双稳系统的随机能量共振和作功效率

分析了处于双稳系统中的布朗粒子与外界的周期性外力和热随机力的功、热交互作用,建立了基于Langevin方程的随机能量平衡方程.围绕着受周期力、随机力和阻尼力共同作用的Langevin方程,采用动力学和非平衡热力学相结合的方法,从以"力"为立足点转到以"能量"为研究核心,深入分析了布朗粒子沿单一轨线运动时系统与环境之间的能量交换和作功效率,揭示了双稳系统的随机能量共振现象. 关键词： 双稳系统 随机能量共振 作功效率     

周期性双势垒锯齿势中温差驱动的布朗热机

研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明：当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率. 关键词： 布朗热机 双势垒锯齿势 热漏 热力学性能     

周期外力对频率涨落的过阻尼谐振子所作的功和能量随机共振

研究了周期外力对频率涨落的过阻尼谐振子系统作功的特点. 结果揭示了瞬时功率随时间的周期变化出现不对称性. 研究结果还揭示周期外力一个周期对系统所做的功随乘法噪声强度的变化出现非单调行为, 系统是否出现能量随机共振与抑制并存, 由乘法噪声与加法噪声之间互关联的符号决定. 关键词： 过阻尼谐振子 频率涨落 周期外力作功 能量随机共振与抑制     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

非保守力作用下二维耦合布朗粒子的定向输运

本文主要研究二维耦合布朗粒子在非保守外力作用下的定向输运问题.研究发现,非保守外力有促进二维耦合棘轮定向输运的效果.同时,在保守力(弹簧弹力)和非保守外力的相互协作与竞争中耦合布朗粒子的反向输运能够获得增强.特别地,随着弹簧原长或弹性系数的改变,二维耦合布朗粒子的定向运动都能够产生反向,这意味着耦合作用能够诱导二维布朗棘轮流反转的产生.实验上,通过选取不同种类的外力(保守力及非保守力),能够对二维耦合布朗粒子的分离技术提供新的方案.     

时间非对称外力驱动分数阶布朗马达的定向输运

本文研究了周期对称势中时间非对称外力驱动的布朗粒子输运现象, 建立了分数阶布朗马达输运模型. 其中外力是零均值的, 而分数阶阶数则刻画了客观环境的非均匀性程度. 通过将模型离散化进行数值模拟, 讨论了分数阶阶数、系统参量和外部参量与定向流之间的依赖关系. 研究表明, 即使没有倾斜势场的作用, 时间非对称外力也可以诱导系统产生定向输运; 输运速度随分数阶阶数的增大而单调递增; 当阶数固定时, 系统的输运速度会随着势垒高度、噪声强度非单调变化, 表现出广义随机共振现象. 分析指出, 分数阶郎之万方程所刻画的输运现象是在整数阶模型基础上的一个推广, 进而为输运现象提供了一个可能更为真实的模型.     

活性布朗粒子运动的稳态解

拟可积Hamilton系统随机平均法可以用来研究活性布朗粒子运动.介绍了该随机平均法，利用它详细求解了布朗粒子运动的动力学方程，该方程描述了活性布朗粒子在平面上的运动，粒子受到的激励是Gaussian白噪声，受到的阻尼是Schienbein-Gruler速度依赖的磨擦模型.通过与数字模拟和与实验数据的比较，证明所得稳态解正确.对于Rayleigh和Erdamnn速度依赖的磨擦模型，也给出了稳态解. 关键词： 活性布朗粒子 拟可积Hamilton系统随机平均法 可积性 稳态解     

薄膜生长的随机模型

利用Monte Carlo模型研究了薄膜生长初始阶段岛的形貌与基底温度之间的关系,同时还研究了它们与汽相粒子入射剩余能量之间的关系．模型中考虑了三种动力学过程：粒子入射、吸附粒子扩散和粒子脱附,与以前薄膜生长模型的不同之一在于把入射过程看作独立于其他过程,而扩散和脱附过程是相互关联的．结果表明随基底温度的升高,岛的形貌经历了一个从分散生长、分形生长到凝聚生长的变化过程．低温下随汽相粒子入射和剩余能量增加,岛的形貌也经历了同样的变化过程. 关键词：     

分数阶对数耦合系统在非周期外力作用下的定向输运现象

本文讨论了分数阶对数耦合系统在非周期外力作用情况下, 耦合粒子链的定向输运现象. 由于粒子在黏性介质中的运动具有“记忆性”, 所以本文通过将系统建模为分数阶对数耦合模型来研究各个系统参数对粒子链运动状态的影响. 数值仿真表明: 1)对于此类系统, 只有在存在外力作用的情况下粒子链才能够产生定向输运现象, 并且粒子链平均流速随着外力的增大而增大. 2)对于分数阶阶数较小的系统, 阻尼记忆性对粒子链的运动状态有显著的影响, 具体表现为: 粒子链的平均流速存在上界(这个上界非常小), 无论外力、耦合力以及噪声强度如何变化, 粒子链的平均流速都不会超过这个上界. 当系统的阻尼力很大且外力为零时, 粒子链不会产生定向输运现象. 3) 当系统的阶数与外力较大时, 虽然粒子链能够产生定向流, 但是此时系统对耦合力与噪声具有免疫性. 4) 耦合力与噪声强度对粒子链运动的影响只在外力较小的情况下有所表现. 在这种情况下, 当系统阶数充分大时, 粒子链的平均流速随着耦合力与噪声强度的变化而变化, 并且伴随着定向流的产生.     

Effect of Asymmetry in a Bistable System Subject to Multiplicative Colored Noise

By the method of the stochastic energetics, we investigate the stochastic resonance (SR) phenomenon of an overdamped Brown particle in an asymmetric bistable potential, driven by external periodical signal and multiplicative noise. The expressions have been obtained for the quasi-steady-state probability distribution function. It is found that the input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of the noise strength, whereas the IE turns to be a monotonic function of the correlation time of the noise. The effect of potential asymmetry is also studied on SR and IE.     

基于参数展开的同伦分析法在强非线性随机动力系统中的应用

将基于参数展开的同伦分析法(PE-HAM)进行了推广，使之适用于谐和激励与随机噪声联合作用下的强非线性随机动力系统. 通过构造合适的同伦映射，将对强非线性随机动力系统响应的求解转化为对一组线性随机微分方程的求解. 进一步研究了受到谐和与Gauss白噪声激励的强非线性Duffing振子，由PE-HAM得到了该系统的解过程和稳态概率密度的解析表达式. 数值模拟的结果说明了PE-HAM方法的精确性. 关键词： PE-HAM方法 强非线性随机动力系统 稳态概率密度 解过程 随机激励     

Molecular Motor Cycles: From Ratchets to Networks

Molecular motor cycles are studied in the framework of stochastic ratchets in which the motor moves along a 1-dimensional track, can attain M internal states, and can undergo transitions between these levels at K spatial positions. These ratchets can be mapped onto a stochastic network of KM discrete states. The network is governed by a Master equation, fulfills a vertex rule, and satisfies detailed balance in the absence of enzymatic activity and external force. Any pathway of the motor cycle which leads to a forward or backward step of the motor corresponds to a certain sequence of transitions spanning this network. The dependence of the motor velocity on the transition rates can be determined for arbitrary values of K and M and exhibits some simple and universal features.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

Stochastic optimal control for norovirus transmission dynamics by contaminated food and water

Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.     

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to （2＋1）-Dimensional Stochastic Dispersive Long Wave System

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the （2＋ 1）-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.     

A Kinetic Theory Approach to Quantum Gravity

We describe a kinetic theory approach to quantum gravity by which we mean a theory of the microscopic structure of space-time, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotty poles: quantum matter field on the right and space-time on the left. Each rung connecting the corresponding knots represents a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein–Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: (1) deduce the correlations of metric fluctuations from correlation noise in the matter field; (2) reconstituting quantum coherence—this is the reverse of decoherence—from these correlation functions; and (3) use the Boltzmann–Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding space-time counterparts. This will give us a hierarchy of generalized stochastic equations—call them the Boltzmann–Einstein hierarchy of quantum gravity—for each level of space-time structure, from the the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).     

From Random Matrices to Stochastic Operators

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.