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

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

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.     

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。     

Reformulation of the path probability method and its application to crystal growth models

The microscopic master equation of a system is derived within the framework of the path probability method (PPM). Then, by extending Morita's method in equilibrium statistical mechanics, the path probability function constructed microscopically can be systematically decomposed to result in the conventional path probability function of cluster approximation when correlations larger than the chosen basic cluster are neglected. In order to critically compare the master equation method with the PPM, the triangle approximation is treated by both methods for crystal growth models. It is found that the PPM gives physically satisfactory kinetic equations, while the master equation (supplemented with a cluster probability in the superposition approximation) does not. The triangle PPM calculation considerably improves the result of the pair approximation for crystal growth velocity in the solid-on-solid model, and compares well with Monte Carlo results.     

Quantum Thermalization and Thermal Entanglement in the Open Quantum Rabi Model

Quantum thermalization and thermal entanglement in the open quantum Rabi model (QRM), in which a two-level system and a single-mode bosonic field are coupled to either two individual heat baths or a common heat bath, are studied. By treating the QRM as an effective multilevel system and deriving global quantum master equations in the eigenstate representation of the QRM, the physical conditions for quantum thermalization of the QRM is studied. It is found that, in the individual heat-bath case, the QRM can only be thermalized when either the two heat baths have the same temperature or the QRM is only coupled to one of the two baths. In the common heat-bath case, differently, the QRM can always be thermalized. Thermal entanglement of the QRM in both the resonant- and non-resonant coupling cases is also studied. The logarithmic negativity for the thermal state of the QRM is obtained in a wide parameter space, ranging from the low- to high-temperature limits, and from the weak- to deep-strong-coupling regimes. This work paves the way toward the study of quantum effects in nonequilibrium ultrastrongly-coupled light-matter systems.     

Solvable models of temporally correlated random walk on a lattice

We seek the conditional probability functionP(m,t) for the position of a particle executing a random walk on a lattice, governed by the distributionW(n, t) specifying the probability ofn jumps or steps occurring in timet. Uncorrelated diffusion occurs whenW is a Poisson distribution. The solutions corresponding to two different families of distributionsW are found and discussed. The Poissonian is a limiting case in each of these families. This permits a quantitative investigation of the effects, on the diffusion process, of varying degrees of temporal correlation in the step sequences. In the first part, the step sequences are regarded as realizations of an ongoing renewal process with a probability densityψ(t) for the time interval between successive jumps.W is constructed in terms ofψ using the continuous-time random walk approach. The theory is then specialized to the case whenψ belongs to the class of special Erlangian density functions. In the second part,W is taken to belong to the family of negative binomial distributions, ranging from the geometric (most correlated) to the Poissonian (uncorrelated). Various aspects such as the continuum limit, the master equation forP, the asymptotic behaviour ofP, etc., are discussed.     

基于极坐标的相向运动图像模糊的递归模型

成像过程中,被摄像目标和摄像机之间的相向运动会造成图像的辐射状模糊,辐射状模糊将减小有效视场,影响成像质量.本文在扇形网格采样的基础上,利用状态空间模型模拟了退化过程,用递归方法解决了空变问题,并利用对状态空间系统求逆的方法对退化图像进行了复原.计算机模拟显示,算法简单,复原图像清晰,取得了较满意的结果.     

考虑停靠站影响的公交运输系统模型

受停靠站影响,公共交通系统运行过程中容易产生集簇现象.本文细致地考虑了公交停靠站长度和停靠站在线路上的分布情况,构建了一个新的公交运输系统元胞自动机模型.数值模拟结果表明,在引入停靠站长度和停靠站分布两种因素后,模型在微观层面上更清晰地刻画了车辆在公交线路上的时空分布,再现了公交运行中的集簇现象,定量地评价了停靠站分布对车辆平均速度的影响.本研究对进一步认识集簇现象的形成机理和优化停靠站设计具有指导意义.     

基于加权改进的AR模型的负载预测研究

负载预测在故障管理中有着十分重要的作用,通过对CPU负载以及内存使用率的预测可以对系统进行实时监控,预知未来时间段资源的可用性,发出异常告警;文中提出一种加权改进的自回归模型,通过对最小二乘法求出的参数进行加权处理,结合时间序列分析理论,建立一个负载预测模型,用于CPU负载和内存使用率的预测;实验证明,对AR模型的参数进行加权的方法优化了参数估计,预测误差减小了60%~80%。     

Coherence Loss of Two-Photon Jaynes-Cummings Model in Dispersive Approximation

Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task.In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain the density operator of the system (field +atom). The coherence losses of the system and of the atom are investigated when two-photon process is involved. We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.     

Simulation of the passively mode-locked laser with a SESAM

By solving the Haus master equation through split step Fourier transform method, several programs which can simulate the soliton mode-locked dynamic processes of the passively mode-locked solid laser with a semiconductor saturable absorber mirror (SESAM) are established, based on a MATLAB environment. The pulse evolution equations are solved numerically. Sample calculations for a diode-pumped Nd³⁺:YVO₄ (0.5% doped) laser with a SESAM are presented to demonstrate the use of the simulation programs and the related formulas. Several theoretical results such as the pulse width, the peak power and the average output power are obtained with a given cavity structure, which are in good agreement with the reported experimental results.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.