Herbart and “Psychological Research on the Strength of a Given Impression”

Herbart in 1812 published an analysis of sensory process formation, using differential equations, and attempted to relate within the same model considerations of upper and lower limits of sensory intensity, and the time course of process evolution within those limits. The analysis he proposed anticipates later psychophysics by at least half a century. It is perhaps the earliest example of a formal nonlinear dynamical treatment in theoretical psychology.     

Hurst exponent determination for digital speckle patterns in roughness control of metallic surfaces

In this paper, we present a study of metallic surface roughness using the Hurst exponent calculated from speckle pattern. A set of samples was prepared using polishing techniques and the roughness was directly measured by means of an optical profilometer. To study the H exponent, an experiment was performed by illuminating the samples using an expanded laser beam and the surface image was captured by a CCD camera. We applied techniques of the Hurst exponent calculation, traditionally calculated from surface profile, in the digitalized speckle patterns generated by the rough surfaces. We showed a clear dependence of the H exponent on roughness of the samples. We demonstrated that this tool is very sensitive to defects in the surfaces and can be used for roughness control.     

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger-Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.     

Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus

It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles. We show that the Lyapunov exponent is continuous for a higher-dimensional analytic category in this paper. It has a modulus of continuity of the form exp(−∣logt∣ ^σ ) for some 0 < σ < 1.     

玻璃化液体中构型熵与展宽弛豫函数关系的研究

The relationship between the transport properties and thermodynamic properties in glass forming liquids was investigated. The configurational entropy of Adam-Gibbs theory on cooperatively rearranging regions and the theoretic function derived from extremal value model were used to propose a brief that non-exponential stretched exponent in KWW form relaxation function is equal to the relative configurational entropy of cooperatively rearranging region in liquids, and is inversely proportional to the critical number of molecules occurring configurational transformation in a cooperatively rearranging region. Therefore, the new physical significance on glassy configuration is imposed on the stretched exponent, and theoretical developments and empirical correlations between the structural relaxation and configurational entropy are established. Further, an improved expression of β(T) was proposed to eliminate the deviation of the fit by using Vogel-Fulcher-Tammann equation from viscosity data at higher temperatures, which conforms well over 200 K temperature range. The improvement on β(T) is correspondent to the improvement on the difference in thermal capacities between isobaric and isochoric processes.     

二自由度耦合非线性随机系统的最大Lyapunov指数和稳定性

利用摄动方法讨论了一类耦合二自由度非线性系统，在小强度白噪声参数激励下系统运动模态的稳定性，获得了系统扩散过程的稳态概率密度的渐近表达式，由此获得了系统运动模态几乎必然稳定的充分必要条件。     

A numerical approach to spherical indentation techniques for material property evaluation

In this work, some inaccuracies and limitations of prior indentation theories, which are based on experimental observations and the deformation theory of plasticity, are investigated. Effects of major material properties on the indentation load-deflection curve are examined via finite element (FE) analyses based on incremental plasticity theory. It is confirmed that subindenter deformation and stress-strain distribution from deformation plasticity theory are quite dissimilar to those obtained from incremental plasticity theory. We suggest an optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to indentation techniques is then proposed by examining the FE solutions at the optimal point. Numerical regressions of obtained data exhibit that the strain-hardening exponent and yield strain are the two key parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides a stress-strain curve and material properties with an average error of less than 3%.     

Chaos control and synchronization of the Φ<Superscript>6</Superscript>-Van der Pol system driven by external and parametric excitations

The dynamical behavior of the Φ⁶-Van der Pol system subjected to both external and parametric excitation is investigated. The effect of parametric excitation amplitude on the routes to chaos is studied by numerical analysis. It is found that the probability of chaos happening increases along with the parametric excitation amplitude increases while the external excitation amplitude fixed. Based on the invariance principle of differential equations, the system is lead to desirable periodic orbit or chaotic state (synchronization) with different control techniques. Numerical simulations are provided to validate the proposed method.     

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基于27种合金钢与铝合金的机械、力学性能，分析对比了3种理论估算疲劳极限方法的估 算结果，发现3种方法中只有两种方法能够比较精确地估算材料的疲劳极限; 当引 入强度系数和应变硬化指数与常规机械与力学性能的关系之后，这两种方法都可借助材料的 常规机械与力学性能估算疲劳极限，估算过程中的限制性条件``高强度钢'应予取消.