Computer simulations of the totally asymmetric simple-exclusion process on chains with a double-chain section in the middle are performed in the case of random-sequential update. The outer ends of the chain segments connected to the middle double-chain section are open, so that particles are injected at the left end with rate alpha and removed at the right end with rate beta. At the branching point of the graph (the left end of the middle section) the particles choose with equal probability 1/2 which branch to take and then simultaneous motion of the particles along the two branches is simulated. With the aid of a simple theory, neglecting correlations at the junctions of the chain segments, the possible phase structures of the model are clarified. Density profiles and nearest-neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained and discussed. Cross correlations are found to exist between equivalent sites of the branches of the middle section whenever they are in a coexistence phase.

We study numerically the wetting properties of model heterogeneous flat substrates. The shapes of three-dimensional liquid drops in equilibrium with such substrates in the framework of the classical capillary theory are obtained. The numerical method used for minimizing the free energy is based on the local variations approach. It has been extended here to treat chemically heterogeneous substrates with "mesa" defects, i.e., sharp boundaries between surface patches with different surface tensions. The method allows inclusion of the gravity and the line tension of the contact line as well as different constraints, e.g. the constant volume constraint. We discuss the implications for the standard and modified Cassie equations and for the interpretation of the experimental data. Two different situations arise regarding the averaging of the contact angle for the two types of substrates considered: that with radial symmetry and that without (the dart board substrate).

An exact and rigorous calculation of the current and density profile in the steady state of the one-dimensional fully asymmetric simple-exclusion process with open boundaries and forward-ordered sequential dynamics is presented. The method is based on a matrix product representation of the steady-state probability distribution. The main idea is to choose a suitable representation in which the scalar products describing the current and local density profile for a chain of arbitrary finite size depend only on the elements in a finite number of rows and columns. This makes possible the use of a truncated finite-dimensional representation of the matrices and vectors involved. After performing the calculations, we lift the truncation by letting its dimensionality go to infinity. In this limit the results become exact for any size of the chain. By rescaling one of the infinitedimensional matrix representations found in the work of Derrida et al. ͓J. Phys. A 26, 1493 ͑1993͔͒ for their algebra, we obtain a symmetric ''propagator'' matrix. Its truncated version is diagonalized by orthogonal transformation for easy calculation of the relevant scalar products. An interpretation of the phase transitions between the different phases is given in terms of eigenvalue splitting from a bounded quasicontinuous spectrum. A precise description of the local density profiles is given for all values of the parameters. It is shown that the leading-order asymptotic form of the position-dependent terms in the local density changes within the low-and high-density phases, signaling the presence of a higher-order transition.