782 research outputs found
No self-similar aggregates with sedimentation
Two-dimensional cluster-cluster aggregation is studied when clusters move
both diffusively and sediment with a size dependent velocity. Sedimentation
breaks the rotational symmetry and the ensuing clusters are not self-similar
fractals: the mean cluster width perpendicular to the field direction grows
faster than the height. The mean width exhibits power-law scaling with respect
to the cluster size, ~ s^{l_x}, l_x = 0.61 +- 0.01, but the mean height
does not. The clusters tend to become elongated in the sedimentation direction
and the ratio of the single particle sedimentation velocity to single particle
diffusivity controls the degree of orientation. These results are obtained
using a simulation method, which becomes the more efficient the larger the
moving clusters are.Comment: 10 pages, 10 figure
Sedimentation and Flow Through Porous Media: Simulating Dynamically Coupled Discrete and Continuum Phases
We describe a method to address efficiently problems of two-phase flow in the
regime of low particle Reynolds number and negligible Brownian motion. One of
the phases is an incompressible continuous fluid and the other a discrete
particulate phase which we simulate by following the motion of single
particles. Interactions between the phases are taken into account using locally
defined drag forces. We apply our method to the problem of flow through random
media at high porosity where we find good agreement to theoretical expectations
for the functional dependence of the pressure drop on the solid volume
fraction. We undertake further validations on systems undergoing gravity
induced sedimentation.Comment: 22 pages REVTEX, figures separately in uudecoded, compressed
postscript format - alternatively e-mail '[email protected]' for
hardcopies
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
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
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 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
Hydrodynamic interactions in colloidal ferrofluids: A lattice Boltzmann study
We use lattice Boltzmann simulations, in conjunction with Ewald summation
methods, to investigate the role of hydrodynamic interactions in colloidal
suspensions of dipolar particles, such as ferrofluids. Our work addresses
volume fractions of up to 0.20 and dimensionless dipolar interaction
parameters of up to 8. We compare quantitatively with Brownian
dynamics simulations, in which many-body hydrodynamic interactions are absent.
Monte Carlo data are also used to check the accuracy of static properties
measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic
interactions slow down both the long-time and the short-time decays of the
intermediate scattering function , for wavevectors close to the peak of
the static structure factor , by a factor of roughly two. The long-time
slowing is diminished at high interaction strengths whereas the short-time
slowing (quantified via the hydrodynamic factor ) is less affected by the
dipolar interactions, despite their strong effect on the pair distribution
function arising from cluster formation. Cluster formation is also studied in
transient data following a quench from ; hydrodynamic interactions
slow the formation rate, again by a factor of roughly two
Viscoelasticity near the gel-point: a molecular dynamics study
We report on extensive molecular dynamics simulations on systems of soft
spheres of functionality f, i.e. particles that are capable of bonding
irreversibly with a maximum of f other particles. These bonds are randomly
distributed throughout the system and imposed with probability p. At a critical
concentration of bonds, p_c approximately equal to 0.2488 for f=6, a gel is
formed and the shear viscosity \eta diverges according to \eta ~ (p_c-p)^{-s}.
We find s is approximately 0.7 in agreement with some experiments and with a
recent theoretical prediction based on Rouse dynamics of phantom chains. The
diffusion constant decreases as the gel point is approached but does not
display a well-defined power law.Comment: 4 pages, 4 figure
Adding control to arbitrary unknown quantum operations
While quantum computers promise significant advantages, the complexity of
quantum algorithms remains a major technological obstacle. We have developed
and demonstrated an architecture-independent technique that simplifies adding
control qubits to arbitrary quantum operations-a requirement in many quantum
algorithms, simulations and metrology. The technique is independent of how the
operation is done, does not require knowledge of what the operation is, and
largely separates the problems of how to implement a quantum operation in the
laboratory and how to add a control. We demonstrate an entanglement-based
version in a photonic system, realizing a range of different two-qubit gates
with high fidelity.Comment: 9 pages, 8 figure
Dynamics of gravity driven three-dimensional thin films on hydrophilic-hydrophobic patterned substrates
We investigate numerically the dynamics of unstable gravity driven
three-dimensional thin liquid films on hydrophilic-hydrophobic patterned
substrates of longitudinal stripes and checkerboard arrangements. The thin film
can be guided preferentially on hydrophilic longitudinal stripes, while fingers
develop on adjacent hydrophobic stripes if their width is large enough. On
checkerboard patterns, the film fingering occurs on hydrophobic domains, while
lateral spreading is favoured on hydrophilic domains, providing a mechanism to
tune the growth rate of the film. By means of kinematical arguments, we
quantitatively predict the growth rate of the contact line on checkerboard
arrangements, providing a first step towards potential techniques that control
thin film growth in experimental setups.Comment: 30 pages, 12 figure
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