In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids.

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A model for extremely flexible tethered membranes is studied by Monte Carlo simulations and scaling arguments. In contrast to the standard string-and-bead models, no finite-range hard-core repulsion is used to ensure self-avoidance. Instead, the elementary triangles are taken to be impenetrable. Although this leads to an extremely floppy tethered network, the surface is found to be asymptotically flat, with a roughness exponent ζ≃0.7, consistent with the result of self-avoiding string-and-bead models. The orientationally averaged scattering intensity, on the other hand, is found to exhibit a nontrivial scaling behavior characteristic of a crumpled object with an effective fractal dimension df≃2.7. This result is compared with recent experiments on graphite oxide sheets.

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Amphiphiles are molecules which have both hydrophilic and hydrophobic parts. In water-and/or oil-like solvent, they self-assemble into extended sheet-like structures due to the hydrophobic effect. The free energy of an amphiphilic system can be written as a functional of its interfacial geometry, and phase diagrams can be calculated by comparing the free energies following from different geometries. Here we focus on bicontinuous structures, where one highly convoluted interface spans the whole sample and thereby divides it into two separate labyrinths. The main models for surfaces of this class are triply periodic minimal surfaces, their constant mean curvature and parallel surface companions, and random surfaces. We discuss the geometrical properties of each of these types of surfaces and how they translate into the experimentally observed phase behavior of amphiphilic systems.

The collisions of neighboring membranes in lamellar phases leads to the formation of passages, or “wormholes”. We study the shape and the fluctuations of theses passages, based on the curvature model of membranes. In particular, we calculate the average radius, the fluctuations of the radius, the asphericity, and the free energy of a wormhole. This requires a careful analysis of the translational zero modes. The free energy of a single wormhole is then used to obtain the density of passages in the low-density limit. We find that the density increases as d4/3 with increasing membrane separation d of the stack, decreases exponentially with increasing saddle-splay modulus $\bar \kappa$, and also decreases rapidly with increasing bending rigidity κ

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