高温下复合核的热裂变速率

在核裂变的动力学描述中,考虑到质量随坐标的连续变化,提出了自由能有效势,导出了一个新的裂变速率公式.改进后的公式对于核温度与势能位垒高度相当的热核裂变同样适用,其结果比Kramers公式更接近于断点裂变速率的朗之万模拟值.     

强耦合光机械腔中的简正模式分裂和冷却

研究由辐射压力与驱动Fabry-Perot光学腔相耦合而产生的腔光机械动力学行为. 通过量子朗之万方程具体研究了机械振子的涨落光谱、机械阻尼与共振频移和基态冷却. 随着输入激光功率的增加,振子的涨落光谱呈现简正模式分裂的现象,并且数值模拟结果和实验结果相符合. 同时推导了有效机械阻尼和共振频移. 红移边带导致了机械模的冷却,蓝移边带引起了机械模的放大. 此外,引入一种近似机制来研究振子的基态冷却,并且考虑在解析边带机制下简正模式分裂对机械振子冷却的影响. 最后,数值讨论了初始浴温度、输入激光功率和机械品质因数这三个因素对机械振子冷却的影响. 关键词： 腔光机械 辐射压力 简正模式分裂 冷却     

朗之万方程及其在蛋白质折叠动力学中的应用

研究了朗之万方程的动力学性质,并用它模拟了蛋白质分子的折叠过程.首先在相空间中对朗之万方程做连续映射,发现做布朗运动的粒子在位置坐标上存在明显的概率分布,这表明蛋白质折叠过程中分子空间构型是非遍历的.此外,本文还通过数值模拟得到了去折叠态蛋白质的紧密度指标,并验证了它与实验结果以及其他理论方法的一致性.本文还提出了一种利用重整化方法研究熔球体状态蛋白质的理论模型,并提供了考虑疏水基影响的蛋白质折叠过程的模拟思路. 关键词： 朗之万方程 蛋白质折叠非遍历性 紧密度指标 重整化     

相关激励形式下保守和非保守耦合振子的能量分布与功率流

作为相关输入形式下保守或非保守耦合系统统计能量分析的基础,本文主要研究耦合振子在比例相关输入条件下的能量分布与功率流.在推导了相关输入条件下耦合振子间的功率流与振子能量的基本关系式和功率平衡方程式及振子能量比的表达式之后,本文分别详细讨论了保守耦合振子和非保守耦合振子系统的能量分布和功率流问题,并与互不相关输入时耦合振子的能量分布与功率流的特点进行了比较,对于各种耦合阻尼情况下的振子能量分布与功率流也进行了数值计算,研究结果表明,相关输入下耦合振子的能量分布与功率流的特征与互不相关输入时的特征有着显著的差别.     

斯特林制冷机中压缩活塞振子与排出器振子相互影响的研究

从振动力学的角度来看 ,斯特林制冷机的工作实际上是压缩活塞振子与排出器振子两个振动系统的耦合与匹配 ,两振动系统的相互影响特性对提高整机性能具有非常重要的意义。文中首先给出了压缩活塞振子与排出器振子两个振动系统相互影响特性的理论分析 ,其次对二者相关影响特性的试验研究结果与模拟结果进行了对比分析和讨论     

多重耦合振子系统的同步动力学

耦合相振子的同步研究对理解复杂系统自组织协同的涌现具有重要的理论意义.相比于传统耦合振子的两体成对耦合,多重耦合近年来得到广泛的关注.当相振子间的多重耦合机制起主要作用时,系统会涌现一系列去同步突变,这一新颖的动力学特性对理解复杂系统群体动力学提供了重要的理论启示.本文研究了平均场的三重耦合Kuramoto系统的同步动力学,发现了去同步转变具有不可逆性,并利用平均场自洽方法和无序态线性稳定性分析揭示了不可逆去同步突变的动力学机制.进一步研究发现,随着振子自然频率分布半宽度的变化,系统会经历一系列去同步驻波态的转变.在相变临界点,系统在高维相空间会通过鞍结分岔导致同步态失稳而塌缩至稳定的低维不变环面.本文的研究揭示了多重耦合函数作用的振子系统的各种协同态及其相变机制,同时可为理解其他复杂系统(如超网络结构)协同态的动力学转变提供理论借鉴.     

一维谐振子束缚的自旋轨道耦合玻色气体

量子光学中的Rabi模型描述了一个与量子谐振子耦合的两能级系统,当耦合强度与振子频率相当时,会产生丰富的物理现象.本文研究了谐波势阱中具有拉曼诱导自旋轨道耦合的Bose气体,通过将受限系统映射为Rabi模型,引入量子光学中的平移Fock态利用变分方法求解了系统的本征能态和基态,发现左右平移Fock态的奇宇称叠加态能量低于平移态的能量,并分别研究了粒子在动量和坐标空间的动力学Zitterbewegung振荡特性以及原子极化的动力学,给出了一个直观清晰的物理图像,与相关实验的结果定性一致.本文的研究结果有助于进一步研究量子光学领域目前难以实现的深度强耦合参数区域的量子Rabi模型,对冷原子物理的研究也有一些借鉴和启发.     

多弹簧振子耦合系统运动研究

通过理论分析,得到了多弹簧振子耦合系统的解析解,利用Matlab对其进行数值模拟,作出了系统的运动曲线及相轨迹,直观地显示了系统的运动情况,并通过对不同数量弹簧振子耦合系统运动曲线及相轨迹的比较、分析,给出了系统的运动特征.     

系统规模对群体行为的效果

影响细胞群体行为的因素是多种多样的, 除了以前研究的细胞通讯方式和环境因素外, 还与现有文献没有或很少研究的细胞数目(即系统规模)有关. 本文研究了系统规模对一类合成多细胞通讯系统的聚类行为的影响. 在该系统中, 单个系统是由压制振动子和基于延迟的松弛振子整合而成的振子, 而振子之间通过群体感应机制相互耦合. 通过分岔分析和数值模拟发现: 细胞数目的增加不仅可以改变平衡态聚类稳定性区间的大小并诱导新的聚类行为, 而且有利于扩大平衡态聚类的吸引域, 表明细胞分化可能与系统规模有密切关系; 细胞数目的增加还可以极大地丰富平衡态聚类和振动聚类的表现形式和共存方式, 为生物体对环境的适应性提供了良好的基础. 我们的结果不仅扩充了耦合系统的动力学行为, 也为理解多细胞现象奠定了基础. 关键词： 系统规模 群体感应 群体行为 耦合振子     

二次耦合光力学系统的一类高维可控自持振荡行为

光力学系统通常的耦合是光压耦合, 是光场强度和纳米振子位移的一次耦合, 但在光场很强和振子振幅较大的光力学系统中, 非线性的耦合效应会变得非常明显和重要, 而且其所产生的非线性效应对制造具有特殊功能的光力学器件具有重要意义. 本文在二次耦合模型的基础上研究了光腔和振子之间通过二次耦合作用达到能 量平衡状态时系统所产生的自持振荡现象, 给出了二次耦合光力学系统的一般模型, 并通过数值方法研究了系统的定态行为和远离定态的极限环动力学行为, 标定了系统定态响应的稳定区域到极限环行为的分岔点. 发现在调节输入场参数(改变耦合系数)以及光腔和振子的弛豫系数时, 系统的相空间会出现一些稳定的高维自持振荡极限环. 通过数值分析发现该四维极限环在三维相空间的投影都趋于稳定的三维周期轨道, 并且该极限环轨道会随外部调控参数的改变发生扭动, 出现类似二维李萨如图样的稳定纽结结构. 该现象表明: 通过光场与振子的能量耦合, 利用一定强度的外部驱动可以有效控制振子的定态响应和振动, 可以让微振子锁定在具有一定振幅和频率的自发振动上, 为开发物理器件提供了可靠的光力学控制系统. 关键词： 光力系统 二次耦合 自持振荡 极限环     

Brownian localization： A generalized coupling model yielding a nonergodic Langevin equation description

A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zerotb law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.     

Anharmonic Oscillator Driven by Additive Ornstein–Uhlenbeck Noise

We present an analytical study of a nonlinear oscillator subject to an additive Ornstein–Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or to a quasi-white noise (i.e., a noise with vanishingly small correlation time). Here, in contrast, we study the small dissipation case (we retain the inertial term) and consider a noise with finite correlation time. Our analysis is non perturbative and based on a recursive adiabatic elimination scheme a reduced effective Langevin dynamics for the slow action variable is obtained after averaging out the fast angular variable. In the conservative case, we show that the physical observables grow algebraically with time and calculate the associated anomalous scaling exponents and generalized diffusion constants. In the case of small dissipation, we derive an analytic expression of the stationary probability distribution function (PDF) which differs from the canonical Boltzmann–Gibbs distribution. Our results are in excellent agreement with numerical simulations.     

Heat Transport in Ordered Harmonic Lattices

We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat current in the limit of system size N→∞. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss results in higher dimensions.     

Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ～ N α , with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τ p and follows a falling exponential function for duration time τ > τ p . For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.     

Molecular dynamics simulation of the response of bi-disperse polyelectrolyte brushes to external electric fields

Langevin dynamics simulations have been performed to investigate the response of bi-disperse and strong polyacid chains grafted on an electrode to electric fields generated by opposite surface charges on the polyelectrolyte(PE)-grafted electrode and a second parallel electrode. Simulation results clearly show that, under a negative external electric field, the longer grafted PE chains are more strongly stretched than the shorter ones in terms of the relative change in their respective brush heights. Whereas under a positive external electric field, the grafted shorter chains collapse more significantly than the longer ones. It was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The effects of smeared and discrete charge distributions of grafted PE chains on the response of PE brushes to external electric fields were also examined.     

Fluctuation theorem in quantum heat conduction

We consider steady-state heat conduction across a quantum harmonic chain connected to reservoirs modeled by infinite collection of oscillators. The heat, Q, flowing across the oscillator in a time interval tau is a stochastic variable and we study the probability distribution function P(Q). We compute the exact generating function of Q at large tau and the large deviation function. The generating function has a symmetry satisfying the steady-state fluctuation theorem without any quantum corrections. The distribution P(Q) is non-Gaussian with clear exponential tails. The effect of finite tau and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain the prediction of quantum heat current fluctuations at low temperatures in clean wires.     

Asymptotics of work distributions: the pre-exponential factor

We determine the complete asymptotic behaviour of the work distribution in driven stochastic systems described by Langevin equations. Special emphasis is put on the calculation of the pre-exponential factor which makes the result free of adjustable parameters. The method is applied to various examples and excellent agreement with numerical simulations is demonstrated. For the special case of parabolic potentials with time-dependent frequencies, we derive a universal functional form for the asymptotic work distribution.     

Influence of polymer-pore interactions on translocation

We investigate the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. An attractive interaction can greatly improve the translocation probability. At the same time, it also increases the translocation time slowly for a weak attraction while an exponential dependence is observed for a strong attraction. For fixed driving force and chain length the histogram of translocation time has a transition from Gaussian distribution to long-tailed distribution with increasing attraction. Under a weak driving force and a strong attractive force, both the translocation time and the residence time in the pore show a nonmonotonic behavior as a function of the chain length. Our simulations results are in good agreement with recent experimental data.     

Linear relaxation processes governed by fractional symmetric kinetic equations

The fractional symmetric Fokker-Planck and Einstein-Smoluchowski kinetic equations that describe the evolution of systems influenced by stochastic forces distributed with stable probability laws are derived. These equations generalize the known kinetic equations of the Brownian motion theory and involve symmetric fractional derivatives with respect to velocity and space variables. With the help of these equations, the linear relaxation processes in the force-free case and for the linear oscillator is analytically studied. For a weakly damped oscillator, a kinetic equation for the distribution in slow variables is obtained. Linear relaxation processes are also studied numerically by solving the corresponding Langevin equations with the source given by a discrete-time approximation to white Levy noise. Numerical and analytical results agree quantitatively.     

多价态高分子链在受体平面上的超选择性吸附

利用三维朗之万动力学模拟研究了多价态高分子链在受体平面上的吸附行为。其在受体平面上的吸附具有超选择性,随着高分子链上配体浓度的增大,发生超选择性吸附时的平面受体浓度范围变窄;而超选择性吸附最显著时的平面受体浓度,即最佳平面受体浓度随着链上配体浓度的增大而减小。对处于吸附态的多价态高分子链的构象性质进行了系统地研究,发现链的平衡回转半径R_g及其水平分量R_g},随着平面受体浓度的增大都存在极大值。其平衡回转半径R_g与其链长N间的标度指数表明当平面受体浓度的增大时,处于吸附态的链构象介于二维链构象和三维链构象之间;随着平面受体浓度的进一步增大,吸附在平面上的多价态高分子链发生轻微的塌缩