Thermodynamics of action and organization in a system

Complexity in nature is astounding yet the explanation lies in the fundamental laws of physics. The Second Law of Thermodynamics and the Principle of Least Action are the two theories of science that have always stood the test of time. In this article, we use these fundamental principles as tools to understand how and why things happen. In order to achieve that, it is of absolute necessity to define things precisely yet preserving their applicability in a broader sense. We try to develop precise, mathematically rigorous definitions of the commonly used terms in this context, such as action, organization, system, process, etc., and in parallel argue the behavior of the system from the first principles. This article, thus, acts as a mathematical framework for more discipline‐specific theories. © 2015 Wiley Periodicals, Inc. Complexity 21: 307–317, 2016     

频散可控格式的一种推广形式及其在爆轰波马赫反射中应用

频散可控格式是高精度捕捉激波的新格式.对原有频散可控格式(DCD)进行了推广,给出了适用于网格点排列不规则情况下的DCD格式,使其具有更广泛的适应性,在此基础上构造了在非结构三角形网格下的DCD格式.用一些典型算例对推广后的DCD格式进行检验,结果表明该格式是合理和可靠的,并能够较好地保留原有DCD格式的二阶精度.把推广后的DCD格式和具有8种组分和20个化学反应的基元反应模型相结合,对氢氧爆轰波在直管道中的传播问题及楔面上马赫反射问题进行计算,计算结果和实验结果比较表明,在非结构三角形网格下的DCD格式能够有效地捕捉爆轰波,在爆轰波阵面上不会产生振荡或是抹平间断现象.     

Symbolic Dynamics of the Piecewise Linear Standard Map

The symbolic dynamics of the sawtooth map is extended to the dissipative piecewise linear standard map. The ordering rules of foliations are derived, and the admissibility condition for allowed symbolic sequences is obtained. A symbolic analysis is given for invariant circles of the piecewise linear standard map without dissipation.     

Dissipative effects of an isolated bubble in water on the sound wave

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水中孤立气泡对声波的耗散作用

本文从气泡壁面线性运动方程出发,对水中孤立气泡的声耗散机理进行了分析。结果表明:气泡对声波具有明显的耗散作用;耗散作用由声散射和声吸收两部份组成;热传导在气泡对声波的耗散作用中起决定性作用;气泡处于谐振时,对声波具有最大的耗散作用。     

The Universal Plateau Structure of Lyapunov Exponents for Period Doubling Cascade Attractors

Using algebraic. analysis method for periodic orbits of Hknon map, we derive the boundary equations of stable window and Lyapunov exponent plateau region on the space of nonintegrability parameter A and dissipation parameter J. Ekom the real root of these equations, we obtain the plateau width of Lyapunov exponent W_p = A_p,max - A_p,min and the stable tvindorv width W_s = A_p,max - A_p,min for high periodic orbits. The calculated result of plateau structure ratio α4 = W_p/W_S for period-4 orbit agrees with the conjectural analytical formula: α4 = 2J²/(1+J⁴). Hence our result presents further evidence of universal dependence of Lyapunov exponent plateau structure on the dissipation parameter for period doubling cascade attractors of nonlinear system in transition from order to chaos.     

Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.     

嵌段共聚物组成对薄膜形貌影响的多体耗散粒子动力学研究

利用多体耗散粒子动力学(Multibody Dissipative Particle Dynamics, Multibody DPD)方法研究了在溶剂蒸发条件下, 嵌段共聚物在表面自组装形成薄膜的过程, 分别考虑了两嵌段共聚物和三嵌段共聚物及不同组成对薄膜形貌的影响. 模拟得到了无序状薄膜和层状薄膜, 并计算了这些薄膜的序参量和薄膜厚度随时间的演化. 结果表明, 嵌段共聚物的组成对薄膜厚度几乎没有影响, 当某种组分的链段很短时, 只能形成序参量较小的无序薄膜, 相反, 则可以得到序参量较大的层状薄膜.     

A Class of Cauchy Problem for Quasilinear Hyperbolic Systems with the Weakly Dissipative Terms

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Regularity and asymptotic behavior of solutions of nonautonomous differential equations

The existence of a nonautonomous approximate inertial manifold is shown for problems of the formu + Au + N(t,u)=0, in whichA is a self-adjoint operator with compact resolvent in a Hilbert spaceH. The operatorN(t, u) = G(u) + F(t, u) is nonlinear withG a monotone gradient that is locally Lipschitz fromD(A ^1/2) intoH, andF:⁺×HH a Lipschitz perturbation that is Hölder continuous int. Weak solutions are shown to be uniformly locally Hölder continuous intoD(A) with equicontinuity in families of solutions with ¦u(0)¦ r.A priori estimates of ¦Au(t)¦ are also verified and used in a skew-product flow to show there is a global attractor whose component elements form a equicontinuous family of solutions.