Quantum Principles and Mathematical Computability

Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then outline a quantum mechanical “algorithm” for one of the insoluble problems of mathematics, the Hilbert's tenth and equivalently the Turing halting problem. The key element of this algorithm is the computability and measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values.     

Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

Abstract We prove that there are non-recursive r.e. sets A and C with A < _T C such that for every set . Both authors are supported by “863” and the National Science Foundation of China     

Feigenbaum Scenario Exhibited by Thin Plate Dynamics

The dimensionless partial differential equations governing thedynamics of a thin flexible isotropic plate with an external load arederived and investigated. The period doubling bifurcations, as well asthe chaotic dynamics, are detected and analyzed. The algorithms leadingto the reduction of the original equations to those of a difference setof ordinary differential and algebraic equations are proposed, comparedto other known methods, and then applied to the problem.Among others, it is shown that, in spite of the system complexity, theFeigenbaum scenario exhibited by one-dimensional maps also governs theroute to chaos in the continuous system under consideration.     

Langford系统Hopf分叉的线性反馈控制

分析Langford系统的Hopf分叉现象，并研究采用线性反馈控制方法控制该系统的Hopf分叉.从理论上推导出受控系统产生Hopf分叉的条件，给出了某些极限环的解析表达式，对该系统进行了分叉点的转移与极限环的稳定性控制.数值模拟说明本文采用的方法对Langford系统的Hopf分叉控制是有效的. 关键词： Langford系统 反馈控制 Hopf分叉 极限环     

谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌

研究了软弹簧Duffing振子在确定性谐和外力和有界随机噪声联合作用下，系统安全盆的侵蚀和混沌现象.推导出系统的随机Melnikov过程，根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值，然后用数值模拟方法计算了系统的安全盆分叉点.结果表明，由于随机扰动的影响，系统的安全盆分叉点发生了偏移，并且使得混沌容易发生. 关键词： Duffing振子 安全盆 分叉 混沌     

An ODE Model of the Motion of Pelagic Fish

A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett. 75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic, are discussed and simulation of the ODEs presented.     

旋转流动的低模分析及仿真研究

为了探讨Couette-Taylor流从层流到湍流过渡的方式以及流动发展到湍流之后混沌吸引子的某些特征等问题,采用低模分析方法研究了Couette-Taylor流的部分动力学行为及仿真问题,讨论了Couette-Taylor流三模态类Lorenz型方程组的动力学行为,包括定态的失稳、极限环的出现、分岔与混沌的演变和全局稳定性分析等。通过线性稳定性分析和数值模拟等方法给出了此三维模型分岔与混沌等动力学行为及其演化历程,并借此解释了Couette-Taylor流试验中观察到的部分涡流的演化过程.基于系统的分岔图、Lyapunov指数谱、功率谱、Poincaré(庞加莱)截面和返回映射等揭示了系统混沌行为的普适特征.     

Mdm2生成速率调控的p53-Mdm2振子的全局动力学和稳定性

肿瘤抑制蛋白p53的动力学在一定程度上可以决定DNA损伤后的细胞命运.p53的动力学行为与p53信号通路中p53-Mdm2振子模块密切相关.然而,p53的负调控子Mdm2的生成速率的增加使其在一些癌细胞中过表达.因此探讨Mdm2生成速率对p53动力学的影响有重要意义.同时,PDCD5作为p53的激活子也调控p53的表达.因此,本文针对PDCD5调控的p53-Mdm2振子模型,通过分岔分析获得了Mdm2生成速率所调控的p53的单稳态、振荡以及单稳态与振荡共存的动力学行为,且稳定性通过能量面进行了分析.此外,噪声强度对p53动力学的稳定性有重要的影响.因此,针对p53的振荡行为,探讨了噪声强度对势垒高度和周期的影响.本文所获得的结果对理解DNA损伤后的p53信号通路调控起到一定的指导作用.