State space approach to magnetohydrodynamic flow of perfectly conducting micropolar fluid with stretch

In this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley & Sons, Ltd.     

从机械能守恒的角度推导单摆简谐振动的周期

本文给出了利用基本的物理原理结合高等数学公式的方法推导单摆做简谐运动的周期公式,可以简明扼要地理解单摆简谐运动的过程.     

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

A two-dimensional (2D) numerical model is developed for the wave simulation and propagation in a wave flume.The fluid flow is assumed to be viscous and incompressible,and the Navier-Stokes and continui...     

Hypercomplex analysis and integration of systems of ordinary differential equations

We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of hypercomplexification, which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati‐type systems, we obtain invariants of Abel‐type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd.     

On asymptotic elastodynamic homogenization approaches for periodic media

A fairly large family of asymptotic elastodynamic homogenization methods is shown to be derivable from Willis exact elastodynamic homogenization theory for periodic media under appropriate approximation assumptions about, for example, frequencies, wavelengths and phase contrast. In light of this result, two long-wavelength and low-frequency asymptotic elastodynamic approaches are carefully analyzed and compared in connection with higher-order strain-gradient media. In particular, these approaches are proved to be unable to capture, at least in the one-dimensional setting, the optical branches of the dispersion curve. As an example, a two-phase string is thoroughly studied so as to illustrate the main results of the present work.     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

n阶不等距常系数线性差分方程的解

利用Mikusinski的算符演算理论和移动算符的幂级数表示,给出了n阶不等距常系数线性差分方程的解法.     

The string of variable density: Perturbative and non-perturbative results

We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very accurate approximations which are compared both with the results of WKB method and with the numerical results obtained with a collocation approach. Finally, we show that the asymptotic behaviour of the energies of the string obtained with perturbation theory, worked to second order in the inhomogeneities, agrees with that obtained with the WKB method and implies a different functional dependence on the density that in two and higher dimensions.     

The identification of the vibration control system parameters designed for continuous miner machines

The Continuous Miner machines are exposed to time dependent loads during normal operation of the rock cutting process. These loads cause vibrations, which have a negative influence on the whole structure of the machine. This phenomenon can be eliminated by applying passive or active vibration control systems (VCS). Generally these systems are coupled with additional elements, which provide dispersion or transfer energy. The energy thus acquired can also reinforce the intended function such as rock cutting operation in the case of mining machines. The objective of this paper is to present the method of numerical identification of VCS parameters for Continuous Miner machines. The main function of the presented system is to reduce displacement of cutting drum by using elastic element joined to machine chassis and applying appropriate algorithm of control of the angular velocity of cutting drum. The method described improves efficiency of mining and increases durability of machine. In order to determine mechanical and control parameters of VCS the genetic algorithm optimisation method conjugated with numerical modal analysis was used. Finally the transient dynamic analysis was performed for the full-scale model of Continuous Miner in order to verify VCS in normal working condition.     

Interlaced solitons and vortices in coupled DNLS lattices

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.