Avalanches in a nonlinear oscillator chain in a periodic potential

We consider the dynamics of a chain of coupled units evolving in a periodic substrate potential. The chain is initially in a flat state and situated in a potential well. A bias force, acting as a weak driving mechanism, is applied at a single unit of the chain. We study the instigation of directed transport in two types of system: (i) a microcanonical situation associated with deterministic and conservative dynamics and (ii) the Langevin dynamics when the system is in contact with a heat bath. Interestingly, for the deterministic and conservative dynamics the directed transport is drastically enhanced compared with its Langevin counterpart. In particular, in the deterministic and conservative regime a self-organised redistribution of energy triggers huge-sized avalanches yielding ultimately accelerated transport of the chain. In contrast, in the thermally-assisted process between avalanches the chain settles always into a pinned metastable state impeding continual accelerated chain motion.     

Modelling of dynamical processes in a molecular crystal by NMR

In this contribution we report on the plastic crystal 1-chloroadamantane dynamics via conventional frequency dependent (¹H and ¹³C) and field cycling NMR measurements. A suitable microscopic dynamical model, worked out from from X-ray analysis is developed and the molecular motions are interpreted in terms of: self diffusion and dipolar molecular axis combined with uniaxial rotation. In the rotator phase the molecules execute a bimodal reorientation process whereas the uniaxial rotation solely persists in the low temperature phase. In both phases, the residence times exhibit an Arrhenius temperature dependence. The results confirm the existence of a dynamic crossover transition predicted by molecular dynamics simulation.     

Perturbed soliton excitations in the DNA double helix

We study the nonlinear dynamics of the inhomogeneous DNA double-helical chain using the dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation, while taking into account the interstrand hydrogen bonding energy, between bases, and the intrastrand inhomogeneous stacking energy and by making an analogy with the Heisenberg model of the Hamiltonian of an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagnetic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of an open state configuration in the DNA double helix. The effect of inhomogeneity in the stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple-scale soliton perturbation theory by solving the associated linear eigenvalue problem and by constructing the complete set of eigenfunctions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of the inhomogeneity. Also it introduces fluctuations in the form of a train of pulses or periodic oscillations in the open state configuration.     

空间关联白噪声影响下小世界神经元网络系统的同步动力学

以电耦合的Terman-Wang小世界神经元网络系统为研究对象, 研究了空间关联白噪声影响下神经元网络系统的同步动力学. 首先将动力学平均场近似理论扩展到受空间关联白噪声影响下的小世界网络系统中, 将描述网络系统动力学演化的2N维随机微分方程简化为11个确定性的矩微分方程. 其次, 基于动力学平均场近似理论所推导的矩方程, 讨论了空间关联噪声、网络结构参数对神经元网络系统同步动力学的关键影响, 发现较大的噪声空间关联系数、耦合强度及节点平均度均对神经元网络系统同步放电具有积极作用. 进一步地, 利用计算机仿真数值模拟原神经元网络系统的同步动力学, 并与基于动力学平均场近似理论所得到的结果进行比较, 发现二者具有较好的一致性.     

快速象旋转器

在对象旋转器的象旋转特性进行了分析和论证的基础上,提出了快速象旋转器,并进行了数学上的论证,说明此种快速象旋转器在不提高现有象旋转器的转速的情况下,提高了旋转体与本文所提出的快速象旋转器的转速比。为观察到更高速旋转的物体,提供了一个新的途径。     

Theoretical Demonstration of a Newly Designed Micro-Rotator Driven by Optical Pressure on a Light Incident Surface

A newly designed cylindrical optical micro-rotator which has slopes for trapping and rotation on its upper surface is proposed. The cylindrical shape is effective in decreasing viscous drag force (damping factor) in the medium. A ray-tracing method considering the beam waist is employed to analyze the radiation pressure exerted on the upper surface of the rotator. We have demonstrated optical trapping and high speed rotation for various optical beam parameters such as the lens numerical aperture and the Gaussian mode profile as well as rotator shape parameters including oblique angle, height and diameter.     

液晶填充碲酸盐光子晶体光纤偏振旋转器

提出一种液晶填充碲酸盐玻璃的柚子型光子晶体光纤偏振旋转器,利用全矢量有限元法,对液晶填充碲酸盐玻璃的柚子型光子晶体光纤的偏振旋转特性进行数值模拟,并分析了光纤结构参数、环境温度、工作波长等对光纤偏振旋转特性的影响.研究结果表明:此种偏振旋转器具有较高的旋转效率、较低的工作串扰和较短的旋转长度,在工作波长为1.55μm、偏振角度为45°时,其值分别达到99.947%、-32.84dB和197μm;另外,随着光纤薄壁厚度的增加,旋转长度随之升高,随着工作波长的变大,旋转长度随之降低,随着温度的增加,旋转长度随之升高.这种新型的光子晶体光纤为偏振旋转器的研发提供了参考.     

The Theory of Individual Based Discrete-Time Processes

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are hence intrinsic to the system and can induce qualitative changes to the dynamics predicted from the deterministic map. From the Chapman–Kolmogorov equation for the discrete-time Markov process, we derive the analogues of the Fokker–Planck equation and the Langevin equation, which are routinely employed for continuous time processes. In particular, a stochastic difference equation is derived which accurately reproduces the results found from the Markov chain model. Stochastic corrections to the deterministic map can be quantified by linearizing the fluctuations around the attractor of the map. The proposed scheme is tested on stochastic models which have the logistic and Ricker maps as their deterministic limits.     

Thermostatting the atomic spin dynamics from controlled demons

Deterministic dynamics in extended phase space of a constant temperature interacting spin system is formulated. The spin temperature is recovered through the constrained equation of motion and is in agreement with Rugh’s geometrical approach to temperature for classical Heisenberg spin systems. Detailed comparisons are investigated between state-of-the-art stochastic spin dynamics and deterministic dynamics using a chain of thermostats, for which an accelerated convergence structure is found.     

基于哈密顿函数的永磁同步电机混沌系统鲁棒控制

哈密顿系统理论是研究非线性系统的一种重要工具, 近年来在电机调速、控制等方面得到广泛应用. 本文针对永磁同步电机运行中存在的混沌现象, 提出一种基于哈密顿函数的永磁同步电机混沌系统鲁棒控制器设计方法. 将永磁同步电机动态模型变换为类Lorenz混沌方程, 在特定参数下, 通过Lyapunov指数和Lyapunov维数的计算可知系统是混沌的. 令电机转速跟踪给定值得误差方程. 由于误差方程并不具有标准哈密顿函数形式, 将其转化为具有扰动不确定项的哈密顿系统, 并与负载扰动一起作为系统的总扰动量, 设计了一种鲁棒控制器. 控制器由两部分组成, 一部分基于互联与阻尼配置法, 实现任意转速的有效跟踪, 另一部分实现扰动补偿. 仿真表明, 控制器使电机迅速脱离混沌状态, 并能实现转速趋近跟踪, 验证了控制器的可行性与有效性. 该方法扩展了哈密顿函数的适用范围, 具有一定的优越性.     

Phase synchronization in tilted deterministic ratchets

We study phase synchronization for a ratchet system. We consider the deterministic dynamics of a particle in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues, which represent regions of synchronization in parameter space, and discuss their implications for transport in ratchets.     

反射式光学电压互感器光路建模及偏振误差分析

光路系统的偏振误差极大地制约着准互易反射式光学电压互感器的准确度.借助琼斯矩阵,建立了分立光学器件及光纤熔接点的传输模型,推导出完整的电压互感器光路系统的数学模型.以此模型为基础,对电压互感器中的偏振误差进行了仿真分析.结果表明：光源偏振度、起偏器消光比及起偏器与相位调制器的对轴角度主要影响系统的检测灵敏度|法拉第准直旋光器的旋光角度、法拉第准直旋光器与BGO晶体的对轴角度误差是主要的偏振误差源,影响系统的测量准确度及稳定性|根据电子式电压互感器IEC60044-7 0.2S级标准,法拉第旋光角度误差应该小于1.6°,旋光器与BGO晶体对轴角度误差小于1.85°.该研究对准互易反射式光学电压互感器光路设计和误差抑制具有一定的参考价值和指导意义.     

Globally enumerating unstable periodic orbits for observed data using symbolic dynamics

The unstable periodic orbits of a chaotic system provide an important skeleton of the dynamics in a chaotic system, but they can be difficult to find from an observed time series. We present a global method for finding periodic orbits based on their symbolic dynamics, which is made possible by several recent methods to find good partitions for symbolic dynamics from observed time series. The symbolic dynamics are approximated by a Markov chain estimated from the sequence using information-theoretical concepts. The chain has a probabilistic graph representation, and the cycles of the graph may be exhaustively enumerated with a classical deterministic algorithm, providing a global, comprehensive list of symbolic names for its periodic orbits. Once the symbolic codes of the periodic orbits are found, the partition is used to localize the orbits back in the original state space. Using the periodic orbits found, we can estimate several quantities of the attractor such as the Lyapunov exponent and topological entropy.     

How complex is the dynamics of Peptide folding?

Classical molecular dynamics simulations of the folding of alanine peptides in aqueous solution are analyzed by constructing a deterministic model of the dynamics, using methods from nonlinear time series analysis. While the dimension of the free energy landscape increases with system size, a Lyapunov analysis shows that the effective dimension of the dynamic system is rather small and even decreases with chain length. The observed reduction of phase space is a nonlinear cooperative effect that is caused by intramolecular hydrogen bonds that stabilize the secondary structure of the peptides.     

磁场中双折射光纤的琼斯矩阵等效模型

采用延迟器与旋光器的串联模型, 研究磁场中双折射光纤的偏振传输特性, 将它们的琼斯矩阵按照两种不同的顺序级联相乘, 导出了两种等效模型中等效相位延迟量、等效快轴方向和等效旋光角的解析表达式。研究发现, 当光纤同时具有线双折射和圆双折射时, 单位长度的等效相位延迟量并不等于其固有的线双折射, 等效旋光角也不等于其法拉第旋转角, 它们同时都与光纤的固有线双折射和磁场引起的圆双折射相关联。且在不同级联顺序的两种等效模型中, 等效相位延迟器的快轴方向都不与光纤的双折射主轴重合, 而是分别向两个相反的方向偏移一定的角度, 偏移角为等效旋光角的一半。     

Debye limit of the stochastic rotation operator

A procedure is proposed for calculating in Debye approximation physical quantities related to steady state random thermal motion. The results are expressed in terms of the stochastic rotation operator. Explicit expressions are derived for this operator and its ensemble average in the case of a rotating molecule which is modelled as a sphere, linear rotator or asymmetric rotator. The relevance of these expressions for certain dielectric and nuclear magnetic relaxation processes is considered.     

Magnetic dimer motion effects in a rotating magnetic field (A qualitative model of magnetoviscosity and permittivity in magnetorheological suspensions)

The motion of a pair of uniform interacting spherical mesoscopic particles situated in a viscous fluid under the influence of a rotating magnetic field was studied. The coupling interactions between the particles were chosen as a superposition of steric and dipolar pair potentials (for the dipoles parallel to the external field). The model dynamics consisting of particular rotation and vibration modes is the result of the interplay of viscous and interaction forces. The transition from the synchronous to the asynchronous regime of dimer rotation has been found. The results were discussed from a synergetic point of view. A qualitative picture of behaviour of the effective magnetoviscosity and permittivity for dimerized magnetorheological suspension has been given.     

Linear AAD interaction and the relativistic rotator

It is shown that the weak-potential limit allows us to reveal quite naturally the presence of the relativistic rotator in linear AAD interaction. In the language of extended constraint dynamics it is able to give all required rotator generators including the evolution equation of the Hamilton-Jacobi type suitable for rigorous quantization.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Analysis of an anisotropic plate Faraday rotator coated with multilayer dielectric plates

The analysis of an anisotropic plate Faraday rotator coated with multilayer dielectric plates is presented by means of the matrix methods in conjunction with Fourier transformation technigues. It provides a closed-form representation of the electromagnetic field over the whole multilayer regions. The treatment does not limit the direction of the biased magnetic field and the numbers of the coated dielectric plates. Numerical results are presented and compared with that calculated with the method in ref.[1], and full-waveguide-band bandwidth for 47.5°±1.5° rotation angle is obtained for transmission type rotator in W band. Calculation for reflection type rotator is also presented and compared with the experiments.     

Chain dynamics in a hexadecane melt as seen by neutron scattering and identified by molecular dynamics simulations

Different local and global chain dynamics in a C(16)H(34) melt could be revealed by resolution resolved time-of-flight quasielastic neutron scattering and complementary molecular dynamics simulations. Thereby it has been demonstrated that the measured intermediate scattering functions can validate the simulated data on the pico- to nanosecond timescale. Remarkably the shape of the experimentally measured intermediate scattering functions can be reproduced excellently by molecular dynamics simulations. It was found that although the extracted apparent activation energy corresponds to the long-range diffusion value, the molecular dynamics in this time range are mainly due to local bond rotations and the rotation of entire molecules.