固体介质中弹性波传播机制的细胞自动机有限深势阱模型

CA's Finite Deep Potential Trough Model of the Elastic Wave Propagational Mechanism in Solid Medium

分析了采用细胞自动机研究波动问题的建模方法 ,针对一维、均匀、各向同性固体介质中弹性纵波的微观机制 ,借用了经典弹簧振子模型、细胞自动机格子气模型 ,以及量子力学中的无限深势阱模型 ,建立了一个细胞自动机有限深势阱模型 .从量子力学角度出发 ,基于介观物理和纳米概念 ,以微观粒子的德布罗意假设为基础 ,利用薛定谔方程 ,讨论了该模型中粒子 (分子组 )的振动速度与粒子物质波波速之间的联系 ,给出了模型中的波动方程 ,得出 ζ =Vp(ζ为粒子振动速度 ,Vp 为物质波纵波波速 ) .同时还讨论了模型中粒子的大小和能量传递问题 ,引入引力场 ,得出了能量及引力势的量子化条件 .另外 ,对声波速度、格子气粒子振动速度和本文模型中分子组振动速度进行了比较 ;还对本文模型中的粒子能量分布作了分析 .

Some building methods of studying fluctuated questions was analyzed by means of CA. Then, it works over the micromechanism of the elastic P-wave propagation in solid medium that is one-dimensional, homogeneous and isotropic. In this study, it cites classic spring vibrator model, CA's Lattice Gas model and infinite deep potential trough model in the quantum mechanics. A CA's finite deep potential trough is brought forward. In this paper, being based on the de Broglie wave hypothesis, mesoscope physics, nano-concept and utilizing the Schrodinger equation, the new model starts from the angle of the quantum mechanics, then discusses the relation between the vibratory velocity and the physical wave velocity of particles (the molecular group). It comes to the wave equation and the relation (represents the particle vibratory velocity and stands for the physical wave velocity). Meanwhile after introducing the gravitational field, the thesis discusses the size and the energy transmission problem of particles, and then gets the quantized condition of the energy and the gravitational potential. Moreover, comparing the new model with the acoustic wave and the Lattice Gas, it analyzes the velocities among them. In addition, it dissects the energy of the molecular group. Finally, the prospects are looked forward to in this field.