Fluctuation of Parameters in Tumor Cell Growth Model

We study the steady state properties of a logistic growth model in the presence of Gaussian white noise.Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution functionand its extrema have been investigated. It is found that the fluctuation of the tumor birth rate reduces the populationof the cells while the fluctuation of predation rate can prevent the population of tumor cells from going into extinction.Noise in the system can induce the phase transition.     

Transient fluctuation of the prosperity of firms in a network economy

The transient fluctuation of the prosperity of firms in a network economy is investigated with an abstract stochastic model. The model describes the profit which firms make when they sell materials to a firm which produces a product and the fixed cost expense to the firms to produce those materials and product. The formulas for this model are parallel to those for population dynamics. The swinging changes in the fluctuation in the transient state from the initial growth to the final steady state are the consequence of a topology-dependent time trial competition between the profitable interactions and expense. The firm in a sparse random network economy is more likely to go bankrupt than expected from the value of the limit of the fluctuation in the steady state, and there is a risk of failing to reach by far the less fluctuating steady state.     

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.     

Genotype selection model with two time-correlated white noises

We study the steady state properties of a genotype selection model in the presence of two time correlated Gaussian white noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution has been investigated. The fluctuation of both the mutation factor and the genetic factor can break the balance of the gene selection. The fluctuation of the genetic factor can facilitate the gene separation which allows us to select one gene-type haploid from a gene group while the fluctuation of the mutation factor impedes the gene separation. Remarkably, the correlation time between the two noises can induce the system to change from two states to one.     

On the Fluctuation Relation for Nosé-Hoover Boundary Thermostated Systems

We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nosé-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in (D.J. Searles, et al., J. Stat. Phys. 128:1337, 2007), for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate Λ and of the dissipation function Ω, a similar relaxation regime at shorter averaging times is found. The quantity Ω satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity Λ appears to begin a monotonic convergence after such times. This is consistent with the fact that Ω and Λ differ by a total time derivative, and that the tails of the probability distribution function of Λ are Gaussian.     

Green-Kubo Formulas with Symmetrized Correlation Functions for Quantum Systems in Steady States: The Shear Viscosity of a Fluid in a Steady Shear Flow

For a quantum system in a steady state with a constant current of heat or particles driven by a temperature or chemical potential difference between two reservoirs attached to the system, the fluctuation theorem for the current was previously shown to lead to the Green-Kubo formula for the linear response coefficient for the current expressed in terms of the symmetrized correlation function of the current density operator. In this article, we show that for a quantum system in a steady state with a constant rate of work done on the system, the fluctuation theorem for a quantity induced in the system also leads to the Green-Kubo formula expressed in terms of the symmetrized correlation function of the induced quantity. As an example, we consider a fluid in a steady shear flow driven by a constant velocity of a solid plate moving above the fluid.     

Mdm2生成速率调控的p53-Mdm2振子的全局动力学和稳定性

肿瘤抑制蛋白p53的动力学在一定程度上可以决定DNA损伤后的细胞命运.p53的动力学行为与p53信号通路中p53-Mdm2振子模块密切相关.然而,p53的负调控子Mdm2的生成速率的增加使其在一些癌细胞中过表达.因此探讨Mdm2生成速率对p53动力学的影响有重要意义.同时,PDCD5作为p53的激活子也调控p53的表达.因此,本文针对PDCD5调控的p53-Mdm2振子模型,通过分岔分析获得了Mdm2生成速率所调控的p53的单稳态、振荡以及单稳态与振荡共存的动力学行为,且稳定性通过能量面进行了分析.此外,噪声强度对p53动力学的稳定性有重要的影响.因此,针对p53的振荡行为,探讨了噪声强度对势垒高度和周期的影响.本文所获得的结果对理解DNA损伤后的p53信号通路调控起到一定的指导作用.     

Nonequilibrium fluctuation relation for sheared micellar gel in a jammed state

We show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress, and in all cases show similar symmetry properties as predicted by the Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear-rate fluctuations increase with the decrease of the system size.     

三能级Upper-ladder型系统中的

三能级Upper-ladder型系统中,在旋波、慢变振幅近似下,求解了考虑驱动场相位扩散后的系统密度矩阵运动方程,并给出了这个三能级梯型系统稳态线性解析解.利用对密度矩阵运动方程的稳态线性解析解的数值模拟结果,研究相位扩散对无反转激光增益、色散和粒子数差的影响;利用对密度矩阵运动方程的数值模拟结果,分析相位的扩散对无反...     

First-Order-Like Phase Transition Induced by Two Different Kinds of Noise in Dispersive Optical Bistability

With unified colored noise approximation, the steady state distribution function in dispersive optical bistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phase transition is a/so derived with numerical method. It is found that the number of extremes at non-zero values of the output field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-fike phase transition.     

驱动场相位涨落对开放四能级系统的影响

考虑驱动场相位存在涨落,给出了开放四能级系统的稳态解析解,通过它分析了该系统由于驱动场相位涨落引起的有限线宽对增益、色散和粒子数差的影响.分析显示：线宽的变化不能改变无反转激光系统的特性;线宽的增大必须提高抽运阈值;相对来说退出速率很小时,线宽对增益、色散和粒子数差的影响较弱;当线宽不为零时该系统仍能获得无吸收高色散.     

Effects of phase fluctuation in an open four-level inversionless lasing system

A steady analytical solution of an open four-level inversionless lasing system with a driving field having the phase fluctuation has been given, and the effects of the finite width due to the phase fluctuation on the gain, dispersion, and population difference have been analyzed by using the numerical simulation from the steady analytical solution. It is found that: with the linewidth increasing, the gain decreases and the absolute value of population difference between levels coupled by the probe field increases, but the variation of the linewidth cannot change the properties of the inversionless lasing and refractive index increase of the system; when the linewidth does not equal to zero, the system can still get a high refractive index with zero absorption, and these conclusions have very obvious difference from those obtained in other inversionless lasing systems.     

单模激光系统输入信号后的稳态平均光强相对涨落

研究了具有实虚部间关联的量子噪声和抽运噪声驱动的单模激光系统输入信号后的统计性质,采用线性化近似方法计算了系统的稳态平均光强相对涨落,分析了量子噪声实虚部间关联系数、量子噪声强度、抽运噪声强度、输入信号振幅和频率、净增益等对稳态平均光强相对涨落的影响,发现在量子噪声实虚部间弱关联、小噪声、远离阚值、信号振幅不大和频率较高的条件下激光场的统计涨落较小。     

Nonequilibrium work fluctuations in a driven Ising model

Monte Carlo simulations of a sheared Ising model are used to study nonequilibrium fluctuations of mechanical work. The validity of the transient (starting from equilibrium) and the steady state fluctuation relations is verified. A fluctuation relation has been also shown to hold for the mechanical work done on the system, during the transition between two nonequilibrium steady states corresponding to different drivings.     

Lack of partial thermal equilibrium in pinch discharges

Measurements of the deuterium Balmer line intensities in the early phase of a theta pinch discharge show strong deviations from steady state population of levels considerably above the collision limit, even if criteria for the relaxation times of these levels are well satisfied. Solutions of time dependent rate equations for a hydrogen plasma confirm these observations. In cases of rising electron temperatures and rising degree of ionization the population of the ground level deviates by orders of magnitude from the steady state population of the momentary electron temperature and density. The population rates from the highly overpopulated ground level into levels above the collision limit then successfully compete with population rates from other levels and the continuum. Under such circumstances the relaxation time of excited levels above the collision limit into thermal equilibrium is determined by the relaxation time of the ground level into its steady state population.     

Onsager-Machlup Theory and Work Fluctuation Theorem for a Harmonically Driven Brownian Particle

We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition (also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.     

驱动场相位扩散对三能级梯型系统无反转激光的影响

在旋波、慢变振幅近似下,求解考虑了驱动场相位扩散后的系统密度矩阵运动方程,并给出了这个三能级梯型系统稳态线性解析解.利用得到的稳态线性解析解分析驱动场相位扩散是如何影响该系统输出无反转激光的.对稳态线性解析解数值计算的结果显示:由于驱动场相位扩散会导致无反转激光增益减小;即使由于驱动场相位扩散引起的线宽足够大,在该系统中仍能够获得无反转激光;线宽往往是破坏无反转激光产生和折射率的提高;因驱动场相位扩散导致无反转激光增益的减小,并不是总能够通过增大驱动场的Rabi频率得到补偿.     

Fluctuation Theorem for Currents and Schnakenberg Network Theory

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution.     

Einstein Relation for Nonequilibrium Steady States

The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds if the steady state satisfies detailed balance. More generally, we consider nonequilibrium steady states where detailed balance does not hold and show how a generalisation of the Einstein relation may be derived in certain cases. In particular, for the asymmetric simple exclusion process and a driven diffusive dimer model, the external perturbation creates and annihilates particles thus breaking the particle conservation of the unperturbed model.     

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