By H. Thomas (auth.), Professor Dr. Harry Thomas (eds.)
This quantity comprises the notes of lectures given on the university on "Nonlinear Dy namics in Solids" held on the Physikzentrum undesirable Honnef, 2-6 October 1989 lower than the patronage of the Deutsche Physikalische Gesellschaft. Nonlinear dynamics has turn into a hugely energetic study zone, due to many attention-grabbing advancements over the past 3 many years within the theoretical research of dynamical approaches in either Hamiltonian and dissipative platforms. examine has been occupied with a number of difficulties, similar to the features of standard and chaotic movement in Hamiltonian dynamics, the matter of quantum chaos, the forma tion and homes of solitary spatio-temporal buildings, the incidence of odd attractors in dissipative structures, and the bifurcation eventualities resulting in advanced time behaviour. till lately, predictions of the idea were validated predominantly on insta bilities in hydrodynamic structures, the place many fascinating experiments have supplied priceless enter and feature resulted in a fruitful interplay among test and idea. Fluid platforms are definitely solid applicants for acting fresh experiments unfastened from anxious impacts: with fluids, in comparison to solids, it really is easier to arrange reliable samples, the proper size and time scales are in simply available levels, and it truly is attainable to do measurements "inside" the fluid, since it might be crammed in after the development of the equipment. additional, the idea describing the macroscopic dynamics of fluids is definitely confirmed and comprises simply only a few parameters, all of that have recognized values.
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Scholl Institut fUr Theoretische Physik, Technische Universitiit Berlin, Hardenbergstrasse 36, W-l000 Berlin 12, Fed. Rep. of Germany An introduction to the theoretical description of current instabilities in semiconductors is given. Various physical mechanisms are surveyed, and the self-organized formation of spatio-temporal structures, in particular breathing current filaments, is discussed. 1. Introduction Semiconductors are complex nonlinear dynamic systems which can in many cases exhibit electrical instabilities, like current runaway, switching between a nonconducting and a conducting state, or spontaneous oscillations of current or voltage, when they are driven far from thermodynamic equilibrium by strong external electric fields, optical irradiation, or current injection .
Call Xl, say, is denoted in Fig. 11 by a small circle. e. the embedding dimension m was not sufficient to span the attractor to its full extent. e. in the phase space with the correct dimension, is denoted by a cross, and its distance to Xl is distm+l (i, j (1, m + 1)). distm+~ (i: j(k, m)) > 1 , distm+l(Z, J(k, m + 1)) - (20) is larger than one, as follows from Fig. II, and it becomes equal to one only if the nearest neighbor to a point in R m also remains the nearest neighbor to this point in Rm+l.
L) without explicit use of n*(R). l) attention to Re = & here. 9) where Bo(Ro) and Bq(m(£II» are functions which incorporate the vanishing boundary conditions at Ro = ~R and = 0, respectively, and are unity in the bulk. 1,3) in terms of the "breathing" mode. Self-generated oscillations induced by periodically breathing current filaments correspond to limit cycles in the (&, £11) phase space. 9,1O) around the state Ro = £11 = £0. This is a special case of the general conditions discussed in Sect.
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