Layering instability in a confined suspension flow.

We show [J. Fluid Mech. 592, 447 (2007)] that swapping (reversing) trajectories in confined suspension flows prevent collisions between particles approaching each other in adjacent streamlines. Here we demonstrate that by inducing layering this hydrodynamic mechanism changes the microstructure of suspensions in a confined Couette flow. Layers occur either in the near-wall regions or span the whole channel width, depending on the strength of the swapping-trajectory effect. While our theory focuses on dilute suspensions, we postulate that this new hydrodynamic mechanism controls the formation of a layered microstructure in a wide range of densities.

Mutual information and redundancy in spontaneous communication between cortical neurons.

An important question in neural information processing is how neurons cooperate to transmit information. To study this question, we resort to the concept of redundancy in the information transmitted by a group of neurons and, at the same time, we introduce a novel concept for measuring cooperation between pairs of neurons called relative mutual information (RMI). Specifically, we studied these two parameters for spike trains generated by neighboring neurons from the primary visual cortex in the awake, freely moving rat. The spike trains studied here were spontaneously generated in the cortical network, in the absence of visual stimulation. Under these conditions, our analysis revealed that while the value of RMI oscillated slightly around an average value, the redundancy exhibited a behavior characterized by a higher variability. We conjecture that this combination of approximately constant RMI and greater variable redundancy makes information transmission more resistant to noise disturbances. Furthermore, the redundancy values suggest that neurons can cooperate in a flexible way during information transmission. This mostly occurs via a leading neuron with higher transmission rate or, less frequently, through the information rate of the whole group being higher than the sum of the individual information rates-in other words in a synergetic manner. The proposed method applies not only to the stationary, but also to locally stationary neural signals.

Motion of a spherical particle near a planar fluid-fluid interface: the effect of surface incompressibility.

Hydrodynamic coupling of a spherical particle to an undeformable planar fluid-fluid interface under creeping-flow conditions is discussed. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. In the incompressible surfactant limit, a uniform surfactant concentration is maintained by Marangoni stresses associated with infinitesimal surfactant redistribution. Our detailed numerical calculations show that the effect of surface incompressibility on lateral particle motion is accurately accounted for by the first reflection of the flow from the interface. For small particle-interface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particle-wall gaps, the transverse and lateral particle resistance coefficients can be rescaled onto corresponding universal master curves. The scaling functions depend on a scaling variable that combines the particle-wall gap with the viscosity ratio between fluids on both sides of the interface. A logarithmic dependence of the contact value of the lateral resistance function on the viscosity ratio is derived. Accurate numerical calculations are performed using our Cartesian-representation method.

Hydrodynamic coupling of spherical particles to a planar fluid-fluid interface: theoretical analysis.

We have developed a new technique (based on our Cartesian-representation method) to describe hydrodynamic interactions of a spherical particle with an undeformable planar fluid-fluid interface under creeping-flow conditions. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. We consider the effect of surface incompressibility and surface viscosity on particle motion. The new algorithm allows to calculate particle mobility coefficients for hydrodynamically coupled particles, moving either on the same or on the opposite sides of the interface.

The intensity correlation function in evanescent wave scattering.

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.

Streaming potential studies of colloid, polyelectrolyte and protein deposition.

Recent developments in the electrokinetic determination of particle, protein and polyelectrolyte monolayers at solid/electrolyte interfaces, are reviewed. Illustrative theoretical results characterizing particle transport to interfaces are presented, especially analytical formulae for the limiting flux under various deposition regimes and expressions for diffusion coefficients of various particle shapes. Then, blocking effects appearing for higher surface coverage of particles are characterized in terms of the random sequential adsorption model. These theoretical predictions are used for interpretation of experimental results obtained for colloid particles and proteins under convection and diffusion transport conditions. The kinetics of particle deposition and the structure of monolayers are analyzed quantitatively in terms of the generalized random sequential adsorption (RSA) model, considering the coupling of the bulk and surface transport steps. Experimental results are also discussed, showing the dependence of the jamming coverage of monolayers on the ionic strength of particle suspensions. In the next section, theoretical and experimental results pertaining to electrokinetics of particle covered surfaces are presented. Theoretical models are discussed, enabling a quantitative evaluation of the streaming current and the streaming potential as a function of particle coverage and their surface properties (zeta potential). Experimental data related to electrokinetic characteristics of particle monolayers, mostly streaming potential measurements, are presented and interpreted in terms of the above theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of experiments performed for polyelectrolyte and protein covered surfaces. The utility of the electrokinetic measurements for a precise, in situ determination of particle and protein monolayers at various interfaces is pointed out.

Equilibrium and nonequilibrium thermodynamics of particle-stabilized thin liquid films.

Our recent quasi-two-dimensional thermodynamic description of thin liquid films stabilized by colloidal particles is generalized to describe nonuniform equilibrium states of films in external potentials and nonequilibrium transport processes produced in the film by gradients of thermodynamic forces. Using a Monte Carlo simulation method, we have determined equilibrium equations of state for a film stabilized by a suspension of hard spheres. Employing a multipolar-expansion method combined with a flow-reflection technique, we have also evaluated the short-time film-viscosity coefficients and collective particle mobility.

Hydrodynamic crystals: collective dynamics of regular arrays of spherical particles in a parallel-wall channel.

Simulations of over 10;{3} hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel accelerated Stokesian-dynamics algorithm relies on simplifications associated with the Hele-Shaw asymptotic far-field form of the flow scattered by the particles. The simulations reveal propagation of particle-displacement waves, deformation, and rearrangements of a particle lattice, propagation of dislocation defects in ordered arrays, and long-lasting coexistence of ordered and disordered regions.

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods.

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction phi. For low rod concentrations, the correction to the Einstein diffusion constant of the sphere due to the presence of rods is a linear function of phi with the slope alpha proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two-body hydrodynamic interactions are calculated using the so-called bead model in which the rod of aspect ratio p is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated using the multipole method with the accuracy controlled by a multipole truncation order and limited only by the computational power. A remarkable accuracy is obtained already for the lowest truncation order, which enables calculations for very long rods, up to p=1000. Additionally, the bead model is checked by filling the rod with smaller spheres. This procedure shows that for longer rods the basic model provides reasonable results varying less than 5% from the model with filling. An analytical expression for alpha as a function of p is derived in the limit of very long rods. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.

Application of Lempel-Ziv complexity to the analysis of neural discharges.

Pattern matching is a simple method for studying the properties of information sources based on individual sequences (Wyner et al 1998 IEEE Trans. Inf. Theory 44 2045-56). In particular, the normalized Lempel-Ziv complexity (Lempel and Ziv 1976 IEEE Trans. Inf. Theory 22 75-88), which measures the rate of generation of new patterns along a sequence, is closely related to such important source properties as entropy and information compression ratio. We make use of this concept to characterize the responses of neurons of the primary visual cortex to different kinds of stimulus, including visual stimulation (sinusoidal drifting gratings) and intracellular current injections (sinusoidal and random currents), under two conditions (in vivo and in vitro preparations). Specifically, we digitize the neuronal discharges with several encoding techniques and employ the complexity curves of the resulting discrete signals as fingerprints of the stimuli ensembles. Our results show, for example, that if the neural discharges are encoded with a particular one-parameter method ('interspike time coding'), the normalized complexity remains constant within some classes of stimuli for a wide range of the parameter. Such constant values of the normalized complexity allow then the differentiation of the stimuli classes. With other encodings (e.g. 'bin coding'), the whole complexity curve is needed to achieve this goal. In any case, it turns out that the normalized complexity of the neural discharges in vivo are higher (and hence carry more information in the sense of Shannon) than in vitro for the same kind of stimulus.

On the number of states of the neuronal sources.

In a previous paper (Proceedings of the World Congress on Neuroinformatics (2001)) the authors applied the so-called Lempel-Ziv complexity to study neural discharges (spike trains) from an information-theoretical point of view. Along with other results, it is shown there that this concept of complexity allows to characterize the responses of primary visual cortical neurons to both random and periodic stimuli. To this aim we modeled the neurons as information sources and the spike trains as messages generated by them. In this paper, we study further consequences of this mathematical approach, this time concerning the number of states of such neuronal information sources. In this context, the state of an information source means an internal degree of freedom (or parameter) which allows outputs with more general stochastic properties, since symbol generation probabilities at every time step may additionally depend on the value of the current state of the neuron. Furthermore, if the source is ergodic and Markovian, the number of states is directly related to the stochastic dependence lag of the source and provides a measure of the autocorrelation of its messages. Here, we find that the number of states of the neurons depends on the kind of stimulus and the type of preparation ( in vivo versus in vitro recordings), thus providing another way of differentiating neuronal responses. In particular, we observed that (for the encoding methods considered) in vitro sources have a higher lag than in vivo sources for periodic stimuli. This supports the conclusion put forward in the paper mentioned above that, for the same kind of stimulus, in vivo responses are more random (hence, more difficult to compress) than in vitro responses and, consequently, the former transmit more information than the latter.

The Viscosity of Electrostatically Stabilized Dispersions of Spherical Colloid Particles.

The viscosity virial coefficient characteristic of a moderately concentrated dispersion [and proportional to the Huggins coefficient] is calculated for electrostatically stabilized monodisperse suspensions of spherical colloid particles. The energy of interaction between two colloid particles is modeled as the sum of dispersion (van der Waals) and electric double-layer contributions. Comparisons of theoretical predictions and experimental data permit conclusions to be drawn about the adequacy of this model. Copyright 1999 Academic Press.

The Viscosity of Polymerically Stabilized Dispersions of Spherical Colloid Particles.

A recently developed theory and computational procedure are used to generate theoretical estimates of the viscosity virial coefficient for polymerically stabilized monodisperse suspensions of spherical colloid particles. Numerical results are presented for representative values of the five parameters that characterize the interactions among the colloid particles. Copyright 1999 Academic Press.