Biomedical subjects

A I Shushin

Publications and source records attributed to A I Shushin.

3 recordsLinked to original sources

PubMed2001

Anomalous two-state model for anomalous diffusion.

An anomalous two-state model (ATSM) with the anomalous long-tailed kinetics of transitions between states is proposed to describe the specific features of anomalous diffusion (AD) and AD-assisted transitions (ADAT) in the double-well potential. In the ATSM the system is assumed to undergo the conventional diffusion in both states but with different diffusion coefficients. The anomalous features of diffusion result from the modulation of the diffusion coefficient caused by transitions between ATSM states. The anomalous space-time evolution predicted by the ATSM is treated within the continuous time random walk theory. With the use of the proposed ATSM the transient behavior of the AD and the ADAT is analyzed in detail. We found a large variety of different (and sometimes peculiar) types of the space-time behavior of the free AD and ADAT. The free AD is found to be of subdiffusion or superdiffusion type for fairly long time depending on the relation between the parameters of the ATSM. The kinetics of the ADAT can be either conventional (exponential) or anomalous (of inverse power type) for different parameters of the model and time.

Journal Article↗

PubMed2001

Effect of local molecular shape and anisotropic reactivity on the rate of diffusion-controlled reactions.

The role of distance-dependent anisotropic reactivity and molecular geometry in the vicinity of localized reaction centers in influencing the rate of bimolecular diffusion-controlled reactions is analyzed in detail, both analytically and numerically. The effect of local molecular shape is considered within the model of reflective hemispheres of small radius l(h) on the surfaces of otherwise spherical molecules of radius R (l(h) << R). The distance-dependent reactivity is modeled by reactive hemispheres of radius l(r) on top of the reflective hemispheres (l(r) << R). It is shown that the presence of the reflective hemispheres leads to a markedly large increase of the reaction rate. The maximum effect is ~R/l(h) >> 1 times, as described by the ratio of local to average molecular curvature. It is observed for l(h) approximately R(l(r)/R)(1/2) >> l(r). The effect of thickness of the reaction regions is described within the model of reactive cylinders of height l(r) and angular radius theta << 1. It is shown that the characteristic parameter in the expansion of the reaction rate as a function of l(r)/R is l(r)/(Rtheta(2)), and therefore, even for small relative thickness d = l(r)/theta, its effect on the rate is very strong, i.e., the conventional model of reactive patches, which assumes zero thickness of the reaction region, may considerably underestimate the reaction rate.

Anisotropy↗

PubMed2001

Effect of anisotropic reactivity on the rate of diffusion-controlled reactions: comparative analysis of the models of patches and hemispheres.

A comparative analysis of two models of anisotropic reactivity in bimolecular diffusion-controlled reaction kinetics is presented. One is the conventional model of reactive patches (MRP), where the surface of a molecule is assumed to be reactive over a certain region (circular patch) with the rest of the surface being inert. Another one is the model of reactive hemispheres (MRH), assuming that a molecule is reactive within a certain distance from a point on its surface. The accuracy of the known and newly derived simple analytical expressions for the reaction rate is tested by comparison with the simulation results obtained by the original Brownian dynamics method. These formulas prove to be quite accurate in the practically important limit of strong anisotropy corresponding to small size of the reactive patches or hemispheres. Numerical calculations confirm earlier predictions that the MRP rates are much smaller than the MRH rates for the same radii of the reactive regions, especially in the case where both reacting molecules are anisotropic.

Algorithms↗