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At least 685 records · Page 38Linked to original sources
PubMed1985

The role of polymer matrix structure and interparticle interactions in diffusion-limited drug release.

A lattice random-walk model is used to simulate diffusion in a porous polymer. This model may be useful for the practical design of drug-release systems. Both interacting and noninteracting particles (random walkers) were allowed to diffuse through a pore with a single exit hole. It was found that the specific interactions among the diffusing particles have little influence on the overall release rate. Diffusion through more complicated structures was investigated by simulating the diffusion of particles through two pores connected by a constricted channel whose length and width were varied. The overall rate of release was found to be proportional to the width of the constricted channel. When the length of the channel was greater than or equal to the length of the pore, the rate of release was also inversely proportional to the channel length. From a practical standpoint, release rates can be decreased (and times for release increased) by one or two orders of magnitude by decreasing the width and expanding the length of the interconnecting channels in the polymer matrix.

Delayed-Action Preparations↗
PubMed2000

Angular structure of lacunarity, and the renormalization group

We formulate the angular structure of lacunarity in fractals, in terms of a symmetry reduction of the three point correlation function. This provides a rich probe of universality, and first measurements yield new evidence in support of the equivalence between self-avoiding walks (SAW's) and percolation perimeters in two dimensions. We argue that the lacunarity reveals much of the renormalization group in real space. This is supported by exact calculations for random walks and measured data for percolation clusters and SAW's. Relationships follow between exponents governing inward and outward propagating perturbations, and we also find a very general test for the contribution of long-range interactions.

Journal Article↗
PubMed1994

Dispersive locomotion of human neutrophils in response to a steroid-induced factor from monocytes.

A monocyte-derived factor that stimulates the locomotion of human neutrophils on an albumin-coated glass surface has been prepared from the culture supernatant of dexamethasone-treated human monocytes and called STMS (steroid-treated monocyte supernatant). A modified cell tracking program has been developed and the parameters of locomotion determined by the analysis of Gail and Boone for cells moving in a persistent random walk. Cells moving in uniform concentrations of STMS, interleukin-8 (IL-8) and N-formyl-methionyl-leucyl-phenylalanine (fMLP) chosen to give a sub-maximal speed of locomotion show persistent, random and constrained random diffusion, respectively, with augmented diffusion coefficients of 0.8 +/- 0.1, 0.14 +/- 0.02 and 0.12 +/- 0.03 microns 2 per second for STMS, IL-8 and fMLP, respectively. The augmented diffusion coefficient and the underlying persistence are therefore sensitive quantitative assay parameters for STMS activity and the qualitative characteristics of locomotion allow STMS activity to be distinguished from that of all other factors tested. The contribution of lowered adhesion to locomotion was examined in a novel tilt-assay, which demonstrated that cells in the presence of STMS, but not other factors, moved down slope with significantly increased speed while maintaining contact with the substratum. The results were interpreted in terms of the bipolar form of STMS-treated cells, contrasting with multipolar forms in response to other agents. This together with low adhesiveness plus an inherent tendency of a single locomotor focus to continue motion in its original direction has been used to explain the difference between response to STMS and other factors.(ABSTRACT TRUNCATED AT 250 WORDS)

Cell Adhesion↗
PubMed1992

Base compositional structure of genomes.

We model the base compositional structure of the human and Escherichia coli genomes. Three particular properties are first quantified: (1) There is a significant tendency for any region of either genome to have a strand-symmetric base composition. (2) The variation in base composition from region to region, within each genome, is very much larger than expected from common homogeneous stochastic models. (3) A given local base composition tends to persist over a scale of at least kilobases (E. coli) or tens of kilobases (human). Multidomain stochastic models from the literature are reviewed and sharpened. In particular, quantitative measurements of the third property lead us to suggest a significant shift in the style of domain models, in which the variation of A+T content with position is modeled by a random walk with frequent small steps rather than with large quantum jumps. As an application, we suggest a way to reduce the amount of computation in the assembly of large sequences from sequences of randomly chosen fragments.

Escherichia coli↗
PubMed2000

Diffusion and deformations of single hydra cells in cellular aggregates.

Cell motion within cellular aggregates consists of both random and coherent components. We used confocal microscopy to study the center of mass displacements and deformations of single endodermal Hydra cells in two kinds of cellular aggregates, ectodermal and endodermal. We first carefully characterize the center of mass displacements using standard statistical analysis. In both aggregates, cells perform a persistent random walk, with the diffusion constant smaller in the more cohesive endodermal aggregate. We show that a simple parametric method is able to describe cell deformations and relate them to displacements. These deformations are random, with their amplitude and direction uncorrelated with the center of mass motion. Unlike for an isolated cell on a substrate, the random forces exerted by the surrounding cells predominate over the deformation of the cell itself, causing the displacements of a cell within an aggregate.

Animals↗
PubMed2002

Transport with multiple-rate exchange in disordered media.

We investigate transport of particles subject to exchange using the continuous-time random-walk framework. Transition is controlled by macroscale, and exchange by both macroscale and microscale disorder. A wide class of exchange mechanisms is represented using the multiple-rate exchange model. Particles are transported along random trajectories viewed as one-dimensional lattices. The solution of the transport problem is obtained in the form of the crossing-time density, h(t;L), at an exit surface L; h is dependent on two functions, g and f. g characterizes exchange controlled by microscale disorder. The joint density f is central for the solution as it relates the microscale and macroscale disorder along random trajectories. For the case of transition and exchange disorder, we show that power-law exponent eta (characterizing microscale disorder) and power-law exponents alpha(tau) and alpha(mu) (characterizing macroscale disorder), define two regions delimited by a line alpha(tau)=alpha(mu)(eta+1): One in which the asymptotic transport is dominated by transition, and one in which it is dominated by the exchange. For the case of transition disorder with uniform exchange, both transition and exchange can influence the late-time behavior of h(t). Microscale exchange processes will unconditionally influence the late-time behavior of h(t) only if eta<0. If eta>0, exchange will dominate at late time provided that transition is asymptotically Gaussian.

Journal Article↗
PubMed1996

Transverse relaxation in random bead packs: comparison of experimental data and numerical simulations.

Inverse Laplace transform techniques are commonly used to convert nuclear magnetic resonance (NMR) relaxation data in porous media into lifetime distributions. In this connection, we present a direct comparison of T2 measurements made on monosized packings of sintered glass beads and numerical simulations based on the grain consolidation model. Three systems, with porosities of 0.38, 0.22, and 0.14, were studied, and in each case we found that the position and width of the measured T2 distribution was well represented by the random walk simulations. These systems are generally in the fast diffusion (weak surface relaxation) regime and have relatively narrow T2 distributions. For this reason, we have found that inverse Laplace transform techniques are particularly sensitive to random noise in the measured and simulated decay spectra.

Computer Simulation↗
PubMed2005

Structure and transport properties of nanostructured materials.

In the present manuscript, we have presented the simulation of nanoporous aluminum oxide using a molecular-dynamics approach with recently developed dynamic charge transfer potential using serial/parallel programming techniques (Streitz and Mintmire Phys. Rev. B 1994, 50, 11996). The structures resembling recently invented ordered nanoporous crystalline material, MCM-41/SBA-15 (Kresge et al. Nature 1992, 359, 710), and inverted porous solids (hollow nanospheres) with up to 10 000 atoms were fabricated and studied in the present work. These materials have been used for separation of gases and catalysis. On several occasions including the design of the reactor, the knowledge of surface diffusion is necessary. In the present work, a new method for estimating surface transport of gases based on a hybrid Monte Carlo method with unbiased random walk of tracer atom on the pore surface has been introduced. The nonoverlapping packings used in the present work were fabricated using an algorithm of very slowly settling rigid spheres from a dilute suspension into a randomly packed bed. The algorithm was modified to obtain unimodal, homogeneous Gaussian and segregated bimodal porous solids. The porosity of these solids was varied by densification using an arbitrary function or by coarsening from a highly densified pellet. The surface tortuosity for the densified solids indicated an inverted bell shape curve consistent with the fact that at very high porosities there is a reduction in the connectivity while at low porosities the pores become inaccessible or dead-end. The first passage time distribution approach was found to be more efficient in terms of computation time (fewer tracer atoms needed for the linearity of Einstein's plot). Results by hybrid discrete-continuum simulations were close to the discrete simulations for a boundary layer thickness of 5lambda.

Journal Article↗
PubMed2003

Sandpile models and random walkers on finite lattices.

Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] and stochastic, such as the Manna model [S.S. Manna, J. Phys. A 24, L363 (1991)] are studied on finite square lattices with open boundaries. The avalanche size distribution P(L)(n) is calculated for a range of system sizes, L. The first few moments of this distribution are evaluated numerically and their dependence on the system size is examined. The sandpile models are conservative in the sense that grains are conserved in the bulk and can leave the system only through the boundaries. It is shown that the conservation law provides an interesting connection between the sandpile models and random-walk models. Using this connection, it is shown that the average avalanche sizes (L) for the BTW and Manna models are equal to each other, and both are equal to the average path length of a random walker starting from a random initial site on the same lattice of size L. This is in spite of the fact that the sandpile models with deterministic (BTW) and stochastic (Manna) toppling rules exhibit different critical exponents, indicating that they belong to different universality classes.

Journal Article↗
PubMed2005

Corrections to the law of mass action and properties of the asymptotic t=infinity state for reversible diffusion-limited reactions.

For diffusion-limited reversible A+A<==>B reactions we reexamine two fundamental concepts of classical chemical kinetics-the notion of "chemical equilibrium" and the "law of mass action." We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance mu apart of each other at time moment t, may associate forming a B particle at the rate k+(mu). In turn, any randomly moving B particle may spontaneously dissociate at the rate k-(lambda) into a geminate pair of As "born" at a distance lambda apart of each other. Within a formally exact approach based on Gardiner's Poisson representation method we show that the asymptotic t=infinity state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio k+(mu)k-(mu) does not depend on mu for any mu.

Journal Article↗
PubMed2001

Criticality in a model with absorbing states.

We study a one-dimensional model that undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted us to predict the exact location of the critical point and critical exponents in this model. The exponents delta=0.5 and z=2 follows from random-walk-type arguments. The exponents beta=nu( perpendicular) are found to be nonuniversal and encoded in the singular part of reactivation probability, as recently discussed by H. Hinrichsen (cond-mat/0008179). A related model with quenched randomness is also studied.

Journal Article↗
PubMed2004

Front propagation in reaction-dispersal models with finite jump speed.

The continuous-time random walk and the Hamilton-Jacobi method are used to reach analytical expressions for the speed of traveling fronts in reaction-dispersal models. In this work the waiting time and jump length are assumed to be coupled random variables. The jump length for any jump is selected according to the waiting time at the end of the previous jump, and in consequence jumps of finite speed are performed. We study the effect of finite jump speed of the particles on the speed of the traveling fronts and find that in the parabolic and hyperbolic limits it can exceed the jump speed of the particles. We report analytical expressions for different probability distribution functions. Finally, we introduce the possibility that several particle speeds are allowed, so different dispersal mechanisms can be considered simultaneously.

Journal Article↗
PubMed2005

Bios data analyzer.

The Bios Data Analyzer (BDA) is a set of computer programs (CD-ROM, in Sabelli et al., Bios. A Study of Creation, 2005) for new time series analyses that detects and measures creative phenomena, namely diversification, novelty, complexes, nonrandom complexity. We define a process as creative when its time series displays these properties. They are found in heartbeat interval series, the exemplar of bios .just as turbulence is the exemplar of chaos, in many other empirical series (galactic distributions, meteorological, economic and physiological series), in biotic series generated mathematically by the bipolar feedback, and in stochastic noise, but not in chaotic attractors. Differencing, consecutive recurrence and partial autocorrelation indicate nonrandom causation, thereby distinguishing chaos and bios from random and random walk. Embedding plots distinguish causal creative processes (e.g. bios) that include both simple and complex components of variation from stochastic processes (e.g. Brownian noise) that include only complex components, and from chaotic processes that decay from order to randomness as the number of dimensions is increased. Varying bin and dimensionality show that entropy measures symmetry and variety, and that complexity is associated with asymmetry. Trigonometric transformations measure coexisting opposites in time series and demonstrate bipolar, partial, and uncorrelated opposites in empirical processes and bios, supporting the hypothesis that bios is generated by bipolar feedback, a concept which is at variance with standard concepts of polar and complementary opposites.

Creativity↗
PubMed2000

Probability of dimer reassociation in two dimensions

We study the problem of dimer dissociation and reassociation in two dimensions through a random-walk-like calculation. In order to find the probability of dimer reassociation after a given number of hops, we give the exact analytical solution for the probability of a first return into a given region (rhombus) for a two-dimensional random walker on a squared lattice.

Journal Article↗
PubMed2003

Numerical studies of the transport behavior of a passive solute in a two-dimensional incompressible random flow field.

We study the transport behavior of a passive scalar in a two-dimensional (2D) time-independent Gaussian random velocity field by efficient and highly accurate numerical simulations. The model under consideration has been used in order to gain basic understanding of transport processes in incompressible flow through heterogeneous porous media. The velocity field is derived from the linearized solution of the Darcy equation with a Gauss-distributed log-hydraulic conductivity. The transport of a passive scalar is studied by a high precision random-walk method, which allows for a systematic nonperturbative study of the ensemble and effective dispersion coefficients. The conclusive numerical results validate the range of applicability of the perturbation theory and the consistency of nonperturbative approaches to the transport problem in a random medium. Furthermore, we observe closed streamlines in incompressible 2D Gaussian random fields, which restricts the direct applicability of the simulation method for transport in heterogeneous porous media, and questions the results of similar studies that do not observe this phenomenon.

Journal Article↗
PubMed2006

DNA electrophoresis in microfluidic post arrays under moderate electric fields.

The dynamics of long DNA moving through microfluidic arrays of micron-sized posts under a moderate electric field are modeled by a Scher-Lax continuous-time random walk. The microscale model consists of a repetitive sequence of three steps: (i) collision with the post and extension into two arms, (ii) electric-field-driven unhooking from the post, and (iii) uniform translation until the next collision. The model features two random variables: the initial offset between the two arms of the polymer during a given collision and the distance traveled between collisions. For experimentally realistic values of the electric field strength and DNA molecular weight, scaling laws indicate that the chain will generally be in a stem-flower conformation when unhooking from the post. Compared to a taut-chain model at the same field strength, the stem-flower conformation reduces the time engaged with the post and increases the collision frequency. Analytical expressions for the mean velocity and dispersivity are derived as a function of the post density, post spacing, free-solution mobility, Kuhn length, and sequence length. The incomplete extension of the chain does not strongly affect the mean velocity, but tends to increase the dispersivity relative to a taut chain. As a result, the separation resolution decreases as the field decreases for a moderate field, in agreement with experiments. The quantitative agreement between the model and experimental data is satisfactory, especially considering that the model contains no adjustable parameters.

DNA↗
PubMed2001

Large-scale heterogeneity of the fossil record: implications for Phanerozoic biodiversity studies.

Patterns of origination, extinction and standing diversity through time have been inferred from tallies of taxa preserved in the fossil record. This approach assumes that sampling of the fossil record is effectively uniform over time. Although recent evidence suggests that our sampling of the available rock record has indeed been very thorough and effective, there is also overwhelming evidence that the rock record available for sampling is itself distorted by major systematic biases. Data on rock outcrop area compiled for post-Palaeozoic sediments from Western Europe at stage level are presented. These show a strongly cyclical pattern corresponding to first- and second-order sequence stratigraphical depositional cycles. Standing diversity increases over time and, at the coarsest scale, is decoupled from surface outcrop area. This increasing trend can therefore be considered a real pattern. Changes in standing diversity and origination rates over time-scales measured in tens of millions of years, however, are strongly correlated with surface outcrop area. Extinction peaks conform to a random-walk model, but larger peaks occur at just two positions with respect to second-order stratigraphical sequences, towards the culmination of stacked transgressive system tracts and close to system bases, precisely the positions where taxonomic last occurrences are predicted to cluster under a random distribution model. Many of the taxonomic patterns that have been described from the fossil record conform to a species-area effect. Whether this arises primarily from sampling bias, or from changing surface area of marine shelf seas through time and its effect on biodiversity, remains problematic.

Animals↗
PubMed2002

Quantum multibaker maps: extreme quantum regime.

We introduce a family of models for quantum mechanical, one-dimensional random walks, called quantum multibaker maps (QMB). These are Weyl quantizations of the classical multibaker models previously considered by Gaspard, Tasaki, and others. Depending on the properties of the phase's parametrizing the quantization, we consider only two classes of the QMB maps: uniform and random. Uniform QMB maps are characterized by phases that are the same in every unit cell of the multibaker chain. Random QMB maps have phases that vary randomly from unit cell to unit cell. The eigenstates in the former case are extended while in the latter they are localized. In the uniform case and for large variant Planck's over 2pi, analytic solutions can be obtained for the time-dependent quantum states for periodic chains and for open chains with absorbing boundary conditions. Steady state solutions and the properties of the relaxation to a steady state for a uniform QMB chain in contact with "particle" reservoirs can also be described analytically. The analytical results are consistent with, and confirmed by, results obtained from numerical methods. We report here results for the deep quantum regime (large variant Planck's over 2pi ) of the uniform QMB, as well as some results for the random QMB. We leave the moderate and small variant Planck's over 2pi results as well as further consideration of the other versions of the QMB for further publications.

Journal Article↗