Large-scale grid-enabled lattice-Boltzmann simulations of complex fluid flow in porous media and under shear

Well designed lattice-Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed matter systems. In the present paper, we present some preliminary results on the large scale three-dimensional lattice-Boltzmann simulation of binary immiscible fluid flows through a porous medium derived from digitised x-ray microtomographic data of Bentheimer sandstone, and from the study of the same fluids under shear. Simulations on such scales can benefit considerably from the use of computational steering and we describe our implementation of steering within the lattice-Boltzmann code, called LB3D, making use of the RealityGrid steering library. Our large scale simulations benefit from the new concept of capability computing, designed to prioritise the execution of big jobs on major supercomputing resources. The advent of persistent computational grids promises to provide an optimal environment in which to deploy these mesoscale simulation methods, which can exploit the distributed nature of compute, visualisation and storage resources to reach scientific results rapidly; we discuss our work on the grid-enablement of lattice-Boltzmann methods in this context.Comment: 17 pages, 6 figures, accepted for publication in Phil.Trans.R.Soc.Lond.

Towards a mesoscopic model of water-like fluids with hydrodynamic interactions

We present a mesoscopic lattice model for non-ideal fluid flows with directional interactions, mimicking the effects of hydrogen-bonds in water. The model supports a rich and complex structural dynamics of the orientational order parameter, and exhibits the formation of disordered domains whose size and shape depend on the relative strength of directional order and thermal diffusivity. By letting the directional forces carry an inverse density dependence, the model is able to display a correlation between ordered domains and low density regions, reflecting the idea of water as a denser liquid in the disordered state than in the ordered one

Kinetics of phase transitions in two dimensional Ising models studied with the string method

The kinetics of phase transitions in the two dimensional Ising model under different conditions is studied using the string method. The key idea is to work in collective variables, consisting of block of spins, which allow for a continuous approximation of the collective variable state-space. The string method computes the minimum free energy path (MFEP) in this collective variable space, which is shown to explain the mechanism of the phase transformation (in particular, an approximation of its committor function, its free energy and its transition state). In this paper the theoretical background of the technique as well as its computational aspects are discussed in details. The string method is then used to analyze phase transition in the Ising model with imposed boundary conditions and in a periodic system under an external field of increasing magnitude. In each case, the mechanism of the phase transformation is elucidated

Simulation studies of protein-induced bilayer deformations, and lipid-induced protein tilting, on a mesoscopic model for lipid bilayers with embedded proteins

AbstractBiological membranes are complex and highly cooperative structures. To relate biomembrane structure to their biological function it is often necessary to consider simpler systems. Lipid bilayers composed of one or two lipid species, and with embedded proteins, provide a model system for biological membranes. Here we present a mesoscopic model for lipid bilayers with embedded proteins, which we have studied with the help of the dissipative particle dynamics simulation technique. Because hydrophobic matching is believed to be one of the main physical mechanisms regulating lipid-protein interactions in membranes, we considered proteins of different hydrophobic length (as well as different sizes). We studied the cooperative behavior of the lipid-protein system at mesoscopic time- and lengthscales. In particular, we correlated in a systematic way the protein-induced bilayer perturbation, and the lipid-induced protein tilt, with the hydrophobic mismatch (positive and negative) between the protein hydrophobic length and the pure lipid bilayer hydrophobic thickness. The protein-induced bilayer perturbation was quantified in terms of a coherence length, ξP, of the lipid bilayer hydrophobic thickness profile around the protein. The dependence on temperature of ξP, and the protein tilt-angle, were studied above the main-transition temperature of the pure system, i.e., in the fluid phase. We found that ξP depends on mismatch, i.e., the higher the mismatch is, the longer ξP becomes, at least for positive values of mismatch; a dependence on the protein size appears as well. In the case of large model proteins experiencing extreme mismatch conditions, in the region next to the so-called lipid annulus, there appears an undershooting (or overshooting) region where the bilayer hydrophobic thickness is locally lower (or higher) than in the unperturbed bilayer, depending on whether the protein hydrophobic length is longer (or shorter) than the pure lipid bilayer hydrophobic thickness. Proteins may tilt when embedded in a too-thin bilayer. Our simulation data suggest that, when the embedded protein has a small size, the main mechanism to compensate for a large hydrophobic mismatch is the tilt, whereas large proteins react to negative mismatch by causing an increase of the hydrophobic thickness of the nearby bilayer. Furthermore, for the case of small, peptidelike proteins, we found the same type of functional dependence of the protein tilt-angle on mismatch, as was recently detected by fluorescence spectroscopy measurements

On the assumptions underlying milestoning

Milestoning is a procedure to compute the time evolution of complicated processes such as barrier crossing events or long diffusive transitions between predefined states. Milestoning reduces the dynamics to transition events between intermediates (the milestones) and computes the local kinetic information to describe these transitions via short molecular dynamics (MD) runs between the milestones. The procedure relies on the ability to reinitialize MD trajectories on the milestones to get the right kinetic information about the transitions. It also rests on the assumptions that the transition events between successive milestones and the time lags between these transitions are statistically independent. In this paper, we analyze the validity of these assumptions. We show that sets of optimal milestones exist, i.e., sets such that successive transitions are indeed statistically independent. The proof of this claim relies on the results of transition path theory and uses the isocommittor surfaces of the reaction as milestones. For systems in the overdamped limit, we also obtain the probability distribution to reinitialize the MD trajectories on the milestones, and we discuss why this distribution is not available in closed form for systems with inertia. We explain why the time lags between transitions are not statistically independent even for optimal milestones, but we show that working with such milestones allows one to compute mean first passage times between milestones exactly. Finally, we discuss some practical implications of our results and we compare milestoning with Markov state models in view of our findings