A Time-Distinguished Analysis of the Harmonic Structure from a Model Molecular Ion

We present high-order harmonic generation spectra resulted from a single-electron model molecular ion exposed to intense laser fields by numerically solving a one-dimensional time-dependent Schrodinger equation. There are three plateaus in the spectra and the maximal cutoff energy is Ip 8.5Up, when the inter-nuclear distance R     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.     

Stochastic Four-State Mechanochemical Model of F1-ATPase

F₁-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the central γ-subunit rotates inside the α₃β₃ cylinder. Astochastic four-state mechanochemical coupling model of F$_{1}$-ATPase isstudied with the aid of the master equation. In this model, the ATPhydrolysis and synthesis are dependent on ATP, ADP, and Pi concentrations.The effects of ATP concentration, ADP concentration, and the external torqueon the occupation probability of binding-state, the rotation rate and thediffusion coefficient of F₁-ATPase are investigated. Moreover, theresults from this model are compared with experiments. The mechanochemicalmechanism F₁-ATPase is qualitatively explained by the model.     

Stochastic Four-State Mechanochemical Model of F1-ATPase

F1-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the central γ-subunit rotates inside the α3β3 cylinder. A stochastic four-state mechanochemical coupling model of F1-ATPase is studied with the aid of the master equation. In this model, the ATP hydrolysis and synthesis are dependent on ATP, ADP, and Pi concentrations. The effects of ATP concentration, ADP concentration, and the external torque on the occupation probability of binding-state, the rotation rate and the diffusion coefficient of F1-ATPase are investigated. Moreover, the results from this model are compared with experiments. The mechanochemical mechanism F1-ATPase is qualitatively explained by the model.     

Motion and Efficiency of a Two-State Model for a Single Molecular Motor

We discussed the directed motion and the energy conversion efficiency of a particle in two-state ratchet potentials with white noise. We studied the effective potential of multi-state. The two-state potential is equivalent to an effective potential that has a nonzero average slope on a large scale in general. The incline of the effective potential is crucial to the directed motion and the efficiency. We also discussed the relationship between the efficiency and the kinetic parameters such as the strength of the noise and the transition rates between the two states. We notice that there exists a maximal efficiency when the noise strength and the fluctuating rates take appropriate values.     

Four-State Quantum Chain as a Model of Sequence Evolution

A variety of selection-mutation models for DNA (or RNA) sequences, well known in molecular evolution, can be translated into a model of coupled Ising quantum chains. This correspondence is used to investigate the genetic variability and error threshold behaviour in dependence of possible fitness landscapes. In contrast to the two-state models treated hitherto, the model explicitly takes the four-state nature of the nucleotide alphabet into account and allows for the distinction of mutation rates for the different base substitutions, as given by standard mutation schemes of molecular phylogeny. As a consequence of this refined treatment, new phase diagrams for the error threshold behaviour are obtained, with appearance of a novel phase in which the nucleotide ordering of the wildtype sequence is only partially conserved. Explicit analytical and numerical results are presented for evolution dynamics and equilibrium behaviour in a number of accessible situations, such as quadratic fitness landscapes and the Kimura 2 parameter mutation scheme.     

Effective Potential of a Two-State Model for Molecular Motor

We study force generation and motion of molecular motors using a simple two-state model in the paper. Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that are periodic and polar. The current and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the current is also calculated. It is shown that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states.     

Impact of Colored Noise on Population Model with Allee Effect

We study a population model with strong and weak Allee effect driven by internal noise and external noise.Firstly, a single-species population model with Allee effect under environmental colored noise is established, then stable and unstable states are analyzed and interpreted in biology. After that, stationary probability distribution(SPD) of population is derived based on Fokker-Planck equation. Next, mean first-passage time(MFPT) is defined in order to quantify the transition between extinction state and survival state with Allee effect. It is found that population will not extinct when weak Allee effect exists. It is not beneficial to survival of the population with the increase of Allee threshold no matter whether strong Allee effect or weak Allee effect. When strong Allee effect occurs, the correlation time of multiplicative noise plays a positive role in survival of population, while the correlation time of additive noise has a negative effect. Crucially, the phenomenon of resonant activation is firstly discovered in population dynamics with Allee effect. The conclusions we obtain can be applied to the further research of population dynamics in ecology.     

非均匀分布纵向耦合束不稳定性的研究

利用Vlasov方程研究了非均匀分布情形下的纵向多束团不稳定性.当束团均匀分布时,由该方法所得到的结果与ZAP程序给出的结果一致;对于非均匀分布的情形,由该分析解得到的结果与模拟跟踪方法所得到的结果接近.     

Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.     

采用双核模型研究超重核合成机制

本文首先介绍了两种描述低能重离子核反应的理论,然后基于这些理论发展了一个描述超重核合成的理论模型,即双核模型(dinuclear system model)。不同于Adamian 的处理,本文的模型采用数值求解主方程的方法来描述重离子的熔合过程,重点讨论了熔合过程中主方程的发展演化,选择一维至三维不同的宏观自由度说明重离子熔合机制,为今后进一步发展模型与预言新核素提供理论依据。