Biomedical subjects

John J Kozak

Publications and source records attributed to John J Kozak.

4 recordsLinked to original sources

PubMed2006

Aggregation of dipolar colloidal particles: geometric effects.

To understand the importance of confinement and the influence of translational degrees of freedom on aggregation of dipolar colloidal particles, we calculate numerically-exact values for the mean encounter time for two nonspherically symmetric molecules to form a two-molecule cluster, regarded here as a precursor to aggregation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a "dimer" in the sense that each molecule is specified to occupy two adjacent lattice sites. The two dimers undergo simultaneous translation, and the mean times for their encounter are determined. Exact numerical results are obtained via application of the theory of finite Markov processes. The results allow one to examine in a detailed way the interplay among such factors as geometrical confinement, system size, translational motion, and specific orientational effects in influencing the aggregation event. The results are compared with previously reported theoretical predictions and experiments on the behavior of dipolar colloidal particles in the presence of an applied magnetic field.

Journal Article↗

PubMed2003

Lattice model of the early stages of the electrification of a cloud.

The early stages of the microphysics of the electrification process within a cloud are considered using a two-dimensional lattice model. Using insights generated from Monte Carlo simulations and the theory of finite Markov processes, the mean walk length statistics of the particles, the instantaneous electric potential and electric field profiles, the time evolution of electrostatic energy and their dependence on system size are studied. Some unexpected features of the kinetics of electrification and of the statistics of crossings of the threshold for an electric discharge to occur are brought out.

Journal Article↗

PubMed2003

Geometrical effects in protein nucleation.

To understand the importance of protein anisotropy and the influence of translational and rotational degrees of freedom on the nucleation event, we calculate numerically-exact values for the mean encounter time for two non-spherically symmetric molecules to form a cluster, regarded here as a precursor to nucleation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a 'dimer' in the sense that each molecule is specified to occupy two lattice sites. The two dimers undergo simultaneously translation and/or rotation, and the mean times for their encounter are determined. Exact numerical results are obtained for small lattices via application of the theory of finite Markov processes, and the results corroborated and extended to large lattices by performing Monte Carlo simulations. These calculations allow one to understand in a detailed way the interplay among geometrical anisotropy, translational and internal (rotational) degrees of freedom and system size in influencing the seminal nucleation event.

Crystallization↗

PubMed2002

Analytic expression for the mean time to absorption for a random walker on the Sierpinski gasket.

The exact analytic expression for the mean time to absorption (or mean walk length) for a particle performing a random walk on a finite Sierpinski gasket with a trap at one vertex is found to be T((n))=[3(n)5(n+1)+4(5(n))-3(n)]/(3(n+1)+1) where n denotes the generation index of the gasket, and the mean is over a set of starting points of the walk distributed uniformly over all the other sites of the gasket. In terms of the number N(n) of sites on the gasket and the spectral dimension d of the gasket, the precise asymptotic behavior for large N(n) is T((n))-->1/3(2N(n))(2/d)-N1.464. This serves as a partial check on our result, as it is (a) intermediate between the known results T-N2 (d=1) and T-N ln N (d=2) for random walks on d-dimensional Euclidean lattices and (b) consistent with the known result for the asymptotic behavior of the mean number of distinct sites visited in a random walk on a fractal lattice.

Journal Article↗