深部储层动力学刍议

随着非线性科学的发展及其在地学中的应用,人们逐渐认识到深中储层并非是一封闭、孤立的系统,而是一典型的耗散系统,其含油气性受深部壳幔结构控制。借助非线性动力学思想,尝试提出“深部储层动力学”这一全新的概念及它的基本研究内容和解决问题的方法。     

Chaos in an enzyme reaction

Dynamic systems are usually thought to have either monotonic or periodic behaviour. Although the possibility of other types of behaviour has been recognised for many years, the existence of non-monotonic, non-periodic behaviour in dynamic systems has been firmly established only recently. It is termed chaotic behaviour. A review on the rapidly expanding literature on chaos in discrete model systems described by difference equations has been published by May. R?ssler, on the other hand, has discussed a few published works on systems of differential equations with chaotic solutions, and he has proposed a three-component chemical model system which he argues has chaotic solutions [figure see text]. The argument is based on a theorem by Li and Yorke. Here we report the finding of chaotic behaviour as an experimental result in an enzyme system (peroxidase). Like R?ssler we base our identification of chaos on the theorem by Li and Yorke.     

The jamming route to the glass state in weakly perturbed granular media

It has been suggested that a common conceptual framework known as 'jamming' (refs 1 and 2) may be used to classify a wide variety of physical systems; these include granular media, colloidal suspensions and glass-forming liquids, all of which display a critical slowdown in their dynamics before a sudden transition to an amorphous rigid state. Decreasing the relevant control parameter (such as temperature, drive or inverse density) may cause geometrical constraints to build up progressively and thus restrict the accessible part of the system's phase space. In glass-forming liquids (thermal molecular systems), jamming is provided by the classical vitrification process of supercooling, characterized by a rapidly increasing and apparently diverging viscosity at sufficiently low temperatures. In driven (athermal) macroscopic systems, a similar slowdown has been predicted to occur, notably in sheared foam or vibrated granular media. Here we report experimental evidence for dynamic behaviour, qualitatively analogous to supercooling, in a driven granular system of macroscopic millimetre-size particles. The granular medium is perturbed by isolated tapping or continuous vibration, with the perturbation intensity serving as a control parameter. We observe the random deflection of an immersed torsion oscillator that moves each time the grains rearrange, like a 'thermometer' sensing the granular noise. We caution that our granular analogy to supercooling is based on similarities in the dynamical behaviour, rather than quantitative theory.     

Doping a semiconductor to create an unconventional metal

Landau-Fermi liquid theory, with its pivotal assertion that electrons in metals can be simply understood as independent particles with effective masses replacing the free electron mass, has been astonishingly successful. This is true despite the Coulomb interactions an electron experiences from the host crystal lattice, lattice defects and the other approximately 10(22) cm(-3) electrons. An important extension to the theory accounts for the behaviour of doped semiconductors. Because little in the vast literature on materials contradicts Fermi liquid theory and its extensions, exceptions have attracted great attention, and they include the high-temperature superconductors, silicon-based field-effect transistors that host two-dimensional metals, and certain rare-earth compounds at the threshold of magnetism. The origin of the non-Fermi liquid behaviour in all of these systems remains controversial. Here we report that an entirely different and exceedingly simple class of materials-doped small-bandgap semiconductors near a metal-insulator transition-can also display a non-Fermi liquid state. Remarkably, a modest magnetic field functions as a switch which restores the ordinary disordered Fermi liquid. Our data suggest that we have found a physical realization of the only mathematically rigorous route to a non-Fermi liquid, namely the 'undercompensated Kondo effect', where there are too few mobile electrons to compensate for the spins of unpaired electrons localized on impurity atoms.     

基于Volterra模型的一类通信系统的参数辨识

分析了Volterra级数理论对于非线性系统的模型建造的意义，提出了一类通信系统的适用于系统辨识的新模型──Volterra离散频域模型．应用此模型对一个具体的通信系统有效地进行了非线性故障诊断和参数辨识．     

Hysteresis in the perception of motion direction as evidence for neural cooperativity

When elements of a parallel network, such as the human brain, are extensively interconnected, the network can exhibit 'cooperative behaviour'. Such behaviour, which is characterized by order-disorder transitions, multi-stable states, and a form of memory called 'hysteresis', has been observed in human stereopsis and has motivated models of stereopsis that incorporate cooperative networks. More recently, cooperative phenomena have also been observed in human visual motion perception. This report strongly supports a cooperative interpretation of motion perception by demonstrating hysteresis in the perception of motion direction. The results agree quantitatively with a mathematical model incorporating nonlinear excitatory and inhibitory interactions among direction-selective elements.     

考虑土体非线性特性的一维固结理论研究

根据压缩曲线的性质,提出了用双曲线模拟土体压缩非线性性质的方法,在对太沙基固结理论的假设做了修正后,推导了非线性固结问题及其解,并将解与底部可测孔压的固结试验结果进行了对比。研究表明,考虑土体非线性性质的一维固结问题的解比太沙基固结理论解要接近试验结果,且求解过程与太沙基固结理论同样方便简单。     

An adaptive strategy for controlling chaotic system

This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems : Duffing oscillator and Rǒssler chaos.     

Feedback Linearization H∞ Control and Its Application to Excitation Systems

This work presents a new design method based on differential geometry and the nonlinear H∞ approach which has verified that the H∞ control for the feedback linearization system is equivalent to a nonlinear H∞control for the primitive nonlinear control system in the sense of differential game theory. In addition, this kind of design method is used for nonlinear robust optimal excitation control of a multi-machine system. The controller constructed is implemented via purely local measurement. Moreover, it is independent of the parameters of power networks. Simulations are performed on a single-infinite system. It has been demonstrated that the nonlinear H∞ excitation controller is more effective than the other nonlinear excitation controller in dynamic performance improvement for variation of operational states and parameters in power systems.     

Breakdown of Fermi-liquid theory in a copper-oxide superconductor.

The behaviour of electrons in solids is well described by Landau's Fermi-liquid theory, which predicts that although electrons in a metal interact, they can still be treated as well defined fermions, which are called 'quasiparticles'. At low temperatures, the ability of quasiparticles to transport heat is given strictly by their ability to transport charge, as described by a universal relation known as the Wiedemann-Franz law, which hitherto no material has been known to violate. High-temperature superconductors have long been thought to fall outside the realm of Fermi-liquid theory, as suggested by several anomalous properties, but this has yet to be shown conclusively. Here we report an experimental test of the Wiedemann-Franz law in the normal state of a copper-oxide superconductor, (Pr,Ce)2CuO4, which reveals that the elementary excitations that carry heat in this material are not fermions. This is compelling evidence for the breakdown of Fermi-liquid theory in high-temperature superconductors.     

传染病动力学的一个细胞自动机模型

由细胞自动机出发提出一个传染病流行的非线性动力学模型，由计算机数值模拟，应用自组织临界理论分析结果，发现发病率和治愈率均为５０％时存在着分界点。在分界点两侧，患病集团分布和传染持续时间分布分别服从指数律和幂律，免疫体的分布具有不同的分数维。     

Use of behavioural stochastic resonance by paddle fish for feeding

Stochastic resonance is the phenomenon whereby the addition of an optimal level of noise to a weak information-carrying input to certain nonlinear systems can enhance the information content at their outputs. Computer analysis of spike trains has been needed to reveal stochastic resonance in the responses of sensory receptors except for one study on human psychophysics. But is an animal aware of, and can it make use of, the enhanced sensory information from stochastic resonance? Here, we show that stochastic resonance enhances the normal feeding behaviour of paddlefish (Polyodon spathula), which use passive electroreceptors to detect electrical signals from planktonic prey. We demonstrate significant broadening of the spatial range for the detection of plankton when a noisy electric field of optimal amplitude is applied in the water. We also show that swarms of Daphnia plankton are a natural source of electrical noise. Our demonstration of stochastic resonance at the level of a vital animal behaviour, feeding, which has probably evolved for functional success, provides evidence that stochastic resonance in sensory nervous systems is an evolutionary adaptation.     

Structural relaxation in supercooled water by time-resolved spectroscopy

Water has many kinetic and thermodynamic properties that exhibit an anomalous dependence on temperature, in particular in the supercooled phase. These anomalies have long been interpreted in terms of underlying structural causes, and their experimental characterization points to the existence of a singularity at a temperature of about 225 K. Further insights into the nature and origin of this singularity might be gained by completely characterizing the structural relaxation in supercooled water. But until now, such a characterization has only been realized in simulations that agree with the predictions of simple mode-coupling theory; unambiguous experimental support for this surprising conclusion is, however, not yet available. Here we report time-resolved optical Kerr effect measurements that unambiguously demonstrate that the structural relaxation of liquid and weakly supercooled water follows the behaviour predicted by simple mode-coupling theory. Our findings thus support the interpretation of the singularity as a purely dynamical transition. That is, the anomalous behaviour of weakly supercooled water can be explained using a fully dynamic model and without needing to invoke a thermodynamic origin. In this regard, water behaves like many other, normal molecular liquids that are fragile glass-formers.     

Non-linear dynamics of cardiac excitation and impulse propagation

Extremely complex frequency-dependent patterns of excitation and impulse propagation can be shown in cardiac tissues. Such complex behaviour can be analysed using methods derived from chaos theory, which is concerned with the non-linear dynamics of deterministic systems that have irregular periodicities as well as an exquisite sensitivity to the initial conditions. We report here that the general response patterns of non-oscillatory cardiac conducting tissues, when driven rhythmically by repetitive stimuli from their surroundings, are similar to those of other deterministic systems showing chaotic dynamics. Such patterns include phase locking, period-doubling bifurcation and irregular activity. We have used electrophysiological techniques and analytical arguments to explain this unforeseen behaviour and to provide some key information about its mechanisms. The study of these dynamics is of general application to the understanding of disordered phenomena in excitable media, and may provide new insight about the origin of fatal cardiac arrhythmias.     

Correlated electrons in delta-plutonium within a dynamical mean-field picture

Given the practical importance of metallic plutonium, there is considerable interest in understanding its fundamental properties. Plutonium undergoes a 25 per cent increase in volume when transformed from its alpha-phase (which is stable below 400 K) to the delta-phase (stable at around 600 K), an effect that is crucial for issues of long-term storage and disposal. It has long been suspected that this unique property is a consequence of the special location of plutonium in the periodic table, on the border between the light and heavy actinides-here, electron wave-particle duality (or itinerant versus localized behaviour) is important. This situation has resisted previous theoretical treatment. Here we report an electronic structure method, based on dynamical mean-field theory, that enables interpolation between the band-like and atomic-like behaviour of the electron. Our approach enables us to study the phase diagram of plutonium, by providing access to the energetics and one-electron spectra of strongly correlated systems. We explain the origin of the volume expansion between the alpha- and delta-phases, predict the existence of a strong quasiparticle peak near the Fermi level and give a new viewpoint on the physics of plutonium, in which the alpha- and delta-phases are on opposite sides of the interaction-driven localization-delocalization transition.     

二自由度平面机械手的模糊建模与模糊控制

本文以二自由度平面机械手为例，尝试用线性系统理论和模糊控制理论解决非线性系统问题。要点是：把一个整体非线性动力学模型看成是多个局部线性模型的模糊逼近；把整个非线性系统的控制看成是多个局部线性系统控制的模糊逼近。这种方法称为并行分配补偿法。本文建立了二自由度平面机械手的模糊模型并在此基础上用并行分配补偿法对系统进行了综合，最后用仿真进行了验证，证明了并行分配补偿法的成功和所建模型的合理性。     

Observation of random-phase lattice solitons

The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or 'discrete') solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.     

Mechanisms of extensive spatiotemporal chaos in Rayleigh-Benard convection

Spatially extended dynamical systems exhibit complex behaviour in both space and time--spatiotemporal chaos. Analysis of dynamical quantities (such as fractal dimensions and Lyapunov exponents) has provided insights into low-dimensional systems; but it has proven more difficult to understand spatiotemporal chaos in high-dimensional systems, despite abundant data describing its statistical properties. Initial attempts have been made to extend the dynamical approach to higher-dimensional systems, demonstrating numerically that the spatiotemporal chaos in several simple models is extensive (the number of dynamical degrees of freedom scales with the system volume). Here we report a computational investigation of a phenomenon found in nature, 'spiral defect' chaos in Rayleigh-Benard convection, in which we find that the spatiotemporal chaos in this state is extensive and characterized by about a hundred dynamical degrees of freedom. By studying the detailed space-time evolution of the dynamical degrees of freedom, we find that the mechanism for the generation of chaotic disorder is spatially and temporally localized to events associated with the creation and annihilation of defects.     

半刚性钢框架稳定理论的扣件式钢管满堂支撑体系极限承载力分析

在考虑直角扣件半刚性以及材料、几何非线性等因素的情况下,对两个扣件式钢管满堂支撑体系模型(无剪刀撑S1模型、有剪刀撑S2模型)进行非线性屈曲分析,得到体系竖向荷载-位移曲线,确定了体系极限承载力.采用半刚性钢框架稳定理论,对无剪刀撑S1模型承载力进行计算.将所得结果与数值结果对比,验证了半刚性钢框架稳定理论在计算体系承载力的可行性.对直角扣件的转动性能进行试验,得到弯矩-转角曲线.采用ANSYS中的COMBIN39弹簧单元对直角扣件的转动进行模拟.     

The conformation of membranes

Membranes composed of amphiphilic molecules are highly flexible surfaces that determine the architecture of biological systems and provide a basic structural element for complex fluids such as microemulsions. Physical theories have been developed to describe many aspects of their conformational behaviour, such as the preferred shapes and shape transformations of closed vesicles, and the shape fluctuations, random-surface configurations, and adhesion and unbinding of interacting membranes. Understanding of these phenomena has been much improved through fruitful interactions between theory and experiment.