DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME (Ⅳ)

ＩｎｔｒｏｄｕｃｔｉｏｎＬａｇｒａｎｇｉａｎｍｅｃｈａｎｉｃｓｉｓａｎｉｍｐｏｒｔａｎｔｐａｒｔｏｆａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ.ＩｔｉｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆＮｅｗｔｏｎｉａｎｍｅｃｈａｎｉｃｓ.Ｎｅｗｔｏｎｉａｎｍｅｃｈａｎｉｃｓｉｓｅｓｔａｂｌｉｓｈｅｄｏｎｔｈｅｃｏｎｆｉｇｕｒａｔｉｏｎｓｐａｃｅ—Ｒｉｅｍａｎｎｉａｎｍａｎｉｆｏｌｄ .Ｌａｇｒａｎｇｉａｎｍｅｃｈａｎｉｃｓｉｓｅｓｔａｂｌｉｓｈｅｄｏｎｉｔｓｔａｎｇｅｎｔｂｕｎｄｌｅ ,Ｈａｍｉｌｔｏｎｉａｎｍｅｃｈａ…     

INSTRUCTIONS TO AUTHORS

1 .ＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ (ＡＭＭ )ｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍｅｃｈａｎｉｃａｌａｎｄｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｍｅｃｈａｎｉｃｓａｎｄｍａｔｈｅｍａｔｉｃａｌｍｅｔｈｏｄｓｉｎｍｅｃｈａｎｉｃｓａｓｗｅｌｌａｓａｐｐｌｉｅｄｍａｔｈｅｍａｔｉｃｓｒｅｌｅｖａｎｔｔｏｎｅｏｔｅｒｉｃｍｅｃｈａｎｉｃｓ.2 .ＡＭＭｐｕｂｌｉｓｈｅｓｏｎｅｖｏｌｕｍｅａｎｎｕａｌｌｙｃｏｎｓｉｓｔｉｎｇｏｆ 1 2ｉ…     

INSTRUCTIONS TO AUTHORS

1 .ＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ (ＡＭＭ )ｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍｅｃｈａｎｉｃａｌａｎｄｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｍｅｃｈａｎｉｃｓａｎｄｍａｔｈｅｍａｔｉｃａｌｍｅｔｈｏｄｓｉｎｍｅｃｈａｎｉｃｓａｓｗｅｌｌａｓａｐｐｌｉｅｄｍａｔｈｅｍａｔｉｃｓｒｅｌｅｖａｎｔｔｏｎｅｏｔｅｒｉｃｍｅｃｈａｎｉｃｓ.2 .ＡＭＭｐｕｂｌｉｓｈｅｓｏｎｅｖｏｌｕｍｅａｎｎｕａｌｌｙｃｏｎｓｉｓｔｉｎｇｏｆ 1 2ｉ…     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME (Ⅲ)

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｄｉｓｃｕｓｓｎｏｎ＿ｓｔａｔｉｏｎａｒｙＨａｍｉｌｔｏｎｉａｎｍｅｃｈａｎｉｃｓ .Ｈａｍｉｌｔｏｎｉａｎｍｅｃｈａｎｉｃｓｉｓａｎｉｍｐｏｒｔａｎｔｐａｒｔｙｏｆａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ[1].ＴｈｅｓｔａｔｉｏｎａｒｙＨａｍｉｌｔｏｎｉａｎｍｅｃｈａｎｉｃｓｉｓｅｓｔａｂｌｉｓｈｅｄｏｎｔｈｅｃｏｔａｎｇｅｎｔｂｕｎｄｌｅｏｆｔｈｅｃｏｎｆｉｇｕｒａｔｉｏｎｓｐａｃｅ—Ｒｉｅｍａｎｎｉａｎｍａｎｉｆｏｌｄｏｆｍｏｔｉｏｎａｌｓｙｓ…     

THE LIE SYMMETRIES AND CONSERVED QUANTITIES OF VARIABLE-MASS NONHOLONOMIC SYSTEM OF NON-CHETAEV''''S TYPE IN PHASE SPACE

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｓｙｍｍｅｔｒｙａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｉｓａｎｉｍｐｏｒｔａｎｔｔｏｐｉｃｉｎｍａｔｈｅｍａｔｉｃｓ,ｍｅｃｈａｎｉｃｓａｎｄｐｈｙｓｉｃｓ .ＴｈｅｍｏｄｅｒｎｔｈｅｏｒｉｅｓｏｆｓｙｍｍｅｔｒｙａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｉｎｃｌｕｄｅＮｏｅｔｈｅｒｓｙｍｍｅｔｒｙｔｈｅｏｒｙａｎｄＬｉｅｓｙｍｍｅｔｒｙｔｈｅｏｒｙ .Ｉｎ 1979Ｍ .Ｌｕｔｚｋｙａｎｄｏ…     

The conservation law of second-order non-holonomic system of non-chetaev' s type

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｎｏｔｏｎｌｙｈａｓｉｍｐｏｒｔａｎｃｅｉｎｍａｔｈｅｍａｔｉｃｓｂｕｔａｌｓｏｒｅｖｅａｌｓｐｒｏｆｏｕｎｄｐｈｙｓｉｃａｌｌａｗ .Ｔｈｅｒｅａｒｅｍａｎｙｍｅｔｈｏｄｓｉｎｆｉｎｄｉｎｇｃｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆａｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍ .Ｉｎａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓｔｈｅｔｒａｄｉｔｉｏｎａｌｍｅｔｈｏｄｉｓｔｏｄｉｒｅｃｔｌｙｄｅｒｉｖｅｔｈｅｃｉｒｃｕｌａｒｉｎｔｅｇ…     

A FORM INVARIANCE OF CONSTRAINED BIRKHOFFIAN SYSTEM

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｔｈｅｄｙｎａｍｉｃｓｏｆＢｉｒｋｈｏｆｆｉａｎｓｙｓｔｅｍｉｓａｎａｃｔｉｖｅｂｒａｎｃｈｉｎｔｈｅｍｏｄｅｒｎｃｌａｓｓｉｃａｌｍａｔｈｅｍａｔｉｃｓａｎｄａｍｏｄｅｒｎｄｅｖｅｌｏｐｉｎｇｄｉｒｅｃｔｉｏｎｉｎｍａｔｈｅｍａｔｉｃｐｈｙｓｉｃｓ ,ａｎｄｃａｎｂｅａｐｐｌｉｅｄｔｏｑｕａｎｔｕｍｍｅｃｈａｎｉｃｓ,ｓｔａｔｉｓｔｉｃａｌｍｅｃｈａｎｉｃｓ ,ｂｉｏｌｏｇｉｃｐｈｙｓｉｃｓ,ｍｅｃｈａｎｉｃｓｏｆｓｐａｃｅｆｌｉｇｈｔａｎｄｓｏｍｅｆｉｅ…     

Analysis of a Partially Debonded Conducting Rigid Elliptical Inclusion in a Piezoelectric Matrix

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｅｔｏｔｈｅｉｒｉｎｔｒｉｎｓｉｃｅｌｅｃｔｒｏｍｅｃｈａｎｉｃａｌｃｏｕｐｌｉｎｇｐｒｏｐｅｒｔｉｅｓ,ｐｉｅｚｏｅｌｅｃｔｒｉｃｃｅｒａｍｉｃｓｈａｖｅｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｕｓｅｄｉｎｄｅｓｉｇｎｏｆｖａｒｉｏｕｓｅｌｅｃｔｒｏｎｉｃａｎｄｅｌｅｃｔｒｏｍｅｃｈａｎｉｃａｌｄｅｖｉｃｅｓｓｕｃｈａｓｓｅｎｓｏｒｓａｎｄａｃｔｕａｔｏｒｓ.Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｍｅｃｈａｎｉｃａｌａｎａｌｙｓｉｓｏｆｄｉｓｌｏｃａｔｉｏｎｓ ,ｃｒａｃｋｓ,ｃａｖｉｔｉｅ…     

Pseudo-division algorithm for matrix multivariable polynomial and its application

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｏｂｌｅｍｏｆｇｉｖｅｎｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎａｎｄｓｅｅｋｉｎｇｉｔｓｅｑｕｉｖａｌｅｎｔＨａｍｉｌｔｏｎｉａｎｉａｎｓｙｓｔｅｍｂｅｌｏｎｇｓｔｏｉｎｖｅｒｓｅｐｒｏｂｌｅｍｏｆａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ,ａｎｄｔｈｅｌａｔｔｅｒｉｓｏｎｅｏｆｐｒｉｍｅｐｒｏｂｌｅｍｓｉｎｃｌａｓｓｉｃａｌｍｅｃｈａｎｉｃｓ.ＴｈｅｆａｍｏｕｓＰｏｉｎｃａｒｅ＿ＣａｒｔｏｎｐｒｏｂｌｅｍｉｓｔｏｇｅｔｔｈｅＨａｍｉｌｔｏｎｉａｎｉａｎｒｅｇｕｌａ…     

Generalized diagonalization of matrices over quaternion field

Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ａｐｐｌｉｃａｔｉｏｎｓｏｆｑｕａｔｅｒｎｉｏｎｍａｔｒｉｃｅｓａｒｅｂｅｃｏｍｉｎｇｍｏｒｅａｎｄｍｏｒｅｉｍｐｏｒｔａｎｔａｎｄｅｘｔｅｎｓｉｖｅｉｎｒｉｇｉｄｍｅｃｈａｎｉｃｓ,ｑｕａｎｔｕｍｍｅｃｈａｎｉｃｓ,ｃｏｎｔｒｏｌｔｈｅｏｒｙａｎｄｈｅｌｉｃａｌｔｅｃｈｎｏｌｏｇｙ［１～３］．Ｗｉｔｈｔｈｅｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅａｂｏｖｅｄｉｓｃｉｐｌｉｎｅｓ,ｉｔｉｓｇｅｔｔｉｎｇｍｏｒｅａｎｄｍｏｒｅｎｅｃｅｓｓａｒｙｆｏｒｕｓｔｏｆｕｒｔｈ…     

二层流体中波动问题的Hamilton正则方程

研究了两种常密度不可压缩理想流体组成的垂直分层的二流体系统的无旋等熵流动,考虑了上层流体与空气及两层流体间的表面张力。流动区域在水平方向无限伸展,上层流体有限深度,下层流体无限深。利用自由面及分界面相对于静止时平衡位置的偏移以及两层流体的速度势构造了Hamilton函数。为导出Hamilton正则方程引用了Euler描述下的流体运动的变分原理。自由面的位移是Hamilton意义下的正则变量,其对偶变量是上层流体在自由面上取值的速度势与密度的乘积。另一个正则变量是分界面的位移,其对偶变量是下层流体的密度与下层流体速度势在分界面上所取值的乘积减去上层流体密度与上层流体速度势在分界面上所取值的相应乘积。导出的Hamilton结构对分析分层流动中表面波与内波的相互作用是重要的。     

非平整运动海底上n层流动中波浪传播的Hamilton逼近

在海洋水域，界面波对大尺度变化流的作用是一种典型的分层流动现象．考虑一不可压缩、无黏的分层势流运动，建立了一个在非平整运动海底上的n层流体演化系统，并对其进行了Hamilton描述．每层流体具有各自的常密度、均匀流水平速度，其厚度由未扰动和扰动部分构成．相对于顶层流体的自由表面，刚性、运动的海底具有一般地形变化特征．在明确指出n层流体运动的控制方程和各层交界面上的运动学、动力学边界条件(包含各层交界面上张力效应)后，对该分层流动力系统进行了Hamilton构造，即给出其正则方程和其下述的正则变量：各交界面位移和各交界面上的动量势密度差。     

有限深水中骑行波的显式Hamilton描述

小尺度波（扰动波）迭加在大尺度波（未受扰动波）上形成的波动一般之为“骑行波”。研究了有限可变深度的理想不可压缩流体中的骑行波的显式Hamliltn表示，考虑了自由面上流体与空气之间的表面张力。采用自由面高度和自由面上速度势构成的Hamilton正则变量表示骑行波的动能密度，并在未受扰动波的自由面上作一阶展开。运用复变函数论方法处理了二维流动。先用保角变换将物理平面上的流动区域变换到复势平面上的无限长带形区域，然后在复势平面上用Fourier变换解出Laplace方程，最后经Fourier逆变换求出了扰动波速度热所满足的积分方程。作为特例考虑了平坦底部的流动，导出了动能密度的显式表达式。这里给出的积分方程可以替代相当难解的Hamilton正则方程。通过求解积分方程可得出agrange密度的显式表达式。本文提出的方法约研究骑行波的Hamilton描述以及波的相互作用问题提供了新的途径，有助于了解海面的小尺度波的精细结构。     

A meshless method for numerical simulation of depth‐averaged turbulence flows using a k‐ϵ model

A three‐dimensional numerical model is developed to analyze free surface flows and water impact problems. The flow of an incompressible viscous fluid is solved using the unsteady Navier–Stokes equations. Pseudo‐time derivatives are introduced into the equations to improve computational efficiency. The interface between the two phases is tracked using a volume‐of‐fluid interface tracking algorithm developed in a generalized curvilinear coordinate system. The accuracy of the volume‐of‐fluid method is first evaluated by the multiple numerical benchmark tests, including two‐dimensional and three‐dimensional deformation cases on curvilinear grids. The performance and capability of the numerical model for water impact problems are demonstrated by simulations of water entries of the free‐falling hemisphere and cone, based on comparisons of water impact loadings, velocities, and penetrations of the body with experimental data. For further validation, computations of the dam‐break flows are presented, based on an analysis of the wave front propagation, water level, and the dynamic pressure impact of the waves on the downstream walls, on a specific container, and on a tall structure. Extensive comparisons between the obtained solutions, the experimental data, and the results of other numerical simulations in the literature are presented and show a good agreement. Copyright © 2015 John Wiley & Sons, Ltd.     

Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid

The scattering of water waves by a flexible porous membrane barrier in a two-layer fluid having a free surface is analysed in two dimensions. The membrane barrier is extended over the entire water depth in a two-layer fluid, each fluid being of finite depth. In the present analysis, linear wave theory and small amplitude membrane response are assumed. The porous membrane barrier is tensioned and pinned at both the free surface and the seabed. The associated mixed boundary value problem is reduced to a linear system of equations by utilizing a general orthogonality relation along with least-squares approximation method. Because of the flow discontinuity at the interface, the eigenfunctions involved have a discontinuity at the interface and the orthogonality relation used is a generalization of the classical one corresponding to a single-layer fluid. The reflection and transmission coefficients for the surface and internal modes, the free surface and interface elevations and the nondimensional membrane deflection are computed for various physical parameters like the nondimensional tension parameter, porous-effect parameter, fluid density ratio, ratio of water depths of the two fluids to analyse the efficiency of a porous membrane as a wave barrier in the two-layer fluid.     

Forced capillary-gravity wave motion of two-layer fluid in three-dimensions

A class of problems associated with forced capillary-gravity wave motion in a channel are analyzed in the presence of surface and interfacial tensions in a two-layer fluid in both the cases of finite and infinite water depths. The two and three-dimensional Green functions associated with the capillary-gravity wave problems in the presence of surface and interfacial tensions are derived using the fundamental source potentials. Using the two-dimensional Green function along with Green’s second identity, the expansion formulae for the velocity potentials associated with the capillary-gravity wavemaker problems in two-dimensions are obtained. The two-dimensional results are generalized to derive the expansion formulae for the velocity potentials associated with the forced capillary-gravity wave motion in the presence of surface and interfacial tensions in three-dimensions. Certain characteristics of the eigen-system associated with the expansion formulae are derived. The velocity potentials associated with the free oscillation of capillary-gravity waves in a closed basin and semi-infinite open channel in the presence of surface and interfacial tensions are obtained. The utility of the forced motion in a channel is demonstrated by analyzing the capillary-gravity wave reflection by a wall in a channel in the presence of surface and interfacial tensions. Long wave equations associated with capillary-gravity wave motion in the presence of surface and interfacial tensions are derived under shallow water approximation and the associated dispersion relation are obtained. Various expansion formulae and Green functions derived in the present study will be useful for analyzing a large class of physical problems in ocean engineering and mathematical physics.     

Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape

We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.      

Hamiltonian Formulation for the Motion of a Two-Fluid System with Free Surface

In this work, a theoretical investigation is performed on modeling interfacial and surface waves in a layered fluid system. The physical system consists of two immiscible liquid layers of different densities ₁ > ₂ with an interfacial surface and a free surface, inside a prismatic-section tank. On the basis of the potential formulation of the fluid motion, we derive a nonlinear system of partial differential equations using the Hamiltonian formulation for irrotational flow of the two fluids of different density subject to conservative force. As a consequence of the assumption of potential velocity, the dynamics of the system can be described in terms of variables evaluated only at the boundary of the fluid system, namely the separation surface and the free surface. This Hamiltonian formulation enables one to define the evolution equations of the system in a canonical form by using the functional derivatives.     

Analytical solutions of singularities moving with an arbitrary path when two fluids are present

The derivations are carried out for the velocity potentials of singularities moving withan arbitrary path either in the upper fluid or in the lower fluid with or without a horizontalbottom when two fluids are present.In such a case,the pressure distribution is no longerequal to a constant or zero at the free interface.Taking the influence of an upper fluid uponthe lower fluid into consideration,a series of fundamental solutions in closed forms arepresented in this paper.