Wave propagation and energy exchange in a spatio-temporal material composite with rectangular microstructure

We consider propagation of waves through a spatio-temporal doubly periodic material structure with rectangular microgeometry in one spatial dimension and time. Both spatial and temporal periods in this dynamic material are assumed to be of the same order of magnitude. A “double Floquet” solution is obtained in the special case when the wave equation t(ρut)−z(kuz)=0 allows for the separation of variables. We also consider a checkerboard microgeometry where variables cannot be separated. The squares in a space-time checkerboard are assumed to be filled with materials having equal impedance but different phase speeds. Within certain parameter ranges, we observe numerically the formation of distinct and stable limiting characteristic paths (“limit cycles”) that attract neighbouring characteristics after a few time periods. The average speed of propagation along the limit cycles remains the same throughout certain ranges of parameters of the microgeometry (the “plateau effect”). We formulate, as a hypothesis, the statement saying that a checkerboard structure is on a plateau if and only if it yields stable limit cycles. A dynamic material is a thermodynamically open system, as it is involved in a permanent exchange of energy and momentum with the environment. Material assemblages that produce the limit cycles are special in this aspect. Specifically, to make a wave travel through such an assemblage, we find analytically that an external agent may need to supply infinite energy and this may be so regardless of the wave frequency. For spatio-temporal laminates, however, an accumulation of energy (parametric resonance) may emerge only for frequencies that are not too low relative to some characteristic frequency of the system.     

On pedigree polytopes and Hamiltonian cycles

In this paper we define a combinatorial object called a pedigree, and study the corresponding polytope, called the pedigree polytope. Pedigrees are in one-to-one correspondence with the Hamiltonian cycles on K_n. Interestingly, the pedigree polytope seems to differ from the standard tour polytope, Q_n with respect to the complexity of testing whether two given vertices of the polytope are nonadjacent. A polynomial time algorithm is given for nonadjacency testing in the pedigree polytope, whereas the corresponding problem is known to be NP-complete for Q_n. We also discuss some properties of the pedigree polytope and illustrate with examples.     

高技术用混合气体节制冷循环

高技术用混合气体节制冷循环吴沛宜，许名尧（西安交通大学动力系西安７１００４９）关键词：技术，气体，制冷循环。ＴＨＥＴＨＲＯＴＴＬＩＮＧＲＥＦＲＩＧＥＲＡＴＩＯＮＣＹＣＬＥＳＵＳＩＮＧＭＩＸＩＮＧＧＡＳＥＳＵＳＥＤＩＮＨＩＧＨＴＥＣＨＮＩＱＵＥ￥ＷｕＰ...     

Sensitivity analysis of oscillatory systems

Methods of sensitivity analysis are extended to find the parametric dependencies of systems of ordinary differential equations which exhibit limit cycle oscillations. The quantitative relations between the system parameters and the observable period, amplitude, phase and cycle shape are developed. These formulae, presented for both the first and second order, are applicable to systems of arbitrary size and complexity. The techniques are used here to develop correlations for period and amplitude in a non-isothermal oscillating stirred-tank chemical reactor, and to find and optimize a beneficial periodic operating strategy for a lumped-parameter catalytic reacting system.     

An algorithm for then×n optimum assignment problem

In this paper we present an algorithm for finding an optimum assignment for ann×n matrixM inn iterations. The method uses systematic permutations on the rows ofM and is based on the properties of optimum assignments. The implementation presented in the paper requires at mostO(n ³) in time andn ²+6n memory locations for solving a densen×n problem.This work was supported by the National Science Foundation Grant NSF ENG 74-19788.     

Poincaré cycles and ergodic behavior of a linear diatomic chain

The ergodic behavior of a linear diatomic chain is shown to be analogous to that of a linear monatomic chain. Starting with the expressions for the time-relaxed correlation functions between any two particles in the chain, we show that the existence of Poincaré cycles is not inconsistent with the development of an equilibrium state. Also, we show that those dynamical variables that are ergodic for the linear monoatomic chain remain ergodic in the diatomic chain. It is shown that the autocorrelation functions for particles with equal or different masses decay in time ast ^–1/2 .This work was completed when the author was associated with the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland and supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF18(600)1315.     

Cycle Action on Treelike Structures

The purpose of this paper is to study the action on cycles of several known classes of oligomorphic groups, that is, infinite permutation groups of countable degree having only finitely many orbits on k-sets for each k. The groups studied here are all related to trees and treelike relational structures. The sequence whose k-th term is the number of orbits in the action on k-cycles is called Parker sequence. It turns out that, if we are dealing with the automorphism group of a suitable relational structure, this sequence counts also the finite substructures admitting a cyclic automorphism; in calculating these sequences for various groups, we shall thus describe and enumerate such substructures.Di più dirò: ch’a gli alberi dà vita [I shall say more: the trees are given life spirito uman che sente e che ragiona. by a human spirit that perceives and reasons.Di più dirò: ch’a gli alberi dà vita spirito uman che sente e che ragiona. Per prova sollo; io n’ho la voce udita che nel cor flebilmente anco mi suona.[I shall say more: the trees are given life by a human spirit that perceives and reasons. I know it by experience: I heard their voice and it still resounds faintly in my heart.]Torquato Tasso, Gerusalemme liberata, XIII, 49     

Conforming finite element computations applied to a spatially periodic,harmonic Navier-Stokes problem

In this paper computations in the two dimensional case of a harmonic Navier-Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non-symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm). Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so-called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.     

Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.