This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems. 相似文献
The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main
objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative.
By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained.
The performance of this formulation is verified by comparison with numerical examples in the literature
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Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005. 相似文献
We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.
We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.
We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.
建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场, 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变, Goldstone bosons场就足够了; 如果要讨论二级相变, 则必须讨论一系列的场, 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity. 相似文献
The relationship of resistivity versus synthesizing temperature of sol gel YBa_2Cu_3O_y samples was studied when prepared under flowing oxygen conditions. A set of high-temperature ρ-T curves was obtained for the whole process. After the sample finished the test measuring, its resistivity was ρ_{300}=9.83×10^{-3 }Ω·cm at room temperature. The ρ-T curve also showed that the orthorhombic-tetragonal phase transformation of sol-gel YBa_2Cu_3O_y sample occurred at 581℃ for the sample in the rising temperature process, but at 613℃ in the cooling process, lower than that of the samples made by using the conventional powder metallurgy methods. 相似文献