Papers by Eligiusz Wajnryb
We review several applications of Lempel-Ziv complexity to the characterization of neural respons... more We review several applications of Lempel-Ziv complexity to the characterization of neural responses. In particular, Lempel-Ziv complexity allows to estimate the entropy of binned spike trains in an alternative way to the usual method based on the relative frequencies of words, with the deÿnitive advantage of no requiring very long registers. We also use complexity to discriminate neural responses to di erent kinds of stimuli and to evaluate the number of states of neuronal sources.
Dynamics of single flexible non-Brownian fibers, tumbling in a Poiseuille flow between two parall... more Dynamics of single flexible non-Brownian fibers, tumbling in a Poiseuille flow between two parallel solid plane walls, is studied with the use of the hydromultipole numerical code, based on the multipole expansion of the Stokes equations, corrected for lubrication. It is shown that for a wide range of the system parameters, the migration rate towards the middle plane of the
Physica A: Statistical Mechanics and its Applications, 1998
A recently developed formalism is used to construct an expression for the viscosity second virial... more A recently developed formalism is used to construct an expression for the viscosity second virial coe cient (proportional to the Huggins coe cient) of a monodisperse suspension of spherical colloid particles with piece-wise constant potentials of interaction. Numerical values are generated for the two special cases of square-well and square-step potentials, both with stick boundary conditions at the solute-solvent interface. Also, presented is a demonstration that the so-called "sticky-sphere" model is incapable of representing a suspension of particles interacting with a square-well potential.
The Journal of Chemical Physics, 2015
We investigate experimentally and theoretically thin layers of colloid particles held adjacent to... more We investigate experimentally and theoretically thin layers of colloid particles held adjacent to a solid substrate by gravity. Epifluorescence, confocal, and holographic microscopy, combined with Monte Carlo and hydrodynamic simulations, are applied to infer the height distribution function of particles above the surface, and their diffusion coefficient parallel to it. As the particle area fraction is increased, the height distribution becomes bimodal, indicating the formation of a distinct second layer. In our theory, we treat the suspension as a series of weakly coupled quasi-two-dimensional layers in equilibrium with respect to particle exchange. We experimentally, numerically, and theoretically study the changing occupancies of the layers as the area fraction is increased. The decrease of the particle diffusion coefficient with concentration is found to be weakened by the layering. We demonstrate that particle polydispersity strongly affects the properties of the sedimented layer, because of particle size segregation due to gravity.
New Journal of Physics, 2015
We use numerical simulations of a bead-spring model chain to investigate the evolution of the con... more We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a dimensionless elastic parameter, we identify two distinct conformational modes with different final size, shape, and orientation. Through further analysis we identify slipknots in the chain. Finally, we provide examples of initial configurations of an "open" trefoil knot that the flow unknots and then knots again, sometimes repeating several times. These changes in topology should be reflected in changes in bulk rheological and/or transport properties.
The Journal of Chemical Physics, 2015
A diffusion equation for Brownian motion with arbitrary frictional coefficient: Application to th... more A diffusion equation for Brownian motion with arbitrary frictional coefficient: Application to the turnover problem Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed. C 2015 AIP Publishing LLC. [http://dx.
We analyze the hydrodynamic interactions between spherical solid particles which are suspended in... more We analyze the hydrodynamic interactions between spherical solid particles which are suspended in a qui-escent fluid and in contact with a planar fluid–gas interface. Stick boundary conditions are assumed on the sphere surfaces, and the free surface boundary conditions are accounted for by the method of images. The one-sphere hydrodynamic resistance operator of such a quasi-two-dimensional system is calculated numer-ically. Using a spherical multipole expansion with symmetry-adjusted basis functions, explicit results are derived for the long-distance terms of the two-sphere mobility tensor up to cubic order in the inverse in-terparticle distance. The point particle model is also constructed, taking into account the constraint forces necessary to keep the point-particles at a fixed 'radius' a apart from the interface. The accuracy of both far field approximations is discussed by comparing them with the precise many-sphere mobility, evaluated by the multipole expansion.
Dynamics of flexible non-Brownian fibers in shear flow at low-Reynolds-number are analyzed numeri... more Dynamics of flexible non-Brownian fibers in shear flow at low-Reynolds-number are analyzed numerically for a wide range of the ratios A of the fiber bending force to the viscous drag force. Initially, the fibers are aligned with the flow, and later they move in the plane perpendicular to the flow vorticity. A surprisingly rich spectrum of different modes is observed when the value of A is systematically changed, with sharp transitions between coiled and straightening out modes, period-doubling bifurcations from periodic to migrating solutions, irregular dynamics and chaos.
Soft matter, Jan 12, 2015
In this article we report on a study of the near-wall dynamics of suspended colloidal hard sphere... more In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.
Physica A: Statistical Mechanics and its Applications, 1998
A recently developed formalism for computing the low-frequency, Newtonian viscosity of moderately... more A recently developed formalism for computing the low-frequency, Newtonian viscosity of moderately dense monodisperse suspensions is extended to include polydisperse suspensions. In the form presented here this general theory is applicable to spherical solute particles suspended in a Newtonian solvent. Explicit formulas are obtained for the viscosity virial coe cients associated with ÿrst and second order terms in powers of the solute volume fraction. It is proved that the second order term in the viscosity virial series for a polydisperse suspension of solute particles is fully characterized by a single, dimensionless function b 2( ), with 06 61. Numerical values are presented for the second order (Huggins) coe cient speciÿc to hard-sphere particles with general stick-slip solute-solvent boundary conditions and for "spherical surfactant particles" as well. Calculations are included also for suspensions with log-normal particle-size distributions.
BMC Neuroscience, 2015
Background: Explaining how the brain processing is so fast remains an open problem (van Hemmen JL... more Background: Explaining how the brain processing is so fast remains an open problem (van Hemmen JL, Sejnowski T., 2004). Thus, the analysis of neural transmission (Shannon CE, Weaver W., 1963) processes basically focuses on searching for effective encoding and decoding schemes. According to the Shannon fundamental theorem, mutual information plays a crucial role in characterizing the efficiency of communication channels. It is well known that this efficiency is determined by the channel capacity that is already the maximal mutual information between input and output signals. On the other hand, intuitively speaking, when input and output signals are more correlated, the transmission should be more efficient. A natural question arises about the relation between mutual information and correlation. We analyze the relation between these quantities using the binary representation of signals, which is the most common approach taken in studying neuronal processes of the brain. Results: We present binary communication channels for which mutual information and correlation coefficients behave differently both quantitatively and qualitatively. Despite this difference in behavior, we show that the noncorrelation of binary signals implies their independence, in contrast to the case for general types of signals. Conclusions: Our research shows that the mutual information cannot be replaced by sheer correlations. Our results indicate that neuronal encoding has more complicated nature which cannot be captured by straightforward correlations between input and output signals once the mutual information takes into account the structure and patterns of the signals.
Small particles (or macromolecules) added to a colloidal solution of much larger species produce ... more Small particles (or macromolecules) added to a colloidal solution of much larger species produce the effective structural force acting between the large particles and the walls. When the large particles are moving, the macromolecules can also produce non-equilibrium effects, which include the hydrodynamic and Brownian resistance forces. Our talk will focus on these non-equilibrium phenomena for a large sphere near a planar wall in a dilute solution of much smaller spherical particles. The gap between the wall and large particle is of the order of the small-particle diameter. It is thus much larger than the size of the lubrication region, and our analysis relies on this length-scale separation. To find the hydrodynamic contribution to the resistance force we evaluate the induced-force distribution on a sphere in a gap between (locally) planar, parallel walls. The pressure field in the original system, where the gap width is slowly varying, is then obtained by solving lubrication equa...
Hydrodynamic interactions of spherical particles in incident Poiseuille flow in a channel with in... more Hydrodynamic interactions of spherical particles in incident Poiseuille flow in a channel with infinite planar walls are investigated. The particles are suspended in a Newtonian fluid, and creeping-flow conditions are assumed. We consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall. Using our highly accurate Cartesian-representation algorithm, 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 s...
Our novel accelerated Stokesian-dynamics algorithm for a system of spherical particles bounded by... more Our novel accelerated Stokesian-dynamics algorithm for a system of spherical particles bounded by two parallel planar walls serves to efficiently follow the dynamics of about 10^3 particles. Its high efficiency is due to simplifications associated with the far-field asymptotics of the scattered flow produced by the particles. By a proper choice of basis Stokes flows (which in the near field tend to Lamb solutions and in the far field to multipolar basis of Hele-Shaw flows), the problem is reduced to a sparse linear system that is solved at a low numerical cost using iterative sparse-matrix manipulation techniques. We also present applications of our algorithm to study suspension transport in microfluidic channels and collective motion of large regular particle arrays in Poiseuille flow.
The effects of confinement on the dynamics of binary encounters between spherical particles in sh... more The effects of confinement on the dynamics of binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of particles. In contrast, in unbounded space spherical particles on open trajectories return to their original streamlines after a binary encounter is completed (with no non-hydrodynamic forces present). The physical origin of the new trajectories is explained in terms of counter-rotation of particle pairs that is driven by the dynamic pressure distribution. The new type of trajectories constitutes the dominant cross-streamline migration mechanism in dilute wall-bounded suspensions. We show that this mechanism is responsible for the unusually large self-diffusivity observed in experiments by Zarraga and Leighton (2002). The effect of the new migra...
Due to the presence of oscillatory structural forces, static and dynamic properties of thin liqui... more Due to the presence of oscillatory structural forces, static and dynamic properties of thin liquid films stabilized by colloidal particles, micelles, or macromolecules differ from the properties of particle-free films. During drainage process, particle-stabilized films often form a stepwise structure with coexisting regions (phases) of uniform but different thickness. We describe film phase equilibria using a quasi-two dimensional thermodynamic formalism. The key quantity in our approach is the film tension. We show that the particle contribution to this quantity results from the anisotropy of the particle osmotic-pressure tensor in the film. The quasi-2d description is also developed for non-equilibrium film states. We show that the motion of particle-stabilized films is analogous to the dynamics of a two-dimensional compressible fluid - the film thickness plays the role of mass density per unit area and film tension the role of pressure. In the linear-response regime, the film dyn...
We present theoretical, numerical, and experimental investigations of evane-scent-wave dynamic li... more We present theoretical, numerical, and experimental investigations of evane-scent-wave dynamic light scattering (EWDLS) in a wall-bounded colloidal suspension of spheres. The first cummulant gamma1 representing the initial decay of the time autocorrelation function of the scattered field is expressed in terms of the hydrodynamic tensor Hw(,q) describing response of the suspension to a spatially varying harmonic force damped exponentially away from the wall. The wavelength of the harmonic spatial variation corresponds to the scattering vector q in the EWDLS experiments, and the exponential decay is characterized by the decay length &-1circ; of the evanescent wave. The hydrodynamic tensor Hw is evaluated using viral expansion at low densities and numerical simulations at higher densities. A complex non-isotropic structure of the tensor Hw(,q) reflects the hydrodynamic particle-wall coupling and wall-induced short range suspension ordering. Our theory and simulations agree well with th...
Starting from the microscopic description of the system, we derive a set of macroscopic transport... more Starting from the microscopic description of the system, we derive a set of macroscopic transport equations for fluid and suspension flow in a parallel-wall channel under Stokes-flow conditions. The transport equations involve a generalized permeability (or mobility) relation that links the suspension-volume and particle fluxes to the macroscopic pressure gradient and lateral force acting on the particles. The matrix of transport coefficients in these equations satisfies the Onsager reciprocal relation. Invoking an analogy between the hydrodynamic and electrostatic problems we propose an approximation for the channel permeability coefficients which is similar to the Clausius--Mossotti approximation for the effective dielectric constant. The transport coefficients are evaluated for fixed and mobile arrays of spherical particles. We find that a densely packed fixed particle array reduces the channel permeability to 1% of the permeability of a particle-free channel. We also discuss app...
Binary collisions between rough (or repulsive) particles in dilute suspension flows are assumed t... more Binary collisions between rough (or repulsive) particles in dilute suspension flows are assumed to lead to particle diffusion that relaxes suspension non-uniformities. Here we show that binary collisions in wall-bounded shear flow may result in an opposite effect, i.e., development of layered particle ordering. We demonstrate that, depending on particle roughness (or repulsion range), the ordering may either extend through the whole channel width or start from the walls and decay exponentially towards the channel center. The key factor in formation of the layered behavior is existence of the swapping (reversing) binary trajectories [J. Fluid Mech. 592].
In this talk we analyze new structural transformations that occur in periodic square arrays of mi... more In this talk we analyze new structural transformations that occur in periodic square arrays of microspheres. During the array evolution, the initial perturbations observed as density waves and vertical particle scatter slowly dissipate and there occurs a sudden transition from the square to hexagonal order with a large number of mobile defects. The resulting suspension structure resembles a hexatic phase. We explain this transformation in terms of a buckling instability that produces vertical displacements of particle rows. Our simulations predict that at the early stages of the array evolution random transverse particle displacements stabilize the particle lattice, preventing coherent movement of particle rows. We discuss implications of this novel stabilizing mechanism for systems such as compressed membranes undergoing thermal fluctuations.
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Papers by Eligiusz Wajnryb