高维非线性动力系统最简规范形的计算

运用可逆线性变换和近恒同变换,研究了不经计算传统规范形,直接计算高维非线性动力系统的最简规范形。引进可逆线性变换,将非线性动力系统的线性矩阵拓扑等价于符合实际研究需求的分块对角线矩阵：相伴矩阵分布在对角线上,其余元素均为0。利用低阶项来化简高阶项,得到了高维非线性动力系统的最简规范形。在该最简规范形中,对应于每一个相伴矩阵的非线性系数矩阵,只有最后一行含有非0元素,其余各行元素均为0。借助Mathematica语言,编制了计算任意高维非线性动力系统的最简规范形的通用程序。运行该程序,分别计算了4维、6维和7维非线性动力系统的直到4阶的最简规范形。     

Towards the simplest hydrodynamic lattice-gas model

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.     

A dynamical model for the Utricularia trap

We propose a model that captures the dynamics of a carnivorous plant, Utricularia inflata. This plant possesses tiny traps for capturing small aquatic animals. Glands pump water out of the trap, yielding a negative pressure difference between the plant and its surroundings. The trap door is set into a meta-stable state and opens quickly as an extra pressure is generated by the displacement of a potential prey. As the door opens, the pressure difference sucks the animal into the trap. We write an ODE model that captures all the physics at play. We show that the dynamics of the plant is quite similar to neuronal dynamics and we analyse the effect of a white noise on the dynamics of the trap.     

Lattice dynamical calculations for the Ta-W alloys

Lattice dynamical calculations are performed on Ta-W alloys with bcc structure in various concentrations. We assume ion-ion interaction through the improved third-neighbor Clark-Gazis-Wallis (CGW) model. The theory has been applied to compute the dispersion curves, frequency spectra and lattice specific heat of the studied alloys. The obtained results are in good agreement with the available experimental ones.     

非共振双Hopf分叉系统最简规范形类的研究

主要在传统规范形的基础上,研究了非共振双Hop f分叉系统的最简规范形。通过对矩阵理论和近恒同变换的应用,详细分析了当n=3和5时,双Hop f分叉系统的最简规范形,得出当n≥5时,传统规范形可以进一步简化,得到系统的最简规范形。最后根据分析和计算的结果,在计算机语言M athem atica的帮助下,发现在非共振双Hop f分叉系统的n(n>5)阶最简规范形方程中,只存在一项k(5相似文献   

The simplest method for calculating energy output and Gurney velocity of explosives

Two correlations are introduced for calculating Gurney velocity as a useful parameter for thermochemical estimation of explosive energy output. For CaHbNcOd explosives, only the chemical composition of high explosive as well as its condensed or estimated gas phase heat of formation, which later is calculated by group additivity rules, is needed for calculating Gurney velocity. The introduced simple correlations in the present work may be applied to any explosive that contains the elements of carbon, hydrogen, nitrogen and oxygen with no difficulties at any loading density. There is no need to use any assumed decomposition reaction in present work. Gurney velocity are calculated for different pure and explosive formulations and compared with measured Gurney velocity at specified loading density. The results show that the agreement is good for present method as compared to previous correlations.     

Hitting times for random dynamical systems

The purpose of this article is to study the hitting times for random dynamical systems. For general systems we give a lower bound in terms of the local dimension. For fast mixing systems we obtain an equality. Moreover, under a power law decay of correlations we obtain lower and upper bounds of the hitting times for absolutely continuous stationary measures.     

Simple dynamical models for vortex breakdown of the B-type

Summary A simple, exact, locally convergent series solution of the Navier-Stokes and continuity equations for steady, incompressible, axisymmetric fluid flow is derived which exhibits the qualitative features of vortex breakdown of the bubble or B-type. This solution, which converges in a neighborhood of the axis of symmetry of the flow, is shown to produce vortex breakdown flows which are in good qualitative agreement with both experimentally and numerically observed B-type vortex breakdown phenomena.     

Stability conditions for non-conservative dynamical systems

The present paper treats dynamic instability problems of non-conservative elastic systems. Starting from general equations of motion, the equations of the perturbed motion are derived. The boundedness of the perturbed motions is studied and sufficient conditions for instability and a necessary condition for stability are deduced. These conditions may determine the instability of non-conservative systems and they are expressed in terms of the properties of generalized tangent damping and stiffness matrices of the systems. Thus, they can easily be incorporated with finite element computations of arbitrary structures.     

一类含参分叉系统最简规范形系数的计算

将参数视为状态变量,在不截断的情况下,研究了非共振含参双Hop f分叉系统的最简规范形。在采用非线性恒同变换时引入了变时间尺度函数及变参数尺度函数两个变换函数,借助于计算机代数语言M athem atica,推导出最一般情况下含一个参数的非共振双Hop f分叉系统的最简规范形的前五阶系数的表达式,并根据其中的规律推导出该系统高阶最简规范形的通式。     

Re-evaluating the process capability indices for non-normal distributions

Classical process capability indices (PCIs) C _p , C _pu , C _pl and C _pk can indicate the potential process capability accurately when the quality characteristic of the product is normally distributed. When the process has a non-normal distribution, classical PCIs will be inappropriate and can misled the assessment of process capability. Zwick (1995), Schneider and Pruett (1995-96) and Tong and Chen (1998) proposed various PCIs for non-normal distributions. This paper compares the accuracy of these indices for several selected non-normal distributions based on the proportion of non-conformity of manufactured product. The results indicate that these PCIs lead to a larger number of errors in various combinations of shape parameters and specification limits. Therefore, this paper proposes three indices, S _pu , S _pl and S _pk , which can reflect accurately the proportion of nonconformity in either normal or non-normal distributions.     

Likelihood-based inference for power distributions

This paper considers likelihood-based inference for the family of power distributions. Widely applicable results are presented which can be used to conduct inference for all three parameters of the general location-scale extension of the family. More specific results are given for the special case of the power normal model. The analysis of a large data set, formed from density measurements for a certain type of pollen, illustrates the application of the family and the results for likelihood-based inference. Throughout, comparisons are made with analogous results for the direct parametrisation of the skew-normal distribution.     

Study of the simplest statistical characteristics of a turbulent flow temperature distribution

The degeneracy of the temperature distribution in homogeneous nonisotropic turbulence is examined. The relations obtained are verified experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 6, pp. 1025–1034, June, 1976.     

Phase-space distributions for high-frequency fields

The Wigner distribution function and various windowed Fourier transforms are examples of phase-space distributions that are used, among other things, to formalize the link between ray and wave optics. It is well known that, in the limit of high frequencies, these distributions become localized for simple wave fields and therefore that the localization can be used to define the associated ray families. This localized form is characterized here for both the Wigner distribution function and a Gaussian windowed Fourier transform. Aside from the greater understanding of the distributions themselves, these results promise a clearer intuition of phase-space-based methods for optical modeling. In particular, regardless of the context, the geometric construction that is presented for estimating the Wigner distribution function gives a valuable appreciation of its highly structured and sometimes surprising form.     

On the determination of grain-size distributions from intercept distributions

A matrix formulation for determining the spatial grain-size distribution of tetrakaidecahedral grains from linear-intercept data is developed. The truncation effect (which stems from the fact that the intersection of single-size grains by a test line gives rise to intercepts of different length) and the sampling effect (which results as a consequence of bigger grains being intersected more frequently than smaller ones) are separately taken into account. The derivation procedure of this formulation is applicable to any other convex shape, provided the linear intercept distribution for single-size grains of the corresponding shape is known. The percentage spatial grain-size distributions obtained by the formulation derived here are similar to those estimated by the Spektor's chord method for spherical grains.     

On the spatial decay for the dynamical problem of thermo-microstretch elastic solids

This paper derives spatial decay bounds for a dynamical problem of thermo-microstretch elasticity defined on a semi-infinite cylindrical region. Previous results for isothermal elastodynamics and the parabolic heat equation lead us to suspect that the solution of the problem should tend to zero faster than a decaying exponential of the distance from the finite end of the cylinder. We prove that an energy expression is actually bounded above by a decaying exponential of a quadratic polynomial of the distance.     

Wedge simulation method for calculating the reliability of linear dynamical systems

In this paper the problem of calculating the probability of failure of linear dynamical systems subjected to random excitations is considered. The failure probability can be described as a union of failure events each of which is described by a linear limit state function. While the failure probability due to a union of non-interacting limit state functions can be evaluated without difficulty, the interaction among the limit state functions makes the calculation of the failure probability a difficult and challenging task. A novel robust reliability methodology, referred to as Wedge-Simulation-Method, is proposed to calculate the probability that the response of a linear system subjected to Gaussian random excitation exceeds specified target thresholds. A numerical example is given to demonstrate the efficiency of the proposed method which is found to be enormously more efficient than Monte Carlo Simulations.