Kinetics of two-step nucleation of crystals

When the nucleation of a stable crystalline phase directly in a supersaturated old phase is greatly retarded, the crystal nuclei might nucleate within faster-forming particles of an intermediate phase. Here we present a theoretical investigation of the kinetics of this two-step nucleation of crystals and derive general expressions for the time dependence of the number of crystals nucleated within the particles of the intermediate phase. The results reveal that crystal nucleation can be strongly delayed by the slow growth of the particles and/or by the slow nucleation of the crystals in them. Furthermore, the linear part of the time dependence of the number of nucleated crystals is determined by the formation rate of the intermediate particles. This is in contrast with the one-step nucleation of crystals when this linear part is determined by the rate of crystal nucleation directly in the old phase. Criteria are proposed for distinction between the one- and two-step nucleation mechanisms, based on the supersaturation dependence of the delay time for nucleation. The application of the theoretical approach to the analysis of experimental data on the nucleation of crystals and other ordered aggregates of protein and other soluble materials is discussed.     

Polymerization dynamics of double-stranded biopolymers: chemical kinetic approach

The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predictions of approximate multilayer models that consider only a finite number of the most relevant polymer configurations. Our theoretical approach is applied to analyze the experimental data on the growth and fluctuations dynamics of individual single actin filaments.     

How Interactions Control Molecular Transport in Channels

The motion of molecules across channels and pores is critically important for understanding mechanisms of many cellular processes. Here we investigate the mechanism of interactions in the molecular transport through nanopores by analyzing exactly solvable discrete stochastic models. According to this approach the channel transport is viewed as a set of chemical transitions between discrete states. It is shown that the strength and spatial distribution of molecule/channel interactions can strongly modify the particle current. Our analysis indicates that the most optimal transport is achieved when the binding sites are near the entrance or exit of the pore depending on the sign of interaction potential. In addition, the role of intermolecular interactions during the channel transport is studied, and it is argued that an increase in the flux can be observed for some optimal interaction strength. The mechanisms of these phenomena are discussed.     

Population dynamics with global regulation: the conserved Fisher equation

We introduce and study a conserved version of the Fisher equation. Within a population biology context, this model describes spatially extended populations in which the total number of individuals is fixed due to either biotic or environmental factors. We find a rich spectrum of dynamical phases including a pseudotraveling wave and, in the presence of the Allee effect, a phase transition from a locally constrained high density state to a low density fragmented state.     

Low-dimensional bose liquids: beyond the gross-pitaevskii approximation

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d相似文献   

DYNAMICS OF SINGLE-MOLECULE ROTATIONS ON SURFACES DEPEND ON SYMMETRY, INTERACTIONS AND MOLECULAR SIZES

Rotating surface-mounted molecules have attracted attention of many research groups as a way to develop new nanoscale devices and materials. However, mechanisms of motion of these rotors at the single-molecule level are still not well understood. Theoretical and experimental studies on thioether molecular rotors on gold surfaces suggest that the size of the molecules, their flexibility and steric repulsions with the surface are important for dynamics of the system. A complex combination of these factors leads to the observation that the rotation speeds have not been hindered by increasing the length of the alkyl chains. However, experiments on diferrocene derivatives indicated that a significant increase in the rotational barriers for longer molecules. We present here a comprehensive theoretical study that combines molecular dynamics simulations and simple models to investigate what factors influence single-molecule rotations on the surfaces. Our results suggest that rotational dynamics is determined by the size and by the symmetry of the molecules and surfaces, and by interactions with surfaces. Our theoretical predictions are in excellent agreement with current experimental observations.     

Effect of Detachments in Asymmetric Simple Exclusion Processes

Asymmetric simple exclusion processes are important for understanding low-dimensional multi-particle dynamic phenomena. The effect of irreversible detachments of particles on dynamics of asymmetric simple exclusion processes is studied using analytical and computer simulation techniques. In the simplest model, where particles can only detach from a single site in the bulk of the system, a theory is presented and used to calculate explicitly phase diagrams and particle density profiles. The complexity of the phase behavior is discussed in terms of a recent domain-wall theory for driven lattice systems. The theoretical results qualitatively and quantitatively agree with computer Monte Carlo simulations.