Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, λ (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class -contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.

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When a drop of water is placed on a rough surface, there are two possible extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets trapped underneath the droplet and the one called the Wenzel (W) state characterized by the homogeneous wetting of the surface. A way to investigate the transition between these two states is by means of evaporation experiments, in which the droplet starts in a CB state and, as its volume decreases, penetrates the surface's grooves, reaching a W state. Here we present a theoretical model based on the global interfacial energies for CB and W states that allows us to predict the thermodynamic wetting state of the droplet for a given volume and surface texture. We first analyze the influence of the surface geometric parameters on the droplet's final wetting state with constant volume and show that it depends strongly on the surface texture. We then vary the volume of the droplet, keeping the geometric surface parameters fixed to mimic evaporation and show that the drop experiences a transition from the CB to the W state when its volume reduces, as observed in experiments. To investigate the dependency of the wetting state on the initial state of the droplet, we implement a cellular Potts model in three dimensions. Simulations show very good agreement with theory when the initial state is W, but it disagrees when the droplet is initialized in a CB state, in accordance with previous observations which show that the CB state is metastable in many cases. Both simulations and the theoretical model can be modified to study other types of surfaces.

We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order k (k = 1,. .. , 5) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first-neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the two-dimensional Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high-density columnar phase undergoes a first-order phase transition with nonstandard scaling to a solidlike phase with short-range ordered domains and, then, to fluidlike configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the three-state Potts model. The 5NN system undergoes two first-order phase transitions, both with nonstandard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

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A simple equation of state is derived for a hard-core lattice gas of side length , and compared to the results of Monte Carlo simulations. In the disordered fluid phase, the equation is found to work very well for a two-dimensional lattice gas of hard squares and reasonably well for the three-dimensional gas of hard cubes. DOI: 10.1103/PhysRevE.75.052101 PACS number͑s͒: 05.50.ϩq Almost forty years ago, Carnahan and Starling published their now famous equation of state for a hard-sphere fluid ͓1͔. Their derivation was based on the simple observation that the leading order virial coefficients for a hard-sphere fluid in three dimensions closely followed a geometric sequence. The assumption that this behavior also extrapolated to higher-order virials allowed Carnahan and Starling to explicitly resum the virial expansion to find a simple, yet very accurate, equation of state.Unfortunately, no such accurate equation of state is known for the case of lattice gases. This is particularly frustrating, since lattice models are widely used to study many complex fluids ranging from microemulsions to electrolytes ͓2-7͔. In this Brief Report, we shall present a very simple equation of state, which works very well for a twodimensional lattice gas of hard squares and reasonably well for a three-dimensional lattice gas of small hard cubes at not too high density.Our discussion is based on a lattice theory of polymer mixtures proposed a long time ago by Flory ͓8͔, who deduced the entropy of mixing to bewhere N 1 and N 2 are the numbers of polymers of types 1 and 2, while 1 and 2 are their respective volume fractions. The form of Eq. ͑1͒ is particularly appealing since it does not contain any reference to the lattice structure and depends only on thermodynamically well-defined variables. The mixture is assumed to fill all the available volume, so that there are no vacancies. If there is only one type of polymer occupying a volume fraction 1 , the rest of the space is taken to be filled by the solvent of 2 =1− 1 . It is clear that the formalism developed by Flory for polymer mixtures should be readily applicable to "hard" nonattracting lattice gases. Consider, for example, a lattice gas of hard hypercubes of volume d ͑the lattice spacing is taken to be 1͒ on a simple hypercubic lattice in d dimensions.1 The Helmholtz free energy of this lattice gas is F m =−TS, since the system is athermal. The free energy densitywhere ␤ =1/k B T, is the particle density, and = d is the volume fraction.We note, however, that in the low-density limit, Eq. ͑2͒ does not reduce to the free energy of the ideal gasTherefore, f m cannot be the total free energy of the system, except for the case of = 1 when Eq. ͑2͒ becomes exact. For polymer mixtures, to obtain the total free energy, Flory added an extra contribution to Eq. ͑2͒ which accounted for the conformational degrees of freedom of polymer chains, the so-called entropy of disorientation ͓8͔. This restored the correct low-density behavior to the theory. For rigid particles, however, the entropy of...

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations...

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