Error Thresholds in Single-Peak Gaussian Distributed Fitness Landscapes

Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes （noise of environments） and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.

Behavior of the Lyapunov Exponent and Phase Transition in Nuclei

Based on the quantum molecular dynamics model,we investigate the dynamical behaviors of the excited nuclear system to simulate the latter stage of heavy ion reactions,which associate with a liquid-gas phase transition.We try to search a microscopic way to describe the phase transition in realnuclei.The Lyapunov exponent is employed and examined for our purpose.We find out that the Lyapunov exponent is one of good microscopic quantities to describe the phase transition in hot nuclei.Coulomb potential and the finite size effect may give a strong influence on the critical temperature.However,the collision term plays a minor role in the process of the liquid-gas phase transition in finite systems.

Current Reversal in a Flashing Correlation Ratchet

A flashing correlation ratchet model is proposed,in which the transport of Brownian particles driven by additive colored noise of Ornstein-Uhlenbeck type in a flashing ratchet is studied by Monte Carlo simulation.The stationary current vs the noise strength and the correlation time is obtained and analyzed.For a fixed rate of potential flashing,the novel phenomena of current reversal and reentry occur.The conditions for the occurrence of these phenomena are found.The in fluence of the flipping rate is also discussed.This finding might be relevant to the fact that the protein motors with similar structure can move in opposite directions on the same kind of microtubule.

Relaxation Property and Stability Analysis of the Quasispecies Models

The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and seeond-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error （mutation） threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.

Effects of Asymmetry of Potential on Stochastic Stokes’ Drift

The directed motion of Brownian particles is generated by a travelling asymmetric potential.The asymptotic behaviour of probability density of the particles at long time is a solitary wave.The Brownian particles can do work against an external opposing force with high efficiency.The analytical expressions of the solitary wave and the efficiency of the Brownian particles are obtained.The average velocity and the efficiency of the particles depends strongly on the travelling speed and the asymmetry of the potential.

Classical Dynamics of a Nucleon in Heavy Nuclei

Within the framework of the two-center shell model,the classically dynamical behaviour of a nucleon in heavy nuclei is investigated when nuclear shape parameters are changed systematically.It is found that there is a good quantum-classical correspondence of nucleonic regular(chaotic)motion so that Bohigas,Giannoni and Schmit conjecture is confirmed once again.

Propagation of Localized Excitations in Desoxyribonucleic Acid

The result that the process by which the pulses,initially distributed in desoxyribonucleic acid(DNA)molecules can resume its form to localize the large amplitude excitations is proposed.This process may play an important role in the dynamics of localized thermal bubble for the transcription of DNA molecules.