67 research outputs found
GPU-accelerated simulation of colloidal suspensions with direct hydrodynamic interactions
Solvent-mediated hydrodynamic interactions between colloidal particles can
significantly alter their dynamics. We discuss the implementation of Stokesian
dynamics in leading approximation for streaming processors as provided by the
compute unified device architecture (CUDA) of recent graphics processors
(GPUs). Thereby, the simulation of explicit solvent particles is avoided and
hydrodynamic interactions can easily be accounted for in already available,
highly accelerated molecular dynamics simulations. Special emphasis is put on
efficient memory access and numerical stability. The algorithm is applied to
the periodic sedimentation of a cluster of four suspended particles. Finally,
we investigate the runtime performance of generic memory access patterns of
complexity for various GPU algorithms relying on either hardware cache
or shared memory.Comment: to appear in a special issue of Eur. Phys. J. Special Topics on
"Computer Simulations on GPUs
Anomalous transport in the crowded world of biological cells
A ubiquitous observation in cell biology is that diffusion of macromolecules
and organelles is anomalous, and a description simply based on the conventional
diffusion equation with diffusion constants measured in dilute solution fails.
This is commonly attributed to macromolecular crowding in the interior of cells
and in cellular membranes, summarising their densely packed and heterogeneous
structures. The most familiar phenomenon is a power-law increase of the MSD,
but there are other manifestations like strongly reduced and time-dependent
diffusion coefficients, persistent correlations, non-gaussian distributions of
the displacements, heterogeneous diffusion, and immobile particles. After a
general introduction to the statistical description of slow, anomalous
transport, we summarise some widely used theoretical models: gaussian models
like FBM and Langevin equations for visco-elastic media, the CTRW model, and
the Lorentz model describing obstructed transport in a heterogeneous
environment. Emphasis is put on the spatio-temporal properties of the transport
in terms of 2-point correlation functions, dynamic scaling behaviour, and how
the models are distinguished by their propagators even for identical MSDs.
Then, we review the theory underlying common experimental techniques in the
presence of anomalous transport: single-particle tracking, FCS, and FRAP. We
report on the large body of recent experimental evidence for anomalous
transport in crowded biological media: in cyto- and nucleoplasm as well as in
cellular membranes, complemented by in vitro experiments where model systems
mimic physiological crowding conditions. Finally, computer simulations play an
important role in testing the theoretical models and corroborating the
experimental findings. The review is completed by a synthesis of the
theoretical and experimental progress identifying open questions for future
investigation.Comment: review article, to appear in Rep. Prog. Phy
Structure and dynamics of binary liquid mixtures near their continuous demixing transitions
The dynamic and static critical behavior of five binary Lennard-Jones liquid
mixtures, close to their continuous demixing points (belonging to the so-called
model H' dynamic universality class), are studied computationally by combining
semi-grand canonical Monte Carlo simulations and large-scale molecular dynamics
(MD) simulations, accelerated by graphic processing units (GPU). The symmetric
binary liquid mixtures considered cover a variety of densities, a wide range of
compressibilities, and various interactions between the unlike particles. The
static quantities studied here encompass the bulk phase diagram (including both
the binodal and the -line), the correlation length, the concentration
susceptibility, the compressibility of the finite-sized systems at the bulk
critical temperature , and the pressure. Concerning the collective
transport properties, we focus on the Onsager coefficient and the shear
viscosity. The critical power-law singularities of these quantities are
analyzed in the mixed phase (above ) and non-universal critical amplitudes
are extracted. Two universal amplitude ratios are calculated. The first one
involves static amplitudes only and agrees well with the expectations for the
three-dimensional Ising universality class. The second ratio includes also
dynamic critical amplitudes and is related to the Einstein--Kawasaki relation
for the interdiffusion constant. Precise estimates of this amplitude ratio are
difficult to obtain from MD simulations, but within the error bars our results
are compatible with theoretical predictions and experimental values for model
H'. Evidence is reported for an inverse proportionality of the pressure and the
isothermal compressibility at the demixing transition, upon varying either the
number density or the repulsion strength between unlike particles.Comment: 15 pages, 12 figure
Anomalous transport resolved in space and time by fluorescence correlation spectroscopy
A ubiquitous observation in crowded cell membranes is that molecular
transport does not follow Fickian diffusion but exhibits subdiffusion. The
microscopic origin of such a behaviour is not understood and highly debated.
Here we discuss the spatio-temporal dynamics for two models of subdiffusion:
fractional Brownian motion and hindered motion due to immobile obstacles. We
show that the different microscopic mechanisms can be distinguished using
fluorescence correlation spectroscopy (FCS) by systematic variation of the
confocal detection area. We provide a theoretical framework for space-resolved
FCS by generalising FCS theory beyond the common assumption of spatially
Gaussian transport. We derive a master formula for the FCS autocorrelation
function, from which it is evident that the beam waist of an FCS experiment is
a similarly important parameter as the wavenumber of scattering experiments.
These results lead to scaling properties of the FCS correlation for both
models, which are tested by in silico experiments. Further, our scaling
prediction is compatible with the FCS half-value times reported by Wawrezinieck
et al. [Biophys. J. 89, 4029 (2005)] for in vivo experiments on a transmembrane
protein.Comment: accepted for publication in Soft Matte
Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod
Slender rods in concentrated suspensions constitute strongly interacting
systems with rich dynamics: transport slows down drastically and the anisotropy
of the motion becomes arbitrarily large. We develop a mesoscopic description of
the dynamics down to the length scale of the interparticle distance. Our theory
is based on the exact solution of the Smoluchowski-Perrin equation; it is in
quantitative agreement with extensive Brownian dynamics simulations in the
dense regime. In particular, we show that the tube confinement is characterised
by a power law decay of the intermediate scattering function with exponent 1/2.Comment: to appear in EP
Enhanced Diffusion of a Needle in a Planar Course of Point Obstacles
The transport of an infinitely thin, hard rod in a random, dense array of
point obstacles is investigated by molecular dynamics simulations. Our model
mimics the sterically hindered dynamics in dense needle liquids. The
center-of-mass diffusion exhibits a minimum, and transport becomes increasingly
fast at higher densities. The diffusion coefficient diverges according to a
power law in the density with an approximate exponent of 0.8. This observation
is connected with a new divergent time scale, reflected in a zig-zag motion of
the needle, a two-step decay of the velocity-autocorrelation function, and a
negative plateau in the non-Gaussian parameter.Comment: accepted for publication in Phys. Rev. Let
Localization phenomena in models of ion-conducting glass formers
The mass transport in soft-sphere mixtures of small and big particles as well
as in the disordered Lorentz gas (LG) model is studied using molecular dynamics
(MD) computer simulations. The soft-sphere mixture shows anomalous
small-particle diffusion signifying a localization transition separate from the
big-particle glass transition. Switching off small-particle excluded volume
constraints slows down the small-particle dynamics, as indicated by incoherent
intermediate scattering functions. A comparison of logarithmic time derivatives
of the mean-squared displacements reveals qualitative similarities between the
localization transition in the soft-sphere mixture and its counterpart in the
LG. Nevertheless, qualitative differences emphasize the need for further
research elucidating the connection between both models.Comment: to appear in Eur. Phys. J. Special Topic
Structure of liquid--vapor interfaces: perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence X-ray diffraction
Grazing-incidence X-ray diffraction (GIXRD) is a scattering technique which
allows one to characterize the structure of fluid interfaces down to the
molecular scale, including the measurement of the surface tension and of the
interface roughness. However, the corresponding standard data analysis at
non-zero wave numbers has been criticized as to be inconclusive because the
scattering intensity is polluted by the unavoidable scattering from the bulk.
Here we overcome this ambiguity by proposing a physically consistent model of
the bulk contribution which is based on a minimal set of assumptions of
experimental relevance. To this end, we derive an explicit integral expression
for the background scattering, which can be determined numerically from the
static structure factors of the coexisting bulk phases as independent input.
Concerning the interpretation of GIXRD data inferred from computer simulations,
we account also for the finite sizes of the bulk phases, which are unavoidable
in simulations. The corresponding leading-order correction beyond the dominant
contribution to the scattered intensity is revealed by asymptotic analysis,
which is characterized by the competition between the linear system size and
the X-ray penetration depth in the case of simulations. Specifically, we have
calculated the expected GIXRD intensity for scattering at the planar
liquid--vapor interface of Lennard-Jones fluids with truncated pair
interactions via extensive, high-precision simulations. The reported data cover
interfacial and bulk properties of fluid states along the whole liquid--vapor
coexistence line. A sensitivity analysis demonstrates the robustness of our
findings concerning the detailed definition of the mean interface position. We
conclude that previous claims of an enhanced surface tension at mesoscopic
scales are amenable to unambiguous tests via scattering experiments
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