Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Molecular line mapping of the giant molecular cloud associated with RCW 106 - II. Column density and dynamical state of the clumps

We present a fully sampled C^{18}O (1-0) map towards the southern giant molecular cloud (GMC) associated with the HII region RCW 106, and use it in combination with previous ^{13}CO (1-0) mapping to estimate the gas column density as a function of position and velocity. We find localized regions of significant ^{13}CO optical depth in the northern part of the cloud, with several of the high-opacity clouds in this region likely associated with a limb-brightened shell around the HII region G333.6-0.2. Optical depth corrections broaden the distribution of column densities in the cloud, yielding a log-normal distribution as predicted by simulations of turbulence. Decomposing the ^{13}CO and C^{18}O data cubes into clumps, we find relatively weak correlations between size and linewidth, and a more sensitive dependence of luminosity on size than would be predicted by a constant average column density. The clump mass spectrum has a slope near -1.7, consistent with previous studies. The most massive clumps appear to have gravitational binding energies well in excess of virial equilibrium; we discuss possible explanations, which include magnetic support and neglect of time-varying surface terms in the virial theorem. Unlike molecular clouds as a whole, the clumps within the RCW 106 GMC, while elongated, appear to show random orientations with respect to the Galactic plane.Comment: 17 pages, to appear in MNRA

3D Spinodal Decomposition in the Inertial Regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].Comment: 4 pages, 3 eps figures, RevTex, minor changes to bring in line with published version. Mobility values added to Table

Towards Better Integrators for Dissipative Particle Dynamics Simulations

Coarse-grained models that preserve hydrodynamics provide a natural approach to study collective properties of soft-matter systems. Here, we demonstrate that commonly used integration schemes in dissipative particle dynamics give rise to pronounced artifacts in physical quantities such as the compressibility and the diffusion coefficient. We assess the quality of these integration schemes, including variants based on a recently suggested self-consistent approach, and examine their relative performance. Implications of integrator-induced effects are discussed.Comment: 4 pages, 3 figures, 2 tables, accepted for publication in Phys. Rev. E (Rapid Communication), tentative publication issue: 01 Dec 200

Noiseless nonreciprocity in a parametric active device

Nonreciprocal devices such as circulators and isolators belong to an important class of microwave components employed in applications like the measurement of mesoscopic circuits at cryogenic temperatures. The measurement protocols usually involve an amplification chain which relies on circulators to separate input and output channels and to suppress backaction from different stages on the sample under test. In these devices the usual reciprocal symmetry of circuits is broken by the phenomenon of Faraday rotation based on magnetic materials and fields. However, magnets are averse to on-chip integration, and magnetic fields are deleterious to delicate superconducting devices. Here we present a new proposal combining two stages of parametric modulation emulating the action of a circulator. It is devoid of magnetic components and suitable for on-chip integration. As the design is free of any dissipative elements and based on reversible operation, the device operates noiselessly, giving it an important advantage over other nonreciprocal active devices for quantum information processing applications.Comment: 17 pages, 4 figures + 12 pages Supplementary Informatio

Persistence exponents in a 3D symmetric binary fluid mixture

The persistence exponent, theta, is defined by N_F sim t^theta, where t is the time since the start of the coarsening process and the "no-flip fraction", N_F, is the number of points that have not seen a change of "color" since t=0. Here we investigate numerically the persistence exponent for a binary fluid system where the coarsening is dominated by hydrodynamic transport. We find that N_F follows a power law decay (as opposed to exponential) with the value of theta somewhat dependent on the domain growth rate (L sim t^alpha, where L is the average domain size), in the range theta=1.23 +-0.1 (alpha = 2/3) to theta=1.37 +-0.2 (alpha=1). These alpha values correspond to the inertial and viscous hydrodynamic regimes respectively.Comment: 9 pages RevTex, 9 figures included as eps files on last 3 pages, submitted to Phys Rev

Fluctuations of elastic interfaces in fluids: Theory and simulation

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a numerical method, we first discuss the dynamical coupling between the interface and the surrounding fluids. An argument is then presented that generalizes the single-relaxation time lattice-Boltzmann method for the simulation of hydrodynamic interfaces to include the elastic properties of the boundary. The implementation of the new method is outlined and it is tested by simulating the static behavior of spherical bubbles and the dynamics of bending waves. By means of the fluctuation-dissipation theorem we recover analytically the equilibrium frequency power spectrum of thermally fluctuating membranes and the correlation function of the excitations. Also, the non-equilibrium scaling properties of the membrane roughening are deduced, leading us to formulate a scaling law describing the interface growth, W^2(L,T)=L^3 g[t/L^(5/2)], where W, L and T are the width of the interface, the linear size of the system and the temperature respectively, and g is a scaling function. Finally, the phenomenology of thermally fluctuating membranes is simulated and the frequency power spectrum is recovered, confirming the decay of the correlation function of the fluctuations. As a further numerical study of fluctuating elastic interfaces, the non-equilibrium regime is reproduced by initializing the system as an interface immersed in thermally pre-excited fluids.Comment: 15 pages, 11 figure

Influence of Hydrodynamic Interactions on Mechanical Unfolding of Proteins

We incorporate hydrodynamic interactions in a structure-based model of ubiquitin and demonstrate that the hydrodynamic coupling may reduce the peak force when stretching the protein at constant speed, especially at larger speeds. Hydrodynamic interactions are also shown to facilitate unfolding at constant force and inhibit stretching by fluid flows.Comment: to be published in Journal of Physics: Condensed Matte

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur

An all silicon quantum computer

A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are Si-29 nuclear spins arranged as chains in a Si-28 (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient. No impurity dopants or electrical contacts are needed. Initialization is accomplished by optical pumping, algorithmic cooling, and pseudo-pure state techniques. Magnetic resonance force microscopy is used for readout. This proposal takes advantage of many of the successful aspects of solution NMR quantum computation, including ensemble measurement, RF control, and long decoherence times, but it allows for more qubits and improved initialization.Comment: ReVTeX 4, 5 pages, 2 figure