660 research outputs found
Kurtosis Based Blind Source Extraction of Complex Noncircular Signals with Application in EEG Artifact Removal in Real Time
First-order virial expansion of short-time diffusion and sedimentation coefficients of permeable particles suspensions
For suspensions of permeable particles, the short-time translational and
rotational self-diffusion coefficients, and collective diffusion and
sedimentation coefficients are evaluated theoretically. An individual particle
is modeled as a uniformly permeable sphere of a given permeability, with the
internal solvent flow described by the Debye-Bueche-Brinkman equation. The
particles are assumed to interact non-hydrodynamically by their excluded
volumes. The virial expansion of the transport properties in powers of the
volume fraction is performed up to the two-particle level. The first-order
virial coefficients corresponding to two-body hydrodynamic interactions are
evaluated with very high accuracy by the series expansion in inverse powers of
the inter-particle distance. Results are obtained and discussed for a wide
range of the ratio, x, of the particle radius to the hydrodynamic screening
length inside a permeable sphere. It is shown that for x >= 10, the virial
coefficients of the transport properties are well-approximated by the
hydrodynamic radius (annulus) model developed by us earlier for the effective
viscosity of porous-particle suspensions
Far-field approximation for hydrodynamic interactions in parallel-wall geometry
A complete analysis is presented for the far-field creeping flow produced by
a multipolar force distribution in a fluid confined between two parallel planar
walls. We show that at distances larger than several wall separations the flow
field assumes the Hele-Shaw form, i.e., it is parallel to the walls and varies
quadratically in the transverse direction. The associated pressure field is a
two-dimensional harmonic function that is characterized by the same multipolar
number m as the original force multipole. Using these results we derive
asymptotic expressions for the Green's matrix that represents Stokes flow in
the wall-bounded fluid in terms of a multipolar spherical basis. This Green's
matrix plays a central role in our recently proposed algorithm [Physica A xx,
{\bf xxx} (2005)] for evaluating many-body hydrodynamic interactions in a
suspension of spherical particles in the parallel-wall geometry. Implementation
of our asymptotic expressions in this algorithm increases its efficiency
substantially because the numerically expensive evaluation of the exact matrix
elements is needed only for the neighboring particles. Our asymptotic analysis
will also be useful in developing hydrodynamic algorithms for wall-bounded
periodic systems and implementing acceleration methods by using corresponding
results for the two-dimensional scalar potential.Comment: 28 pages 5 figure
Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method
This paper describes the results of our theoretical and numerical studies of
hydrodynamic interactions in a suspension of spherical particles confined
between two parallel planar walls, under creeping-flow conditions. We propose a
novel algorithm for accurate evaluation of the many-particle friction matrix in
this system--no such algorithm has been available so far.
Our approach involves expanding the fluid velocity field into spherical and
Cartesian fundamental sets of Stokes flows. The interaction of the fluid with
the particles is described using the spherical basis fields; the flow scattered
with the walls is expressed in terms of the Cartesian fundamental solutions. At
the core of our method are transformation relations between the spherical and
Cartesian basis sets. These transformations allow us to describe the flow field
in a system that involves both the walls and particles.
We used our accurate numerical results to test the single-wall superposition
approximation for the hydrodynamic friction matrix. The approximation yields
fair results for quantities dominated by single particle contributions, but it
fails to describe collective phenomena, such as a large transverse resistance
coefficient for linear arrays of spheres
Brain-Computer Interfaces: Towards Practical Implementations and Potential Applications
[No abstract available
Comparison between the Torquato-Rintoul theory of the interface effect in composite media and elementary results
We show that the interface effect on the properties of composite media
recently proposed by Torquato and Rintoul (TR) [Phys. Rev. Lett. 75, 4067
(1995)] is in fact elementary, and follows directly from taking the limit in
the dipolar polarizability of a coated sphere: the TR ``critical values'' are
simply those that make the dipolar polarizability vanish. Furthermore, the new
bounds developed by TR either coincide with the Clausius-Mossotti (CM) relation
or provide poor estimates. Finally, we show that the new bounds of TR do not
agree particularly well with the original experimental data that they quote.Comment: 13 pages, Revtex, 8 Postscript figure
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
An analysis of the far-field response to external forcing of a suspension in Stokes flow in a parallel-wall channel
The leading-order far-field scattered flow produced by a particle in a
parallel-wall channel under creeping flow conditions has a form of the
parabolic velocity field driven by a 2D dipolar pressure distribution. We show
that in a system of hydrodynamically interacting particles, the pressure
dipoles contribute to the macroscopic suspension flow in a similar way as the
induced electric dipoles contribute to the electrostatic displacement field.
Using this result we derive macroscopic equations governing suspension
transport under the action of a lateral force, a lateral torque or a
macroscopic pressure gradient in the channel. The matrix of linear transport
coefficients in the constitutive relations linking the external forcing to the
particle and fluid fluxes satisfies the Onsager reciprocal relation. The
transport coefficients are evaluated for square and hexagonal periodic arrays
of fixed and freely suspended particles, and a simple approximation in a
Clausius-Mossotti form is proposed for the channel permeability coefficient. We
also find explicit expressions for evaluating the periodic Green's functions
for Stokes flow between two parallel walls.Comment: 23 pages, 12 figure
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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