Fluctuation theorem for the mutation process in in vitro evolution

A proposition based on the fluctuation theorem in thermodynamics is formulated to quantitatively describe molecular evolution processes in biology. Although we cannot give full proof of its generality, we demonstrate via computer simulation its applicability in an example of DNA in vitro evolution. According to this theorem, the evolution process is a series of exponentially rare fluctuations fixed by the force of natural selection

Fluctuation theorem for entropy production at strong coupling

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium,which are helpful for understanding the thermodynamic state evolution.We investigate fluctuation theorems for strong coupling between a system and its reservoir,by path-dependent definition of work and heat satisfying the first law of thermodynamics.We present the fluctuation theorems for two kinds of entropy productions.One is the informational entropy production,which is always non-negative and can be employed in either strong or weak coupling systems.The other is the thermodynamic entropy production,which differs from the informational entropy production at strong coupling by the effects regarding the reservoir.We find that,it is the negative work on the reservoir,rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling.Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.

Nonequilibrium thermodynamics and fluctuation relations for small systems

In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become sig- nificant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluc- tuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.

Resonant tunneling and quantum fluctuation in a driven triple-well system

The influence of parameters such as the strength and frequency of a periodic driving force on the tunneling dynamics is investigated in a symmetric triple-well potential. It is shown that for some special values of the parameters, tunneling could be enhanced considerably or suppressed completely. Quantum fluctuation during the tunneling is discussed as well and the numerical results are presented and analysed by virtue of Floquet formalism.

The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts

Using the linear approximation method, this paper studies the statistical property of a single-mode laser driven by both coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and calculates the steady-state mean normalized intensity fluctuation and intensity correlation time. It analyses the influences of the modulation signal, the net gain coefficient, the noise and its correlation form on the statistical fluctuation of the laser system respectively. It is found that the coloured pump noise modulated by the signal has a great suppressing action on the statistical fluctuation of the laser system; the pump noise self-correlation time and the specific frequency of modulation signal have the result that the statistical fluctuation tends to zero. Furthermore, the ＇colour＇ correlation of pump noise has much influences on the statistical fluctuation of the laser system. Increasing the intensity of pump noise will augment the statistical fluctuation of the laser system, but the intensity of quantum noise and the coefficient of cross-correlation between its real and imaginary parts have less influence on the statistical fluctuation of the laser system. Therefore, from the conclusions of this paper the statistical property can be known and a theoretical basis for steady operation and output of the laser system can be provided.

Influence of Signal and Noise on Statistical Fluctuation of Single-Mode Laser System

On the basis of calculating the steady-state mean normalized intensity fluctuation of a signal-mode laser system driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, we analyze the influence of modulation signal, noise, and its correlation form on the statistical fluctuation of the laser system. We have found that when the amplitude of modulation signal weakens and its frequency quickens, the statistical fluctuation will reduce rapidly. The by reducing the intensity of pump noise and quantum noise. statistical fluctuation of the laser system can be restrained Moreover, with prolonging of colored cross-correlation time, the statistical fluctuation of laser system experiences a repeated changing process, that is, from decreasing to augmenting, then to decreasing, and finally to augmenting again. With the decreasing of the value of cross-correlation coe~cient, the statistical fluctuation will decrease too. When the cross-correlation form between the real part and imaginary part of quantum noise is zero correlation, the statistical fluctuation of laser system has a minimum. Compared with the influence of intensity of pump noise, the influence of intensity of quantum noise on the statistical fluctuation is smaller.

Stochastic fluctuations in the rotation of the bacterial flagellar motor

The bacterial flagellar motor is a nanometer-sized rotary motor that generates the torque to drive the rotation of the flagellar filament.The output torque is an important property of the motor.The motor rotation was usually monitored by attaching aμm-sized bead to a shortened flagellar filament,and the torque was extracted by calculating the torque due to the viscous drag of the medium on the bead rotation.We sought for an independent extraction of the torque from thermal fluctuation in the motor rotation using the fluctuation theorem(FT).However,we identified an overwhelming fluctuation beyond the thermal noise that precluded the use of FT.We further characterized the timescale and the amplitude of this fluctuation,finding that it was probably due to the stepping of the motor.The amplitude of torque fluctuation we characterized here provided new information on the torque-generating interaction potential curve.

DC steady-states analysis of lossy uniform transmission lines

A method for computing DC steady-state solutions in complex frequency-domain is put forward. It starts with complex frequency-domain transmission line equations, obtains the complex expressions of voltage and current at zero initial states, and find the DC steady-state solutions of voltage and current by using the fina value theorem of Laplace transform thory. The solutions are discussed with special internal resistances of DC voltage source and loads. A case study demonstrated that the proposed method is applicable to acquiring the DC steady-state voltage waveform and current waveform without first obtaining the analytic solutions.

Theoretical Analysis of the Fluctuation Theorem Applied to Electric Circuits

We carry out a theoretical analysis of the fluctuations in the Johnson–Nyquist noise in an RC electric circuit being driven by a non-ideal constant current source. Using the appropriate Langevin equation, we derive the fluctuation theorem for the system. This analysis exhibits some interesting features. Firstly, the average of the dissipation function is not necessarily just an instantaneous entropy production, i.e. the work being done on the circuit by the external power source divided by the ambient temperature. Secondly, by appropriate selection of the values for the circuit components,the transient response of the system can be made identical to the nonequilibrium steady state response. In the limit of an ideal current source, the average of the dissipation function reduces to the entropy production. Our analysis accurately reproduces published experimental results.

Fluctuation theorem for entropy production in a chemical reaction channel

Fluctuation theorem for entropy production in a mesoscopic chemical reaction network is discussed. When the system size is sufficiently large, it is found that, by defining a kind of coarse-grained dissipation function, the entropy production in a reversible reaction channel can be approximately described by a type of detailed fluctuation theorem. Such a fluctuation relation has been successfully tested by direct simulations in a linear reaction model consisting of two reversible channels and in an oscillatory model wherein only one channel is reversible.

A fluctuation theorem for Floquet quantum master equations

We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.

地下水位变化对边坡稳定性影响的上限分析

坡体地下水水位变化引起坡内水力梯度的变化是导致边坡失稳的重要因素。通过将强度折减技术与极限上限定理结合,利用安全系数指标对地下水位变化影响下的均质边坡进行了稳定性分析,并进行了对比计算和参数分析。分析中将孔隙水压力当作外力,水位变化对边坡的影响作用通过虚功方程表现出来。对比计算表明:与已有结果的对比可以证明表明本文方法的正确性,且本文是较同类方法略好的上限解答;参数分析表明:坡内地下水位升降对边坡稳定性和潜在破坏面影响较大,地下水位上升引起孔隙水压力增大是坡体发生失稳的重要原因。

考虑周期性波动因素的中长期空中交通流量预测

为准确把握空域单元交通流量的变化趋势和周期性波动规律,综合考虑气候、季节、交通需求等因素,通过分析中长期历史流量数据,在线性增长模型的基础上,建立了考虑周期性波动因素的空中交通流量动态线性改进模型,采用贝叶斯状态估计和预测方法对模型进行求解,提出了一种根据空域单元流量时序数据预测中长期流量及其变化趋势的预测方法.利用国内典型空域单元实际流量数据,对比分析了上述两种模型的预测性能.实例研究表明:与线性增长模型的预测结果相比,本文模型的流量预测结果更符合我国的实际情况,反映了流量周期性波动特点,年流量预测结果的平均绝对误差从3.14%下降到了1.71%,预测误差的标准差从2.01%下降到了0.02%.

球形纳米粒子与半无限大介质间的近场辐射换热研究

本文从涨落电动力学和偶极子近似出发,推导了纳米粒子与半无限大介质在微纳米距离间的辐射换热公式,研究了间距、频率对辐射换热的影响。通过计算,我们发现近场辐射能够在与材料相关的频率上极大地强化换热。这些结果对于近场显微镜、微结构设计和局部加热技术都将会有很重要的指导作用。

多频段干雪特性测量与理论计算比较

利用多频段微波辐射计（９．３７５、３６ＧＨｚ）对长春地区干雪的热辐射进行了遥感测量。雪模拟为一层介电强起伏的随机介质，利用强起伏理论和起伏逸散定理计算干雪辐射亮度温度的零阶近似解。辐射亮度温度数值结果与实验数据进行了比较，二者取得较好的一致性。

中国电信业资费变动的博弈分析

一种行业从不成熟发展到日臻完善,其中厂商的策略对抗发挥着重要作用。本文试图透过市场主体之间的博弈行为,从价格波动的角度分析一般行业的变迁,得出行业发展的规律,并以此为依据分析当前中国移动通信产业的竞争以及应采取的对策选择,即避免恶性价格竞争,先做大产业,后瓜分利益。

纳米一维双原子晶体颗粒的原子均方位移和均方速度

应用作者与合作者已导出的纳米一维双原子晶体颗粒的位移 位移格林函数 ,推导了纳米一维双原子晶体颗粒的速度 速度格林函数 ,并在此基础上 ,应用涨落 耗散定理 ,推导了纳米一维双原子晶体颗粒的原子均方位移公式和原子均方速度公式。数值计算表明 ,纳米晶体颗粒表面原子的均方位移大于内部的原子均方位移 ,而表面原子的均方速度小于内部原子的均方速度 ;当纳米颗粒尺寸减小时 ,表面原子的均方位移和内部原子的均方位移都减小 ,而表面原子的均方速度和内部原子的均方速度几乎不发生变化 ;温度增大时 ,纳米晶体颗粒中各原子的均方位移和均方速度都增大 ,在高温极限 ,各原子的均方位移和均方速度与温度成正比。

水位升降对顺层岩坡稳定性影响的上限分析方法

在构造顺层岩石边坡的简单直线破坏模式基础上,将强度折减技术与极限分析上限定理结合,推导边坡内外水位升降影响条件下的顺层边坡稳定性安全系数的目标表达式,并采用序列二次规划迭代法进行求解。通过算例计算,分析水位变化参数对顺层岩石边坡坡体安全系数和潜在破裂面的影响。研究结果表明:边坡内外水位升降对边坡安全系数和破坏范围存在不可忽视的影响,但当岩层倾角处于一定范围时,岩层倾角对边坡安全系数和破坏范围的控制程度更强。

明渠收缩段水深变化规律模型试验

通过水力学模型试验,对收缩段内水深变化规律进行观测,分析了收缩角、底坡及流量的变化对收缩段内流态影响,总结出三者对水深变化及水面波动的影响规律,得到了收缩段出口Fr随收缩角和流量的变化关系。根据动量定理推导了收缩段内壅水水深的计算公式,公式计算得到的收缩段内水深与试验测得水深基本一致。

香蕉价格波动的经济学分析

香蕉价格波动直接关系到蕉农的收入,影响我国香蕉产业的健康稳定发展。现阐述我国香蕉近几年价格波动的情况,从经济学的视角,运用供求定理对我国香蕉价格波动的情况进行分析。结果表明,香蕉谣言的传播、质量情况、同期上市的水果竞争等因素使香蕉市场的需求情况发生变化,香蕉种植面积扩大、集中上市和运输流通等因素使香蕉市场的供给情况发生变化,需求和供给的共同作用影响了香蕉的市场价格,造成了香蕉价格的波动。应从建立预警机制、强化信息体系建设、发展香蕉精深加工和提高产品质量等方面入手,促进香蕉产业的健康发展。