论文标题
非线性分析的一般潜力和数学原理
Generalized Potential and Mathematical Principles of Nonlinear Analysis
论文作者
论文摘要
在过去的百年中,混乱一直是人类的谜,包括1963年发现的蝴蝶效应以及1977年获得化学诺贝尔奖的耗散结构理论。到目前为止,尚无定量的数学物理方法来解决和分析这些问题。在本文中,提出了使用现场理论来研究非线性系统的想法,并从数学上确定了广义电位的概念。广义潜力的物理本质促进了非线性场的发展,并阐明了广义电位的时空进化定律。然后阐明了保守系统和纯耗散系统的时空进化定律。建立了加速场,保守矢量场和耗散矢量场,以评估物理场的保护程度和耗散程度。最后,讨论了新的现场研究的开发路线和将来促进工程应用程序的前提。
In the past hundred years, chaos has always been a mystery to human beings, including the butterfly effect discovered in 1963 and the dissipative structure theory which won the chemistry Nobel Prize in 1977. So far, there is no quantitative mathematical-physical method to solve and analyze these problems. In this paper, the idea of using field theory to study nonlinear systems is put forward, and the concept of generalized potential is established mathematically. The physical essence of generalized potential promoting the development of nonlinear field is extended and the spatiotemporal evolution law of generalized potential is clarified. Then the spatiotemporal evolution law of conservative system and pure dissipative system is clarified. Acceleration field, conservative vector field and dissipation vector field are established to evaluate the degree of conservation and dissipation of physical field. Finally, the development route of new field research and the precondition of promoting engineering application in the future are discussed.