A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

Direct dynamical test for deterministic chaos

We present a direct and dynamical method to distinguish low-dimensional deterministic chaos from noise. We define a series of time-dependent curves which are closely related to the largest Lyapunov exponent. For a chaotic time series, there exists an envelope to the time-dependent curves, while for a white noise or a noise with the same power spectrum as that of a chaotic time series, the envelope cannot be defined. When a noise is added to a chaotic time series, the envelope is eventually destroyed with the increasing of the amplitude of the noise.

Deterministic Column-Based Matrix Decomposition

In this paper, we propose a deterministic column-based matrix decomposition method. Conventional column-based matrix decomposition (CX) computes the columns by randomly sampling columns of the data matrix. Instead, the newly proposed method (termed as CX_D) selects columns in a deterministic manner, which well approximates singular value decomposition. The experimental results well demonstrate the power and the advantages of the proposed method upon three real-world data sets.

missing data imputation: a fuzzy k-means clustering algorithm over sliding window

Tianjin University of Technology

Evolution-induced catastrophe and its predictability

Both earthquake prediction and failure prediction of disordered brittle media are difficult and complicated problems and they might have something in common. In order to search for clues for earthquake prediction, the common features of failure in a simple nonlinear dynamical model resembling disordered brittle media are examined. It is found that the failure manifests evolution-induced catastrophe (EIC), i.e., the abrupt transition from globally stable (GS) accumulation of damage to catastrophic failure. A distinct feature is the significant uncertainty of catastrophe, called sample-specificity. Consequently, it is impossible to make a deterministic prediction macroscopically. This is similar to the question of predictability of earthquakes. However, our model shows that strong stress fluctuations may be an immediate precursor of catastrophic failure statistically. This might provide clues for earthquake forecasting.

Effects of stochastic extension in ideal microcrack system

The effects of stochastic extension on the statistical evolution of the ideal microcrack system are discussed. First, a general theoretical formulation and an expression for the transition probability of extension process are presented, then the features of evolution in stochastic model are demonstrated by several numerical results and compared with that in deterministic model.

Evolution of ideal micro-crack system

The ideal micro-cracks are treated with the number-density function; the characteristics of their evolution are investigated; a deterministic model is applied to the discussion of their extension. It is discovered that under certain conditions saturation may occur in the number-density. The main features of the statistical formulation are illustrated by several examples and compared with those observed in experiments.

Nutrient dynamics and the eutrophication of shallow lakes Kasumigaura (Japan), Donghu (PR China), and Okeechobee (USA)

We compared the nutrient dynamics of three lakes that have been heavily influenced by point and non-point source pollution and other human activities. The lakes, located in Japan (Lake Kasumigaura), People's Republic of China (Lake Donghu), and the USA (Lake Okeechobee), all are relatively large(>30 km(2)), very shallow (<4 m mean depth), and eutrophic. In all three lakes we found strong interactions among the sediments, water column, and human activities. Important processes affecting nutrient dynamics included nitrogen fixation, light limitation due to resuspended sediments, and intense grazing on algae by cultured fish. As a result of these complex interactions, simple empirical models developed to predict in-lake responses of total phosphorus and algal biomass to external nutrient loads must be used with caution. While published models may provide 'good' results, in terms of model output matching actual data, this may not be due to accurate representation of lake processes in the models. The variable nutrient dynamics that we observed among the three study lakes appears to be typical for shallow lake systems. This indicates that a greater reliance on lake-specific research may be required for effective management, and a lesser role of inter-lake generalization than is possible for deeper, dimictic lake systems. Furthermore, accurate predictions of management impacts in shallow eutrophic lakes may require the use of relatively complex deterministic modeling tools. (C) 2000 Elsevier Science Ltd. All rights reserved.

Stochastic resonance for modulated gain in a single-mode laser

Stochastic resonance (SR) induced by the signal modulation is investigated, by introducing the signal-modulated gain into a single-mode laser system. Using the linear approximation method, we detailedly calculate the signal-to-noise ratio (SNR) of a gain-noise model of the single-mode laser, taking the cross-correlation between the quantum noise and pump noise into account. We find that, SR appears in the dependence of the SNR on the intensities of the quantum and the pump noises when the correlation coefficient between both the noises is negative; moreover, when the cross-correlation between the two noises is strongly negative, SR exhibits a resonance and a suppression versus the gain coefficient, meanwhile, the single-peaked SR and multi-peaked SR occur in the behaviors of the SNR as functions of the loss coefficient and the deterministic steady-state intensity. (c) 2005 Elsevier B.V. All rights reserved.

一种可并行的消息认证码

提出并分析了一种确定的、可并行的消息认证码--DPMAC(deterministic parallelizable message authentication code).它基于分组长度为128-bit的分组密码来构造.使用一个密钥,可以处理任意长度的消息.在底层分组密码是伪随机置换的假设下,使用Game-Playing技术量化了攻击者成功伪造的概率,从而证明了其安全性.

一种可证明安全的消息认证码

消息认证码是保证消息完整性的重要工具,它广泛应用于各种安全系统中.随着可证明安全理论的逐渐成熟,具备可证明安全的消息认证码无疑成为人们的首选.本文基于XOR MAC和PMAC的构造方法,使用分组密码构造了一种确定性、可并行的消息认证码-DXOR MAC(Deterministic XOR MAC).在底层分组密码是伪随机置换的假设下,本文使用Game-Playing技术量化了攻击者成功伪造的概率,从而证明了其安全性.

Chaotic behavior of pulsating heat pipes

Chaotic behavior of closed loop pulsating heat pipes (PHPs) was studied. The PHPs were fabricated by capillary tubes with outer and inner diameters of 2.0 and 1.20 mm. FC-72 and deionized water were used as the working fluids. Experiments cover the following data ranges: number of turns of 4, 6, and 9, inclination angles from 5 degrees (near horizontal) to 90, (vertical), charge ratios from 50% to 80%, heating powers from 7.5 to 60.0 W. The nonlinear analysis is based on the recorded time series of temperatures on the evaporation, adiabatic, and condensation sections. The present study confirms that PHPs are deterministic chaotic systems. Autocorrelation functions (ACF) are decreased versus time, indicating prediction ability of the system is finite. Three typical attractor patterns are identified. Hurst exponents are very high, i.e., from 0.85 to 0.95, indicating very strong persistent properties of PHPs. Curves of correlation integral versus radius of hypersphere indicate two linear sections for water PHPs, corresponding to both high frequency, low amplitude, and low frequency, large amplitude oscillations. At small inclination angles near horizontal, correlation dimensions are not uniform at different turns of PHPs. The non-uniformity of correlation dimensions is significantly improved with increases in inclination angles. Effect of inclination angles on the chaotic parameters is complex for FC-72 PHPs, but it is certain that correlation dimensions and Kolmogorov entropies are increased with increases in inclination angles. The optimal charge ratios are about 60-70%, at which correlation dimensions and Kolmogorov entropies are high. The higher the heating power, the larger the correlation dimensions and Kolmogorov entropies are. For most runs, large correlation dimensions and Kolmogorov entropies correspond to small thermal resistances, i.e., better thermal performance, except for FC-72 PHPs at small inclination angles of theta < 15 degrees.

Optimization of multiple filamentation of femtosecond laser pulses in air using a pinhole

The robustness and prolongation of multiple filamentation (MF) for femtosecond laser propagation in air are investigated experimentally and numerically. It is shown that the number, pattern, propagation distance, and spatial stability of MF can be controlled by a variable-aperture on-axis pinhole. The random MF pattern can be optimized to a deterministic pattern. In our numerical simulations, we configured double filaments to principlly simulate the experimental MF interactions. It is experimentally and numerically demonstrated that the pinhole can reduce the modulational instability of MF and is favorable for a more stable MF evolution. (c) 2007 Optical Society of America.