Wave chaos

Winfree A T 1984 The prehistory of the Belousov-Zhabotinsky osoillator J. Chem. Eduo. 61 661-3 [11 ] Zhabotinsky AM 1991 A history of ohemioal osoillations and waves Chaos 1 379-86... 

Similarities with classical waves are considered. In particular we propose that the networks of electric resonance RLC circuits may be used to study wave chaos. However, being different from quantum billiards there is a resistance from the inductors which gives rise to heat power and decoherence. 

The above arguments show that type II wave chaos is a genuine wave phenomenon in classical wave systems. In the context of quantum mechanics, however, type II quantum chaos is only an approximation. This is because classical walls or dynamic boundaries do not exist in quantum mechanics. The dynamical degrees of freedom of the walls, or boundaries, have to be quantized too, resulting in a higher-dimensional, but purely quantum, system, usually of type I. This fact leads us to a promising... 

Bliimel, R. (1995c). Genuine electromagnetic wave chaos, Phys. Rev. E51, 5520-5523. 

V. Zykov, O. Steinbock, and S. Muller. External forcing of spiral waves. Chaos, 4 509-518, 1994. 

Zhabotinsky AM 1991 A history of chemical oscillations and waves Chaos 1 379-86... 

Caspar, V. Maselko, J. Showalter, K. 1991. Transverse Coupling of Chemical Waves, Chaos I, 435-444. 

T. Yasuda and N. Mori, Roles of sideband instability and mode coupling in forming a water wave chaos. Wave Motion 26(2), 163-185 (1997). 

Scott S K 1994 Oscillations, Waves and Chaos in Chemical Kinetics (Oxford Oxford University Press) A short, final-year undergraduate level introduction to the subject. 

Epstein I R and Pojnian J A 1998 An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves, Patterns and Chaos (Oxford Oxford University Press)... 

The cores of the spiral waves need not be stationary and can move in periodic, quasi-periodic or even chaotic flower trajectories [42, 43]. In addition, spatio-temporal chaos can arise if such spiral waves break up and the spiral wave fragments spawn pairs of new spirals [42, 44]. 

Shock-compression processes are encountered when material bodies are subjected to rapid impulsive loading, whose time of load application is short compared to the time for the body to respond inertially. The inertial responses are stress pulses propagating through the body to communicate the presence of loads to interior points. In our everyday experience, such loadings are the result of impact or explosion. To the untrained observer, such events evoke an image of utter chaos and confusion. Nevertheless, what is experienced by the human senses are the rigid-body effects the time and pressure resolution are not sufficient to sense the wave phenomena. 

Iaml91j Lam, L. and H.C. Morris, editors. Nonlinear Structures in Physical Systems Pattern Formation, Chaos and Waves, Springer- Verlag (1991). 

Mintzer, David, 1 Mitropolsky, Y. A361,362 Mixed groups, 727 Modality of distribution, 123 Models in operations research, 251 Modification, method of, 67 Molecular chaos, assumption of, 17 Miller wave operator, 600 Moment generating function, 269 Moment, 119 nth central, 120... 

Lahey (1990) indicated the applications of fractal and chaos theory in the field of two-phase flow and heat transfer, especially during density wave oscillations in boiling flow. 

Abstract. The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples. 

Chaos provides an excellent illustration of this dichotomy of worldviews (A. Peres, 1993). Without question, chaos exists, can be experimentally probed, and is well-described by classical mechanics. But the classical picture does not simply translate to the quantum view attempts to find chaos in the Schrodinger equation for the wave function, or, more generally, the quantum Liouville equation for the density matrix, have all failed. This failure is due not only to the linearity of the equations, but also the Hilbert space structure of quantum mechanics which, via the uncertainty principle, forbids the formation of fine-scale structure in phase space, and thus precludes chaos in the sense of classical trajectories. Consequently, some people have even wondered if quantum mechanics fundamentally cannot describe the (macroscopic) real world. 

The complex scattering wave function can be specified by nodal points at which u = 0,v = 0. They have great physical significance since they are responsible for current vortices. We have calculated distribution functions for nearest distances between nodal points and found that there is a universal form for open chaotic billiards. The form coincides with the distribution for the Berry function and hence, it may be used as a signature of quantum chaos in open systems. All distributions agree well with numerically computed results for transmission through quantum chaotic billiards. 

These results nicely agree with the Berry conjecture (M.V. Berry, 1977) of quantum chaos according to which the wave function in the chaotic billiard has to be expressed as a sum over an infinite number of plane waves... 

Berggren, K.-F., and A.F. Sadreev. Chaos in quantum billiards and similarities with pure-tone random models in acoustics, microwave cavities and electric networks. Mathematical modelling in physics, engineering and cognitive sciences. Proc. of the conf. Mathematical Modelling of Wave Phenomena , 7 229, 2002. 

Damgov, V. N, Trenchev PI. and Sheiretsky K. Oscillator-Wave Model Properties and Heuristic Instances. Chaos, Solitons and Fractals, Oxford, Vol. 17 (2003), P. 41... 

Some of the main examples of biological rhythms of nonelectrical nature are discussed below, among which are glycolytic oscillations (Section III), oscillations and waves of cytosolic Ca + (Section IV), cAMP oscillations that underlie pulsatile intercellular communication in Dictyostelium amoebae (Section V), circadian rhythms (Section VI), and the cell cycle clock (Section VII). Section VIII is devoted to some recently discovered cellular rhythms. The transition from simple periodic behavior to complex oscillations including bursting and chaos is briefly dealt with in Section IX. Concluding remarks are presented in Section X. 

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