介绍了离散元法的基本理论、计算方法及其应用的现状和最新进展.从离散元法的离散模型特点及便于甄别与其它数值计算方法的关系的角度给予离散元法一个比较宽松的定义.在此基础上阐明了离散元方法与刚体-弹簧模型(rigid body spring mod...介绍了离散元法的基本理论、计算方法及其应用的现状和最新进展.从离散元法的离散模型特点及便于甄别与其它数值计算方法的关系的角度给予离散元法一个比较宽松的定义.在此基础上阐明了离散元方法与刚体-弹簧模型(rigid body spring model,RBSM)方法,不连续变形分析(discontinuous deformation analysis,DDA)方法,分子动力学(molecular dynamics,MD)方法,三维离散元(discrete meso-element dynamic method,DM2)方法及无网格方法(meshless method)等数值计算方法的关系,并讨论了离散元法研究中亟待解决的问题和今后的发展方向.展开更多
A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.展开更多
文摘A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.
