Generalization of Response Number for Dynamic Plastic Response of Shells Subjected to impulsive Loading

A dimensionless number, termed as response number in Zhao [Archive of Applied Mechanics 68 (1998) 524], has been suggested for the dynamic plastic response of beams and plates made up of rigidly perfect plastic materials subjected to dynamic loading. Many theoretical and experimental results can be reformulated into new concise forms with the response number. The concept of a new dimensionless number, response number, termed as Rn(n), is generalized in Zhao [Forschung im Ingenieurwesen 65 (1999) 107] to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. The response number Rn(n) is generalized to the dynamic behaviour of shells of various shapes in the present paper.

Generalization of the JTZ model to open plane wakes

The JTZ model [C. Jung, T. T¶el and E. Ziemniak, Chaos 3, (1993) 555], as a theoretical model of a plane wake behind a circular cylinder in a narrow channel at a moderate Reynolds number, has previously been employed to analyze phenomena of chaotic scattering. It is ex- tended here to describe an open plane wake without the con¯ned nar- row channel by incorporating a double row of shedding vortices into the intermediate and far wake. The extended JTZ model is found in qualitative agreement with both direct numerical simulations and ex- perimental results in describing streamlines and vorticity contours. To further validate its applications to particle transport processes, the in- teraction between small spherical particles and vortices in an extended JTZ model °ow is studied. It is shown that the particle size has signif- icant in°uences on the features of particle trajectories, which have two characteristic patterns: one is rotating around the vortex centers and the other accumulating in the exterior of vortices. Numerical results based on the extended JTZ model are found in qualitative agreement with experimental ones in the normal range of particle sizes.

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Transient effect on ideally plastic stationary crack-tip fields

This paper analyses the transient effect on ideally plastic stationary crack-tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack-tip fields when the inertia forces are not negligible.

Transient effect on ideally plastic stationary crack-tip fields

This paper analyses the transient effect on ideally plastic stationary crack tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack tip fields when the inertial forces are not negligible.

A finite-element analysis of viscoelastically damped sandwich plates

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

Quantum superchemistry in an output coupler of coherent matter waves

We investigate the quantum superchemistry or Bose-enhanced atom-molecule conversions in a coherent output coupler of matter waves, as a simple generalization of the two-color photoassociation. The stimulated effects of molecular output step and atomic revivals are exhibited by steering the rf output couplings. The quantum noise-induced molecular damping occurs near a total conversion in a levitation trap. This suggests a feasible two-trap scheme to make a stable coherent molecular beam.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

Beam conditions for radiation generated by an electromagnetic J 0-correlated Schell-model source

Based on the 2 x 2 (electric field) cross-spectral density matrix, a model for an electromagnetic J(0)-correlated Schell-model beam is given that is a generalization of the scalar J(0)-correlated Schell-model beam. The conditions that the matrix for the source to generate an electromagnetic J(0)-correlated Schell-model beam are obtained. The condition for the source to generate a scalar J(0)-correlated Schell-model beam can be considered as a special case. (C) 2008 Optical Society of America

小波分析和人工神经网络在生态学研究中的应用

墨西哥帽子小波和Morlet小波在生态格局分析中的应用 本研究采用Monte Carlo方法，探讨了对小波分析的格局进行统计显著性检验的普遍方法。为了更好利用小波分析和了解两个常用小波--墨西哥帽子小波和Morlet小波在格局分析中的优缺点，用生态学研究中常见的4个模拟格局和东灵山辽东栎林的样带数据对这两个常用小波的特性进行了分析和比较。研究结果表明：墨西哥帽子小波能较好地分析样带中的斑块和间隙以及它们的位置信息，Morlet小波能较好地分析样带中尺度及其位置信息。不同的小波通常在尺度分析和斑块和间隙分析之间有平衡，所以最好的方法是结合两种小波的优点。小波分析在处理生态数据时，受所使用小波本身特性的制约。用墨西哥帽子小波进行格局分析时，小波能量谱的等值图上不同格局所对应的峰有可能相互重叠，当所分析的多尺度格局的规模差别不大时，所分析格局规模所对应的峰可能相互融合。这些小波能量谱的等值图上不同格局所对应峰的重叠和融合可能会导致格局分析量图上多个峰的相互融合和屏蔽。所以在使用小波分析做格局研究时，也应尽可能地结合小波能量谱和量图上的信息，以得到较全面和精确的格局分析信息。本研究的结论能为小波分析的应用提供指导。 应用二维小波分析对暖温带阔叶林辽东栎更新格局的研究 本研究介绍了一种二维网格空间数据分析方法一二维小波分析。该方法不仅能分析格局的等级结构，而且也能得到所分析结构的位置信息。小波系数等值图上不同格局规模的斑块和间隙可直接和不同尺度上的生态过程和生境条件相联系。小波方差从二维小波分析导出，小波方差可将四维的小波系数降至二维的小波方差函数，并量化所分析格局规模对整个格局的贡献。本研究用三个模拟格局分析了二维小波的特性及二维墨西哥帽子小波和Halo小波的特性。因为自身的特性，Halo小波比墨西哥帽子小波能提供更高的分辨率。本研究也将二维小波分析应用于暖温带阔叶林的辽东栎更新格局研究中，分析的结果表明：辽东栎的更新发生在辽东栎成树斑块和林窗斑块重叠区域。 用交互验证和独立验证来测试神人工经网络模拟水稻分檗动态的泛化能力 人工神经网络不是基于对所模拟过程的理解，而是依赖于对所分析数据的内部结构。所以人工神经网络通常被认为是经验模型而不能外推，而且在训练数据和验证数据的范围之外肯定不能精确地预测所模拟的过程。本研究通过对交互验证和独立验证神经网络模型性能的比较，测试了神经网络模型在预测水稻分檗动态方面的泛化能力。同时，也对几种提高神经网络泛化能力的技术进行了比较。研究结果表明：在训练数据的变量范围内，神经网络在预测水稻分檗动态方面具有泛化能力。较少的训练数据样本导致了对训练数据过度吻合的和不具泛化能力的神经网络。要能使神经网络在预测水稻分檗动态方面具有泛化能力，训练数据的样本量至少9倍于神经网络的权值数目。当神经网络有多个输入变量且训练数据不足以保证神经网络的泛化能力时，建议在训练之前，采用主成分分析、对应分析及类似技术压缩输入变量的个数。在压缩输入变量的个数之后，如果训练数据的样本量还不足以保证神经网络的泛化能力，就应采用提高神经网络泛化能力的技木，如：jittering和强制训练停止等，特别是神经网络与机理模型的复合模型。因为神经网络的泛化能力问题具有普遍性，所以我们的研究结论不只是适用于水稻分檗动态的预测，也适用于其它的农业和生态神经网络模型。

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.

Biomimetic pattern recognition theory and its applications

Biomimetic pattern recogntion (BPR), which is based on "cognition" instead of "classification", is much closer to the function of human being. The basis of BPR is the Principle of homology-continuity (PHC), which means the difference between two samples of the same class must be gradually changed. The aim of BPR is to find an optimal covering in the feature space, which emphasizes the "similarity" among homologous group members, rather than "division" in traditional pattern recognition. Some applications of BPR are surveyed, in which the results of BPR are much better than the results of Support Vector Machine. A novel neuron model, Hyper sausage neuron (HSN), is shown as a kind of covering units in BPR. The mathematical description of HSN is given and the 2-dimensional discriminant boundary of HSN is shown. In two special cases, in which samples are distributed in a line segment and a circle, both the HSN networks and RBF networks are used for covering. The results show that HSN networks act better than RBF networks in generalization, especially for small sample set, which are consonant with the results of the applications of BPR. And a brief explanation of the HSN networks' advantages in covering general distributed samples is also given.

Method for improving classification performance of neural network based on fuzzy input and network inversion

In order to effectively improve the classification performance of neural network, first architecture of fuzzy neural network with fuzzy input was proposed. Next a cost function of fuzzy outputs and non-fuzzy targets was defined. Then a learning algorithm from the cost function for adjusting weights was derived. And then the fuzzy neural network was inversed and fuzzified inversion algorithm was proposed. Finally, computer simulations on real-world pattern classification problems examine the effectives of the proposed approach. The experiment results show that the proposed approach has the merits of high learning efficiency, high classification accuracy and high generalization capability.