YAN Kun. Brief annotation of the connection equation[Report]. Xi’an Modern Nonlinear Science Applying Institute, 18 March 2011


阎坤. 关于连接方程的简略注释[研究报告]. 西安:西安现代非线性科学应用研究所,2011-03-18.
YAN Kun. Brief annotation of the connection equation[Research report]. Xi’an: Xi’an Modern Nonlinear Science Applying Institute, 18 March 2011.

 

关于连接方程的简略注释

阎 坤
(西安现代非线性科学应用研究所  西安 710061)

摘   要:本文给出了连接方程的构造过程及其若干应用的简略注释,讨论了连接方程是一非线性动力学方程的近似等效解析解的分析方法,探讨了自然现象演化过程的规律谱系(或谱阵)及连接纽带大略—简学或维学研究方向,提出了现象在演化过程的状态转变方程,其在一般情况下遵循最优或最简洁路径光滑曲线方程形式这一自然最优原则或自然简洁原则,给出了前偏对称(欠对称或弱对称)方程及后偏对称方程的简洁构造形式,构建了数据曲线或部分连续函数的一种扩展型双曲正切级数近似表示形式,继而提出了自然演化平衡法则,给出了生物生长曲线趋势性方程;依据连接方程的非线性动力学方程近似形式,预言了二个基于非线性动力学方程的电路元件-电存(nonlinstor)和电敏器(geomsentor),其皆为深化型电容器的电路器件,分析了RLCNG 串联电路微分方程的性质;给出了广义分布函数及广义分布密度函数的延展方向与粒子统计分布趋势性方程及其若干条件解,讨论了Planck 量子方程的频率区间性质,探讨了具有近似线性变频解的非线性微分方程形式及在负频率情况下变频波动方程的曲线形态特征,讨论了数据库理论构架(此构架由基础数据库、趋势性方程、解析数据库构成)的一种简洁模式,建立了美国年度能源消费量与GDP关系方程及英国年度人口数量与GDP关系方程,并计算预测了美国年度能源消费极限值与英国年度人口极限值;随后探讨了岩石及单晶高温材料的蠕变过程曲线、半导体分立器件V-A特性曲线、超导材料电阻R(或电阻率 ρ)- 绝对温度 T曲线方程,双晶 Josephson 结直流特性曲线及Shapiro 台阶电流阶跃幅值曲线的趋势拟合方程,机械系统或伺服系统摩擦力-速度特性曲线(包括Coulomb 摩擦、Stribeck摩擦、黏性摩擦、摩擦迟滞及反常摩擦迟滞效应)的趋势拟合方程,Newton冷却定律的扩展方程形式,高聚物熔体流动曲线剪切应力-剪切速率(包括第一Newton区、假塑性区、第二Newton区、胀流区、湍流及反常剪切效应)的趋势性方程等。在唯象及趋势层面,指出了材料蠕变过程曲线与高聚物熔体流动曲线具有类似性质,及材料断裂裂纹扩展结构与流体湍流漩涡嵌套结构这二种现象演化在分形测度表述上具有相通性的研究方向;最后讨论了连接方程在数据拟合及长程预测方面的局限性。

关键词:连接方程,非线性动力学方程,规律谱阵,简学或维学,状态转化方程,自然简洁原则,自然演化平衡法则

YAN  Kun
(Xi’an Modern Nonlinear Science Applying Institute,Xi’an  710061,China)

Abstract In this paper,  brief annotation of a constructing procedure and the applications of connection equation are given. An analytical method of the connection equation as an approximate equivalent analytical solution of nonlinear dynamics equations is discussed. Research direction of Jiansics or Dimennics about spectrum(spectrum array) formed by series of laws and their connections in evolution processes of natural phenomena are explored, an equation of the transformation of the phenomena between the states in evolutionary process is presented, that it follows a natural optimum principle or a natural conciseness principle in general, which having an equation form of the smooth curve with the optimal path or the most concise path, simple constructing forms of forward partial-symmetrical equation(or weak-symmetrical equation) and backward partial-symmetrical equation are given, an approximate expression of extended hyperbolic tangent series for data curve or partial continuous functions is constructed, then natural evolution-balance rule is presented, and tendency equation of biological growth process is given too. According to approximate form of the nonlinear dynamics equation of the connection equation, two new electronic circuit elements(nonlinstor and geomsentor) with deepening charge-controlled capacitor properties based on form of the nonlinear differential equation is predicted, and the nonlinear differential equation for a RLCNG series circuit is also analyzed, extended direction of the general distribution function and the general distribution density function, tendency equation and its conditional solutions of the statistical distributions of the particles are given, properties of the frequency interval of Planck’s quantum equation are explored, nonlinear differential equation  expressions with solution of approximate linear frequency conversion and their characteristics of curve shapes of frequency conversion wave equations at negative frequency are discussed, a concise model of database theoretical framework (this framework to be made up of foundation database, tendency equation, and analytic database) is explored, an equation of relationship between the total annual energy consumption with the annual GDP in the United States, and an equation of relationship between the annual population with the annual GDP in the United Kingdom are established, and limit values of the total annual energy  consumption in the United States and the annual population in the United Kingdom are calculated and predicted. Subsequently, tendency fitting equations of curves are explored, which included the creep process curve of the rock and the single-crystal superalloy, the Volt-Ampere characteristic curve of the discrete semiconductor device, the resistance (or resistivity )-absolute temperature curve of the superconducting material, the direct current I-U characteristic curve of the bicrystal Josephson junction, and the current step amplitude of Shapiro steps, the friction-speed characteristic curve (that included the stages of Coulomb friction, Stribeck friction, viscous friction, friction hysteresis, and anomalous friction hysteresis effect) in mechanical system or servo system, an expanded equation form of the Newton's law of cooling, the shear  stress-shear rate in the flow curve (that included the sections of first Newtonian fluid-flow, pseudoplastic flow, second Newtonian fluid-flow, dilatant flow, turbulent flow, and anomalous shearing effect) of the polymer melts, etc. On phenomenological and tendency levels, research directions of similar property of creep curves of materials with the flow curves of polymer melt, and similarity in the fractal measure of the evolutions of fracture cracks growth structure and fluid turbulent eddies nested structure are pointed out. At the end, limitations of the connection equation in data fitting and long-range forecasting are discussed.

Keywords connection equation, nonlinear dynamics equation, spectrum array of laws, Jiansics or Dimennics, states transforming equation, natural conciseness principle, natural evolution-balance rule

引言

  在数据整理归纳中,连接方程方法可以在现象演化原理研究路线外进行并行探讨分析, 是与原理分析的并行探索路线。对在基础原理尚未完全建立的现象演化过程,连接方程方法则是较为直接的唯象分析途径,为建立现象演化的非线性动力学解析体系及其近似等效解析解方法提供参考描述。连接方程方法同时也对主曲线理论中数据局部骨架的过渡性连接描述提供参考曲线形态,为理想饱和过程及一般阶跃过程的连续渐变阐释提供趋势性方程形式。

  本文简略注释并展开讨论资料1中连接方程形式的构造过程及其部分应用方向,探讨了连接方程作为一较为简洁普适的非线性动力学方程近似等效解析解的分析方法;探讨了自然现象演化过程的规律谱系(谱阵)及连接纽带大略—简学或维学研究方向,指出了现象在演化过程的状态间转化方程,其在一般情况下遵循最优或最简洁路径光滑曲线方程形式这一自然最优原则或自然简洁原则;给出了饱和过程前偏对称(欠对称或弱对称)方程与后偏对称方程的简洁构造形式;给出了数据曲线或部分连续函数的一种拓展型(扩展型)双曲正切级数近似表示形式与自然演化平衡法则、生物生长曲线趋势性方程、及可生成周期性曲线的复合扩展型双曲正切方程;预言了几个新的基于非线性微分方程的电路基础元件(包括电存器nonlinstor、电敏器-geomsentor等),分析了兼容Newton动力学位移-时间方程、RLCNG 串联电路电荷量-时间方程的部分性质;探讨连接方程及其非线性微分方程近似形式在广义分布函数及广义分布密度函数形式延展方向、粒子系统的统计分布趋势方程、Planck 量子方程的频率区间性质、具有近似线性变频特征的微分方程及在负频率与正频率之间转化时变频波动方程曲线的形态特征、数据库理论的一种简洁构架模式中的趋势方程、国家能源消费总量及人口总数与GDP 总值关系方程、国家各阶层人均年收入值与其所占人口比例数关系方程等方面的应用,及在岩石与单晶高温合金蠕变曲线、半导体分立器件V-A特性曲线、超导材料零电阻转变区域R(或电阻率 ρ)-T 曲线、高温超导双晶Josephson 结直流 IU 特性曲线与 Shapiro 台阶电流阶跃幅值、机械系统或伺服系统摩擦力-速度曲线(其中包括Coulomb摩擦、Stribeck摩擦、黏性摩擦、摩擦迟滞、反常摩擦迟滞及复合摩擦迟滞效应)、Newton冷却定律的扩展方程形式、高聚物熔体流动曲线剪切应力-剪切速率关系(包括第一Newton区、假塑性区、第二Newton区、胀流区、湍流及反常剪切效应)等方面的趋势描述方程应用计算。在唯象及趋势层面,指出材料蠕变过程曲线与高聚物熔体流动曲线的相似性质,及材料断裂裂纹扩展与流体湍流漩涡嵌套二种现象演化在多层面机理特征和分形测度表述方面具有相通性的研究方向(包括如Navier-Stokes方程的参考求解方向);最后讨论了连接方程的局限性。

 
 
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