694 research outputs found
Surfactant-induced migration of a spherical drop in Stokes flow
In Stokes flows, symmetry considerations dictate that a neutrally-buoyant
spherical particle will not migrate laterally with respect to the local flow
direction. We show that a loss of symmetry due to flow-induced surfactant
redistribution leads to cross-stream drift of a spherical drop in Poiseuille
flow. We derive analytical expressions for the migration velocity in the limit
of small non-uniformities in the surfactant distribution, corresponding to
weak-flow conditions or a high-viscosity drop. The analysis predicts that the
direction of migration is always towards the flow centerline.Comment: Significant extension with additional text, figures, equations, et
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Short-time rotational diffusion in monodisperse charge-stabilized colloidal suspensions
We investigate the combined effects of electrostatic interactions and
hydrodynamic interactions on the short-time rotational self-diffusion
coefficient in charge-stabilized suspensions. We calculate this coefficient as
a function of volume fraction for various effective particle charges and
amounts of added electrolyte. The influence of the hydrodynamic interactions on
the rotational diffusion coefficient is less pronounced for charged particles
than for uncharged ones. Salt-free suspensions are weakly influenced by
hydrodynamic interactions. For these strongly correlated systems we obtain a
quadratic volume fraction-dependence of the diffusion coefficient, which is
well explained in terms of an effective hard sphere model.Comment: 21 pages, LaTeX, 7 Postscript figures included using epsf, to appear
in Physica
Self-diffusion coefficients of charged particles: Prediction of Nonlinear volume fraction dependence
We report on calculations of the translational and rotational short-time
self-diffusion coefficients and for suspensions of
charge-stabilized colloidal spheres. These diffusion coefficients are affected
by electrostatic forces and many-body hydrodynamic interactions (HI). Our
computations account for both two-body and three-body HI. For strongly charged
particles, we predict interesting nonlinear scaling relations and depending on volume fraction
, with essentially charge-independent parameters and . These
scaling relations are strikingly different from the corresponding results for
hard spheres. Our numerical results can be explained using a model of effective
hard spheres. Moreover, we perceptibly improve the known result for of
hard sphere suspensions.Comment: 8 pages, LaTeX, 3 Postscript figures included using eps
Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls
We study hydrodynamic interactions of spherical particles in incident
Poiseuille flow in a channel with infinite planar walls. The particles are
suspended in a Newtonian fluid, and creeping-flow conditions are assumed.
Numerical results, obtained using our highly accurate Cartesian-representation
algorithm [Physica A xxx, {\bf xx}, 2005], are presented for a single sphere,
two spheres, and arrays of many spheres. We consider the motion of freely
suspended particles as well as the forces and torques acting on particles
adsorbed at a wall. We find that the pair hydrodynamic interactions in this
wall-bounded system have a complex dependence on the lateral interparticle
distance due to the combined effects of the dissipation in the gap between the
particle surfaces and the backflow associated with the presence of the walls.
For immobile particle pairs we have examined the crossover between several
far-field asymptotic regimes corresponding to different relations between the
particle separation and the distances of the particles from the walls. We have
also shown that the cumulative effect of the far-field flow substantially
influences the force distribution in arrays of immobile spheres. Therefore, the
far-field contributions must be included in any reliable algorithm for
evaluating many-particle hydrodynamic interactions in the parallel-wall
geometry.Comment: submitted to Physics of Fluid
Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies
The asymptotic frequency , dependence of the dynamic viscosity of
neutral hard sphere colloidal suspensions is shown to be of the form , where has been determined as a
function of the volume fraction , for all concentrations in the fluid
range, is the solvent viscosity and the P\'{e}clet time. For
a soft potential it is shown that, to leading order steepness, the asymptotic
behavior is the same as that for the hard sphere potential and a condition for
the cross-over behavior to is given. Our result for the hard
sphere potential generalizes a result of Cichocki and Felderhof obtained at low
concentrations and agrees well with the experiments of van der Werff et al, if
the usual Stokes-Einstein diffusion coefficient in the Smoluchowski
operator is consistently replaced by the short-time self diffusion coefficient
for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur
Brownian Dynamics Simulation of Polydisperse Hard Spheres
Standard algorithms for the numerical integration of the Langevin equation
require that interactions are slowly varying during to the integration
timestep. This in not the case for hard-body systems, where there is no
clearcut between the correlation time of the noise and the timescale of the
interactions. Starting from a short time approximation of the Smoluchowsky
equation, we introduce an algorithm for the simulation of the overdamped
Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamics
interactions and briefly discuss the extension to the case of external drifts
Least Dependent Component Analysis Based on Mutual Information
We propose to use precise estimators of mutual information (MI) to find least
dependent components in a linearly mixed signal. On the one hand this seems to
lead to better blind source separation than with any other presently available
algorithm. On the other hand it has the advantage, compared to other
implementations of `independent' component analysis (ICA) some of which are
based on crude approximations for MI, that the numerical values of the MI can
be used for:
(i) estimating residual dependencies between the output components;
(ii) estimating the reliability of the output, by comparing the pairwise MIs
with those of re-mixed components;
(iii) clustering the output according to the residual interdependencies.
For the MI estimator we use a recently proposed k-nearest neighbor based
algorithm. For time sequences we combine this with delay embedding, in order to
take into account non-trivial time correlations. After several tests with
artificial data, we apply the resulting MILCA (Mutual Information based Least
dependent Component Analysis) algorithm to a real-world dataset, the ECG of a
pregnant woman.
The software implementation of the MILCA algorithm is freely available at
http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press
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