A Possible Generalized Form of Jarzynski Equality

The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.     

Schwarzschild black hole as moving puncture in isotropic coordinates

The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1 + log coordinate condition. We compute stationary 1 + log slices of the Schwarzschild spacetime in isotropic coordinates in order to investigate the coordinate singularity that the numerical methods have to handle at the puncture. We present an alternative integration method to obtain isotropic coordinates that simplifies numerical integration and that gives direct access to a local expansion in the isotropic radius near the puncture. Numerical results have shown that certain quantities are well approximated by a function linear in the isotropic radius near the puncture, while here we show that in some cases the isotropic radius appears with an exponent that is close to but unequal to one. This paper is dedicated to the memory of Jürgen Ehlers. I have known JE for a number of years, in particular during his time as founding director of the Albert Einstein Institute in Potsdam. JE was the mentor of my habilitation thesis in 1996, and I am deeply thankful for many insightful discussions. JE combined great breadth and physical intuition with sharp analytical thought. His example inspired me to look beyond the numerical methods and results of numerical relativity to the analytic foundations. For example, while at the AEI, S. Brandt and I introduced “puncture initial data” for the numerical construction of general multiple black hole spacetimes [3]. While the puncture construction starts with an analytic trick of the sort that numerical relativists may devise, it is fair to say that the keen interest in analytical relativity created by JE at the AEI induced us to push our analysis one step further. As a result [3] connects to [26] for an existence and uniqueness proof for such black hole initial data, using weighted Sobolev spaces (see also [4–6]). The present work and its predecessors [9–12] represent an example where numerical experiments led to the discovery of an analytic solution for the 1 + log gauge for the Schwarzschild solution, and the present result, although modest, is of the type which I believe JE would have appreciated.     

Quantum Jarzynski equality with multiple measurement and feedback for isolated system

In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast with the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.     

Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

We show how Jacobian elliptic functions （JEFs） can be used to solve ordinary differential equations （ODEs） describing the nonlinear dynamics of microtubules （MTs）. We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kinkbtype soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.     

Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

Isospectral flow and lax pairs

Certain non-linear differential equations may be considered as compatibility conditions for a linear system of equations, that is, as the vanishing-curvature condition for some connection. It is shown how one can obtain this connection from an isospectral-flow condition using a Foldy-Wouthuysen transformation.     

Chaotic attractors in incommensurate fractional order systems

In this paper, based on the stability theorems in fractional differential equations, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system. This condition is proposed for incommensurate order systems in general, but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems. Though the presented condition is only a necessary (and not sufficient) condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system, chaotic attractors can not be observed and for what parameters and orders, the system may generate chaos. It can also be used as a tool to confirm or reject results of a numerical simulation. Some of the numerical results reported in the previous literature are confirmed by this tool.     

应变超晶格系统的共振行为及其动力学稳定性

在经典力学框架内和Seeger方程基础上,讨论了应变超晶格界面附近的位错动力学行为,指出了系统的非线性共振将导致位错的运动与堆积,并可能造成超晶格的分层或断裂.首先,引入阻尼项,在小振幅近似下,把描述一般位错运动的Seeger方程化为了超晶格系统的广义Duffing方程.利用多尺度法分析了系统的主共振、超共振和子共振,并找到了系统出现这三类共振的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免共振的出现,保证了超晶格材料的完整性和性能的稳定性. 关键词： 位错动力学 应变超晶格 共振 分岔     

A time delay control for a nonlinear dynamic beam under moving load

The bifurcation resulted from moving force may lead to instability for the system. Based on time delay feedback controller, a nonlinear beam under moving load is discussed in the case of the primary resonance and the 1/3 subharmonic resonance. The bifurcation may be eliminated or the bifurcation point's position may be changed. The perturbation method is used to obtain the bifurcation equation of the nonlinear dynamic system. The result indicates time delay feedback controller may work well on this system, but the selection of a proper time delay and its coefficient may depend on the engineering condition. This paper presents some theoretical results.     

Statistical energy analysis, energy distribution models and system modes

Expressions for the energy influence coefficients of a built-up structure are found in terms of the modes of the whole structure. These coefficients relate the time and frequency average energies of the subsystems to the subsystem input powers. Rain-on-the-roof excitation over a frequency band Ω is assumed. It is then seen that the system can be described by an SEA model only if a particular condition involving the mode shapes of the system is satisfied. Broadly, the condition holds if the mode shapes of the modes in the frequency band of excitation are, on average, typical enough of all the modes of the system in terms of the distribution of energy throughout the system. If this condition is satisfied then the system can be modelled using an “quasi-SEA” approach, irrespective of the level of damping or of the strength of coupling. However, the resulting model need not be of a proper SEA form, and in particular the indirect coupling loss factors may not be negligible.     

Conditions for the validity of the Debye integral representation of focused fields

A very simple sufficiency condition is obtained, under which the Debye diffraction integral may be expected to give a good approximation to the solution of a boundary value problem that is generally taken to represent a field in the region of focus. When the angular aperture of the focusing system is sufficiently small, the condition reduces to the requirement that the Fresnel number of the diffracting aperture, when viewed from the geometrical focus, is large compared to unity.     

Deducing the Schrödinger equation from minimum χ2

The most unbiased probabilistic model for the possible values of a characteristic of a quantum system subject to the constraints represented by some known mean values characterizes the system in a steady-state condition. We suppose that random fluctuations alter such a steady-state condition. The probability distribution of the possible deviations from the steady-state condition is estimated by minimizing Pearson's ² subject to the mean fluctuations available. The optimum Pearson function ^* may be interpreted as the wave function of the system and in the case of the harmonic oscillator, the free particle in a box, and the hydrogen atom, the prediction based on it is compatible with that provided by the solution of the corresponding Schrödinger equations.     

Fundamental electrical standards and the quantum metrological triangle

The advent of the fundamental constants R_K (the von Klitzing constant) and K_J (the Josephson constant) in electrical metrology and the growing development of nanotechnologies have totally changed the vision and the practice of the National Metrology Institutes (NMIs), opening a modern era of metrology and arousing a growing interest in a possible re-definition of the international system of units (SI). The Josephson effect (JE) and the Quantum Hall effect (QHE), at the origin of these fundamental constants, constitute the keystone of a new approach to electrical units, when one considers the very high level of reproducibility of these units, never seen before. On the other hand, the Watt balance experiment in which these constants play a part could be the origin of a new SI definition, replacing the mass unit ‘the kilogram’ as a fundamental unit by the Planck constant h. It thus seems that the implementation of experiments aimed at demonstrating the coherency between the theoretical and phenomenological values of these constants is a major objective. In this framework the metrological triangle experiment associating QHE, JE and single electron tunnelling effect would play a major role in checking the consistency of these fundamental constants in terms of the Planck and electron charge constants. This article gives briefly an outline of these quantum phenomena and their metrological applications in NMIs for the realisation of electrical units and the determination of the fundamental constants. To cite this article: F. Piquemal et al., C. R. Physique 5 (2004).     

Determination of the cyclotron generation suppression band width in a plasma relativistic microwave generator

In a plasma-beam system in a finite magnetic field, along with Cherenkov resonance other resonances of beam and plasma waves occur. In a finite-length plasma waveguide, the concurrent wave excited by a beam at Cherenkov resonance is always partially reflected from the ends of the plasma waveguide. The reflected (counterrunning) wave provides feedback and leads to the occurrence of generation regime in such a system. Under the resonance condition for a normal Doppler effect the feedback is suppressed and the generation may cease. This effect can be used in experiments on creation of plasma microwave amplifiers in which microwave generation is harmful.     

边界交流关系、量子系统消耗与量子组织均衡

本文探讨建立以环境提供的熵流为自变量的熵变函数;当熵变化取负值时,此函数可称 作有序生成函数。在此基础上,从量子系统为形成并维持有序化的低熵态而由环境提供可转化为物质的能量流或熵流方面考虑量子系统的消耗,建立量子消耗函数;从量子系统经过非平衡相变而由无序化的高熵态转入有序化的低熵态方面考虑量子系统的补偿,建立量子补偿函数;进而在量子消耗和量子补偿之间取剩余,形成量子组织增益量。量子系统总是在一定的消耗下力图达到最大的组织增益,可将这一目标状态看作量子组织均衡（或量子组织平衡）。     

用于波形数字化的JESD204B高速接口设计

随着高速波形数字化技术在核与粒子物理实验中的广泛应用,其对于ADC速度和精度需求日益增大,从而使电子学系统的PCB布局布线更加复杂、成本更高。为了简化设计,降低成本,提出了用于波形数字化的JESD204B的高速接口设计方法,介绍了JESD204B接口的协议及需求,并提出了基于Altera FPGA和专用JESD204B时钟芯片LMK0482x的具体解决方案。测试结果表明,时钟性能优异且JESD204B链路功能正常,系统性能优异,该方法可以实现JESD204B高速接口设计,并应用于波形数字化技术。At present, due to the wide application of nuclear and particle physics experiments in the waveform digitization technology and the increasing demand of high speed and high accuracy for ADC, the PCB layout is more and more complex and the cost is higher. In order to simplify the design and reduce the cost, this paper put forward the scheme of JESD204B high speed interface for the waveform digitization technology in nuclear and particle physics experiments. Firstly the interface protocol and the demand of JESD204B is introduced. Then the solution based on Altera FPGA and special JESD204B clock chip LMK0482x is proposed. The preliminary test results show that the clock performance is excellent and JESD204B link is functioning normally. Moreover, the system has an excellent performance. The scheme can realize the design of JESD204B high speed interface and therefore be applied to the waveform digitization technology.     

Uncoupled achromatic condition of a dog-leg system with the presence of RF cavities

To merge the beam from either of the two injectors to the main linac, a dog-leg system will be employed in the second Medium Energy Beam Transport(MEBT2) line of the China ADS driving accelerator. The achromatic condition has to be guaranteed to avoid beam center excursion against energy jitter. RF cavities were found to be indispensable to control the bunch length growth in the dog-leg system of MEBT2. The full uncoupling between transverse and longitudinal plane is desired to minimize the growth of projected rms emittances. The uncoupled achromatic condition of this dogleg system with the presence of RF bunching cavities will be deduced using the transfer matrices method. It is found that, to fulfill the uncoupling condition, the distance between the bunching cavities is uniquely determined by the maximum energy gain of the RF cavities. The theoretical analysis is verified by the simulation code TraceWin. The space charge effect on the uncoupled achromatic condition and the beam emittance growth will also be discussed.     

NOVELTY DETECTION IN A CHANGING ENVIRONMENT: REGRESSION AND INTERPOLATION APPROACHES

The technique of novelty detection is now established as a means of performing the lowest level of damage identification. Data are accumulated while the system or structure is operating in normal condition and used to construct a reference model. During subsequent operation of the system, data are compared to the reference and any significant deviations are taken to indicate damage. This approach has potential problems if the system or structure is embedded in a changing environment. If the reference data are only characteristic of a limited range of the environmental parameters, measurements from the system in an undamaged condition but from a different environmental state, may cause the diagnostic to register novelty and thus falsely infer damage. This paper demonstrates a potential solution to the problem via the construction of a reference set parametrized by an environmental variable. Two approaches are considered: regression and interpolation.     

Diffusion dominated dynamics of avalanching systems

A surprisingly large number of systems in nature are thought to be governed by internal dynamics which causes avalanches of various sizes. In such systems energy, which is delivered from outside, is redistributed as a result of the occurrence of localized avalanches. Starting an avalanche requires that some threshold condition be satisfied. Random driving (energy input) brings the system into a strongly inhomogeneous state, so that the probability of triggering an avalanche in a large part of the system is small. In most physical systems energy redistribution may occur due to diffusive processes without avalanches. Diffusion also makes the system more uniform, making large avalanche triggering more probable. The observed behavior of a such system may crucially depend on the competition between diffusion and driving. In this paper, the effects of diffusive processes are investigated using a dissipative, isotropic one-dimensional model, in which avalanches can propagate in both directions. It is shown that the system behavior changes progressively as the diffusion rate increases. In the absence of diffusion, many small avalanches are triggered. Increasing the diffusion rate gradually suppresses these small avalanches and leads to the development of large, quasi-periodic bursts.     

Generalization of the second law for a nonequilibrium initial state

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory.