Dissipation and large thermodynamic fluctuations

The results of recent work of Kipnis, Olla, and Varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation, including non-equilibrium steady states, as a fluctuation-dissipation hypothesis. The basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation. It is shown that this hypothesis leads to a nonlinear version of Onsager-Machlup fluctuation theory that had previously been proposed by Graham. A direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints (Onsager's principle of least dissipation). Following Graham, the theory leads also to a generalized potential, analogous to an equilibrium free energy, for the nonequilibrium steady state and an associated static variational principle. Finally, a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large-deviations theory on a formal analogy with the results of Freidlin and Wentzell for finite-dimensional systems.     

Nonequilibrium quantum phase transition in itinerant electron systems

We study the effect of the voltage bias on the ferromagnetic phase transition in a one-dimensional itinerant electron system. The applied voltage drives the system into a nonequilibrium steady state with a nonzero electric current. The bias changes the universality class of the second order ferromagnetic transition. While the equilibrium transition belongs to the universality class of the uniaxial ferroelectric, we find the mean-field behavior near the nonequilibrium critical point.     

Chronopotentiometry study of a cation-exchange membrane in the presence of cationic surfactant in membrane surface vicinity

In this study, the effect of cationic surfactant (benzalkonium chloride) on the transport of KCl through a sulfonated styrene-divinyl benzene cation-exchange membrane was investigated. The presence of benzalkonium chloride as the cationic surfactant, which interacts with the sulfonic groups on membrane surface, has to disturb the transport of K⁺ ions and directly gives responses in its chronopotentiogram. The electrodialysis of the cationic surfactant solution showed an irreversible monotonous increase of the total system potential due to the fouling phenomena. However, a small amount of cationic surfactant in the membrane surface vicinity was observed to give a fluctuating chronopotentiogram at the high current density. This fluctuation is started by a steep increase and followed by the decrease of potential, which finally relaxed to reach a steady state. This potential fluctuation is proposed to be the response of a structural transformation of surfactant micelles on the membrane surface under perturbation of the externally applied electric field, which is discussed and examined qualitatively in this report.     

Statistical model of current-coupled ion channels in nerve membranes

A statistical model of a driven system is developed. Its microscopic elements are the ion channels through a nerve membrane. Their conductances are stochastically switching under the competing influences of thermal noise and local membrane voltage. A current flow through the membrane induces a coupling between the channels via the electrolytes surrounding the membrane. The long range of the coupling permits a generalized mean field theory for the stationary membrane current as a function of the applied electrode voltage. We derive analytically the macroscopic conductance-voltage-temperature relation for the spatially uniform current state. It shows analogues of first and second order phase transitions. The critical temperature diverges at a finite coupling strength. The theory fits sodium conductance characteristics measured on nerve axon membranes from various species by a variation of only the coupling strength. This supports the hypothesis that this simplest possible model for sodium channels is universal for all species.The work of this author was partially supported by the Deutsche Forschungsgemeinschaft     

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.     

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.     

晶闸管串联开关及同步触发系统研制

为满足脉冲功率源对高电压、大电流开关的需求,利用传统晶闸管均压技术,将多个晶闸管串联,研制出额定电压10kV,额定电流500A的晶闸管串联开关。根据晶闸管的触发原理,设计出同步触发多个晶闸管的触发系统。该触发系统采用绝缘栅双极型晶体管开关对直流电压阻断产生脉宽可调的低压脉冲,经多个隔离脉冲变压器升压,产生多路同步触发信号。对晶闸管触发系统及晶闸管串联开关进行了测试,测试结果表明:晶闸管触发系统可输出20V,1A的多路同步触发信号,触发信号的脉宽30~60μs可调,重复频率100Hz;晶闸管串联开关每路静态均压和动态均压波动小,在高电压条件下能稳定工作。     

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.     

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.     

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.     

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.     

一类自突触作用下神经元电路的设计和模拟

神经元在自突触作用下可以诱发各类放电活动的迁移, 神经元动作电位对电自突触的响应比较敏感. 通常用包含延迟因子和增益的反馈回路电流来刻画自突触对神经元动作电位的影响. 基于Pspice软件, 设计了包含自突触效应的神经元电路, 用以延迟反馈电路来模拟电自突触对电位的调制作用. 研究结果发现: 1)在外界刺激和电自突触回路协同作用下, 神经元电路输出信号可以呈现静息态, 尖峰放电, 簇放电状态. 2)在时变增大的外界刺激下和自突触回路驱动下, 神经元电路的输出电位序列在多种电活动模式之间(静息, 尖峰放电, 簇放电)交替出现, 其机理在于自突触回路具有记忆特性, 神经元对于不同的外界刺激可以做出不同模式的响应. 3)在给定比较大外界刺激下, 改变反馈回路的增益, 发现电路输出的序列也可以呈现不同模式交替, 即神经元对于相同的刺激可以通过自我调节自突触增益来产生不同模式的响应, 其机理可能在于回路的有效反馈, 这有助于理解突触的可塑性.     

Observation of the external-ac-current-induced dc voltage proportional to the steady current in superconducting loops

A dc voltage induced by an external ac current was observed in a system of asymmetric aluminum loops at temperatures corresponding to 0.95–0.98 of the superconducting transition temperature. The voltage magnitude and sign change periodically in a magnetic field with a period corresponding to the magnetic flux quantum through the loop. The amplitude of these oscillations depends nonmonotonically on the amplitude of ac current and is almost independent of its frequency in the range from 100 Hz to 1 MHz. The observed phenomenon is interpreted as the result of displacing the loop into a dynamic resistive state by the external current, where the loop is “switched” back and forth between the closed superconducting state with a nonzero steady current and the nonclosed state with a nonzero resistance along the loop circle. It is shown that voltages are summed up in a system of loops connected in series. For systems with one, three, and twenty loops, the voltage reaches 10, 40, and 300 μ V, respectively.     

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.     

Reversal current observed in micro-and submicro-channel flow under non-continuous DC electric field

In practical applications of biochips and bio-sensors, electrokinetic mechanisms are commonly employed to manipulate and analyze the characteristics of single bio-molecules. To accurately and flexibly control the movement of single molecule within micro-/submicro-fluidic channels, the characteristics of current signals at the initial stage of the flow are systematically studied based on a three-electrode system. The current response of micro-/submicro-fluidic channels filled with different electrolyte solutions in non-continuous external electric field are investigated. It is found, there always exists a current reversal phenomenon, which is an inherent property of the current signals in micro/submicro-fluidics Each solution has an individual critical voltage under which the steady current value is equal to zero The interaction between the steady current and external applied voltage follows an exponential function. All these results can be attributed to the overpotentials of the electric double layer on the electrodes. These results are helpful for the design and fabrication of functional micro/nano-scale fluidic sensors and biochips.     

基于非对称模型的变电所数据融合误差优化研究

牵引变电所作为电力系统中实现变换电能的场所,给电力机车提供稳定可靠的电能。由于机车具有非线性运载特点,在吸收电网电流的同时也在输入谐波电流,引起电网干扰波动和噪声误差、电压畸变等现象,对供电系统安全构成威胁。本文通过建立变电所三相匹配与失配模型,利用自适应数据融合算法仿真检测控制误差的效果和优化误差的最佳方案,合理控制参数的状态和优化参数的规律。结果表明数据融合可以解决局部电网误差波动电流超标和电压畸变,在保障供电质量和电网安全方面效果显著。     

外场对分子纳米结电流-电压特性的影响

针对由金属电极/分子/金属电极组成的分子纳米结,应用扩展主方程的方法,考虑分子纳米结中影响其传输过程的外场、分子内的弛豫过程等因素研究了在外场作用下分子纳米结内的稳定电流和瞬间电流.由于分子内较强的电子-振动耦合,分子纳米结中的电流-电压曲线呈现台阶式非弹性特征.在不同的高斯型脉冲的激发作用下,分子纳米结中电流需要达到稳定的时间也不相同,脉冲宽度在1ps时瞬间电流现象明显,这时分子处于非平衡分布,分子两端的电流存在较大差异.随着脉冲宽度和外场偏压的增加,分子两端的电流趋于平衡.     

Universality class of nonequilibrium phase transitions with infinitely many absorbing states

We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one-among an infinite number-absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks, and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper-critical dimension below which anomalous fluctuation driven scaling appears is d(c)=6, in contrast to a widespread belief. We provide the exponents governing the critical behavior close to or at the transition point to first order in an epsilon =6-d expansion.     

基于能量流动双PWM协调控制

基于双PWM结构,根据系统能量流动分析系统在能量平衡状态和能量不平衡状态下系统各部分间的能量关系,并建立双PWM结构能量数学模型。针对系统输出能量与消耗能量不平衡时造成的直流母线电压波动以及输出功率不匹配的问题,建立关于直流母线电压以及网侧电流d轴分量的约束条件,保证系统能量能够平滑变化。采用约束条件对整流器电压外环以及功率内环进行修正,用以实现整流侧输出能量与逆变侧消耗能量的快速平衡,达到双PWM结构间协调控制的目的。根据仿真结果表明,系统在电机功率突变时,能够实现能量的快速平衡,并且能够减少直流母线电压波动,减少网侧谐波分量和直流侧电容。