Almost Sure Stability Analysis of Parametric Roll in Random Seas Based on Top Lyapunov Exponent

Stability analysis of the upright position of a ship in random head or following seas is presented. Such seas lead to parametric excitation of roll motion due to periodic variations of the righting lever. The development of simple criteria for the occurrence of parametric induced roll motion in random seas is of major interest for improvement of the international code on intact stability provided by the International Maritime Organization. The stability analysis in random seas is based on the calculation of the top Lyapunov exponent using the fact, that a negative top Lyapunov exponent yields no roll motion. With this findings, roll motion can be excluded for specific sea states. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Surf-Riding Threshold of Ships in Random Seas

A possible stability failure in ship dynamics is surf-riding of the ship in waves followed by broaching-to. In order to exclude broaching one thus seeks to prevent the ship from surf-riding. We analyze the surf-riding problem of a ship in random seas as a weakly perturbed Hamiltonian system, where the excitation owing to irregular sea waves is modeled as a Gaussian process. Then, an approximation of the probability of surf-riding in irregular sea waves is obtained using the stochastic Melnikov's method, by which means transitions from the asymmetric periodic surging motion to the surf-riding equilibrium are identified. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotics of Damped Periodic Motions with Random Initial Speed

We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form αU + β, where U is a fixed random variable and α and/or β tend to infinity.     

Polynomial Chaos and the Heave Motion of a Cylinder in Random Seas

The stochastic equation of motion for a heaving cylinder subject to irregular sea waves is solved numerically with the polynomial chaos framework. Thereby, the stochastic forcing is expressed by a truncated Karhunen-Loève expansion and the hydrodynamic radiation is formulated as a state space model. We obtain the mean and the variance of the cylinder heave motion. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

晶体微观结构的数值计算

晶体微观结构是晶体材料在特定物理条件下其多个能量极小平衔态在空间形成的某种微尺度的规则分布．几何非线性的连续介质力学理论可以用能量极小化原理来解释晶体微观结构的形成，并用Young测度来刻画平衡态各变体在空间的概率分布．定性的理解与定量地分析和计算晶体材料的微观结构对于发展和改进高级晶体功能材料，如形状记忆合金、铁电体、磁至伸缩材料等，有重要的意义．本文回顾了近年来晶体微观结构数值计算方面的最新进展．介绍了计算晶体微观结构的几种数值方法及有关的数值分析结果。     

Numerical Computation of Galois Groups

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. We give numerical methods to compute the Galois group and study it when it is not the full symmetric group. One algorithm computes generators, while the other studies its structure as a permutation group. We illustrate these algorithms with examples using a Macaulay2 package we are developing that relies upon Bertini to perform monodromy computations.     

Reliable Numerical Computation in Civil Engineering

Civil engineering is a field – as are many other engineering sciences – where most of the methods used for solving optimization problems are based on experience and experiments, and models using local information, but drawn from global models. The present work outlines an interesting class of problems from this field, and initiates some possible ways to solve those problems utilizing the wide tool capabilities of interval arithmetic for error handling and interval branch-and-bound algorithms to solve the original or modified industrial models automating civil engineers' work. The investigations are in the first state but are promising both in a theoretical and in a practical sense.     

Mathematica数学软件的浮点数值精度问题

本文讨论了 Mathematica软件中的浮点计算精度问题 ,阐明了常量＄ Machine Epsilon的来历 ,有助于正确使用 Mathematica进行科学计算 .     

随机1-集压缩算子的随机不动点指数计算及其应用

利用锥理论给出了随机1-集压缩算子的随机不动点指数的一些计算方法.最后,把抽象结果应用于研究随机Hammerstein型积分方程多重正随机解的存在性.     

考虑空间效应的多支撑管线随机地震响应分析

提出了一种能考虑地震动空间变化效应的多支撑管线随机地震响应分析的解析方法.证明了多点地震作用下结构的平稳随机响应分析可转化为求解支座简谐运动时的确定性响应,直接给出了含有待定系数的简谐响应的形式,并通过边界条件和连续性条件建立待定系数的求解方程.与拟静位移分解法相比,该方法不用计算结构的振型以及拟静位移分量,完全是基于解析推导,因此在计算效率方面优势明显.数值算例中,采用该方法和拟静位移分解法计算了一个6跨管线在空间多点地震作用下的随机响应,对比验证了方法的正确性和高效性.     

Computation of the Expected Volume of a Random Manifold

In this note, we generalize the Kac integral formula for the expected number of real zeros of a random polynomial to the case of systems of equations. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 133–146.     

Numerical Computation of Multivariate Normal Probabilities

Abstract

The numerical computation of a multivariate normal probability is often a difficult problem. This article describes a transformation that simplifies the problem and places it into a form that allows efficient calculation using standard numerical multiple integration algorithms. Test results are presented that compare implementations of two algorithms that use the transformation with currently available software.     

Distribution Functions of Poisson Random Integrals: Analysis and Computation

We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral I(g) = ò₀^T g(s) N(ds)I(g) = displaystyle int_0^T g(s) N(ds), where N is a Poisson random measure with control measure n and g is a suitable kernel function. We do so by combining a Kolmogorov–Feller equation with a finite-difference scheme. We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples. The software used to implement the procedure is available on demand and we demonstrate its use in the paper.     

The Numerical Computation of Connecting Orbits in Dynamical Systems

Structural changes in dynamical systems are often related tothe appearance or disappearance of orbits connecting two stationarypoints (either heteroclinic or homoclinic). Homoclinic orbitstypically arise in one-parameter problems when on a branch ofperiodic solutions the periods tend to infinity (e.g. Guckenheimer& Holmes, 1983). We develop a direct numerical method forthe computation of connecting orbits and their associated parametervalues. We employ a general phase condition and truncate theboundary-value problem to a finite interval by using on bothends the technique of asymptotic boundary conditions; see, forexample, de Hoog & Weiss (1980), Lentini & Keller (1980).The approximation error caused by this truncation is shown todecay exponentially. Based on this analysis and additional numericalinvestigations we set up an adaptive strategy for choosing thetruncation interval.     

Numerical Computation of Connecting Orbits in Delay Differential Equations

We discuss the numerical computation of homoclinic and heteroclinic orbits in delay differential equations. Such connecting orbits are approximated using projection boundary conditions, which involve the stable and unstable manifolds of a steady state solution. The stable manifold of a steady state solution of a delay differential equation (DDE) is infinite-dimensional, a problem which we circumvent by reformulating the end conditions using a special bilinear form. The resulting boundary value problem is solved using a collocation method. We demonstrate results, showing homoclinic orbits in a model for neural activity and travelling wave solutions to the delayed Hodgkin–Huxley equation. Our numerical tests indicate convergence behaviour that corresponds to known theoretical results for ODEs and periodic boundary value problems for DDEs.     

随机窄带噪声作用下非线性碰撞振动系统的稳态响应研究

研究了随机参激作用下一个非线性碰撞振动系统的随机响应.基于Krylov-Bogoliubov平均法,借助第一类改进的Bessel函数,得到了决定平凡解的几乎确定稳定性的最大Lyapunov指数.模拟结果发现,碰撞振动系统的最大Lyapunov指数特性不同于一般的非碰撞系统,其最小值为负.同时,在确定性情形下,得到了骨架曲线方程和不稳定区域的临界方程.进一步,利用矩方法,讨论了系统的一阶和二阶非平凡稳态矩,发现了碰撞振动系统中有频率岛现象的存在.最后,借助FokkerPlanck-Kolmogorov方程,利用有限差分法,讨论了碰撞振动系统中存在的随机跳现象.在随机强度较小时,稳态概率密度集中于响应振幅的非平凡分支;但是随着随机强度的增加,平凡稳态解的概率会变大.     

Bayesian Inference of a Parametric Random Spheroid from its Orthogonal Projections

Methodology and Computing in Applied Probability - The paper focuses on a new method for the inference of a parametric random spheroid from the observations of its 2D orthogonal projections. Such a...     

多维连续型随机变量函数的分布密度的计算法

本文推证了采用曲线积分法求多维随机变量的函数的分布密度的计算公式,既具有解决问题的一般性,又具有良好的实用性,较之其他方法易于记忆、掌握和应用,以典型例子说明问题。     

A Random Numerical Method with Application in Combustion

This paper presents a random numerical method which combines the random vortex method and the random choice method. A random choice method is used for the modeling reaction-diffusion system. The splitting of source terms in two dimensions for the random choice method is tested. A hybrid random vortex method is used for solving the Navier-Stokes equation which governs the fluid motion. With the assumption of incompressibility, the fluid motion can be uncoupled from the chemistry. The method is applied to a flow passing a circular cylinder which is kept cold or heated. In both cases the method demonstrates an ability to resolve turbulent effects on flame front propagation.