were grown in monolayers or incorporated into FPCL`s and exposed to PTF. In monolayer, cell number proliferation was reduced (46.35% in HSHF group and 37.73% in NHF group, p < 0.0001). PTF selectively inhibited collagen III synthesis in the HSHF group while inhibition was more evident to type I collagen synthesis in the NHF group. PTF also reduced contraction in both (HSHF and NHF) FPCL. (C) 2009 Elsevier Ltd and ISBI. All rights reserved.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: A statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types-each one associated, respectively, with the polar-headgroup and the acyl-chain states-which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]

Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.