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Nonlinear Dynamics in Solids by H. Thomas (auth.), Professor Dr. Harry Thomas (eds.)

By H. Thomas (auth.), Professor Dr. Harry Thomas (eds.)

This quantity comprises the notes of lectures given on the college on "Nonlinear Dy­ namics in Solids" held on the Physikzentrum undesirable Honnef, 2-6 October 1989 below the patronage of the Deutsche Physikalische Gesellschaft. Nonlinear dynamics has develop into a hugely lively examine sector, as a result of many fascinating advancements over the past 3 many years within the theoretical research of dynamical strategies in either Hamiltonian and dissipative platforms. study has been excited by various difficulties, akin to the features of standard and chaotic movement in Hamiltonian dynamics, the matter of quantum chaos, the forma­ tion and houses of solitary spatio-temporal constructions, the prevalence of odd attractors in dissipative structures, and the bifurcation eventualities resulting in complicated time behaviour. until eventually lately, predictions of the speculation were proven predominantly on insta­ bilities in hydrodynamic structures, the place many fascinating experiments have supplied worthwhile enter and feature resulted in a fruitful interplay among test and thought. Fluid structures are definitely reliable applicants for acting fresh experiments loose from annoying affects: with fluids, in comparison to solids, it really is easier to arrange strong samples, the appropriate size and time scales are in simply obtainable levels, and it's attainable to do measurements "inside" the fluid, since it should be crammed in after the development of the gear. extra, the speculation describing the macroscopic dynamics of fluids is easily demonstrated and comprises purely only a few parameters, all of that have famous values.

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1 Drift Instabilities The best-known drift instability is the Gunn effect [8]. It is used in Gunn diodes to generate and amplify microwaves at frequencies typically beyond 1 GHz. The mechanism is based upon intervalley transfer of electrons from a state of high mobility to a state of low mobility by the influence of a strong electric field (E > 3 kV/cm). The band structure of GaAs and other III-V compound semiconductors is shown schematically in Fig. 4. At low electric fields the electrons are essentially in the minimum of the central valley, which has a low effective mass m* and hence a high mobility.

E. Do = O:max. e. x(t) in the interval [0, -r]) - to an infinite-dimensional system. The interesting result is that this formally infinite-dimensional system generates a strange attractor with a bounded dimensionality spectrum [6]. 9. 1, T =30. 27 5. Reconstruction of the Attractor from Time Series After having introduced some basic concepts by which chaotic systems are characterized, we consider now the question what can be learned from an experimental time series of one variable x(t) which looks chaotic.

4. At low electric fields the electrons are essentially in the minimum of the central valley, which has a low effective mass m* and hence a high mobility. As the field E is increased, the electrons are heated up and gain enough energy to be transferred to the satellite valley with a higher minimum energy, but larger effective mass, and hence lower mobility. As more and more electrons are transferred, the averaged mobility p, decreases strongly so that the current density j = enp,(E)E decreases with increasing field, as a result of negative differential mobility (NDM).

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