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81.
Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli. 相似文献
82.
The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities. 相似文献
83.
Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts. 相似文献
84.
T.K. Subrahmonian Moothathu 《Journal of Mathematical Analysis and Applications》2011,379(2):656-663
For continuous self-maps of compact metric spaces, we study the syndetically proximal relation, and in particular we identify certain sufficient conditions for the syndetically proximal cell of each point to be small. We show that any interval map f with positive topological entropy has a syndetically scrambled Cantor set, and an uncountable syndetically scrambled set invariant under some power of f. In the process of proving this, we improve a classical result about interval maps and establish that if f is an interval map with positive topological entropy and m?2, then there is n∈N such that the one-sided full shift on m symbols is topologically conjugate to a subsystem of fn2 (the classical result gives only semi-conjugacy). 相似文献
85.
In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
86.
陈农田 《数学的实践与认识》2016,(1):155-161
飞行员操作行为的表现直接影响民航飞行安全.通过对飞行员不安全行为事故致因数据分析,运用德尔菲(Delphi)调查方法,从安全素养、心理因素、飞行技术及生理因素4个方面确定影响飞行员安全行为的指标体系构成.以飞行员行为评价实例,运用序关系法并结合专家调查确定各评价指标的权重系数,分析了职业安全意识、飞行情景意识、特情处理能力以及机组资源管理能力等17个指标对飞行安全行为的显著性影响程度,结论为飞行员安全行为风险分析提供参考. 相似文献
87.
从设计参数特征入手分析影响汽车油耗的因素,利用灰关联分析方法,解析了各设计参数对汽车油耗的影响程度,选择其中灰关联度较大的设计参数作为输入数据,综合工况油耗作为输出数据,构建6-5-1层结构的BP神经网络预测模型,并利用遗传算法获得优化后的BP神经网络的权值和阈值,然后训练BP神经网络得到最优值,最后以国内市场340款汽车作为研究样本,进行有效性验证.研究结果表明,模型利用灰关联分析获得影响汽车油耗的主要因素,简化了网络结构;与优化前的BP神经网络相比,具有更高的预测精度和可靠性. 相似文献
88.
New (3+1)‐dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions 下载免费PDF全文
Abdul‐Majid Wazwaz 《Mathematical Methods in the Applied Sciences》2016,39(4):886-891
In thiswork,we present two new(3+1)‐dimensional nonlinear equationswith Korteweg‐de Vries equation constituting its main part. We show that the dispersive relation is distinct for each model, whereas the phase shift remains the same. We determine multiple solitons solutions, with distinct physical structures, for each established equation. The architectures of the simplified Hirota's method is implemented in this paper. The constraint conditions that fall out which must remain valid in order for themultiple solitons to exist are derived.Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
89.
First, we give an algebraic proof to the Christoffel–Darboux identity of formal orthogonal rational functions on the real line by exposing some underlying algebraic properties. This proof does not involve the three-term recurrence relationship. Besides, it is shown that if a family of rational functions satisfies the Christoffel–Darboux relation, then it also admits a three-term recurrence relationship. Thus, the equivalence between both relations is revealed. 相似文献
90.