Nonlinear Phenomena in Fluids, Solids and other Complex Systems
- P. Cordero
- B. Nachtergaele, Universidad de Chile, Santiago, Chile
This book contains short courses in current topics in nonlinear physics given by distinguished professionals in their fields. These include: nonlinear fluid dynamics, transition to turbulence, quantum hall effect, cellular automata and neural networks, phase transitions. These courses are up to date and are aimed at a wide audience, in particular to graduate students and researchers in the field of nonlinear physics.View full description
- Published: July 1991
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-88791-7
Table of ContentsPreface. Part 1: Fluids. Thermal turbulence (A. Libchaber et al.). Scaling and multiscaling (fractals and multifractals) (L.P. Kadanoff). Weakly nonlinear interactions in fluid dynamics (F. Lund). Interface instabilities in liquid crystals (A.J. Libchaber, J.-M. Flesselles and A.J. Simon). Critical perturbation of Xe dynamics at high pressure (L. Letamendia et al.). Almost integrable magnetic fields in tokomaks (M.V.A.P. Heller, I.L. Caldsas, M.C.R. Andrade). Part 2: Cellular Automata and Neural Networks. On studying the brain as an adaptive disordered system (M.A. Virasoro). RS model for neural networks (J.J. Arenzon, R.M.C. de Almeida and J.R. Iglesias). The efficiency of high order neural networks (P. Perez and I.J. Matus). Study of a slowly cooled SK spin glass (M. Freixa Pascual). Zeros of the partition function in the REM model (C. Moukiarzel and N. Parga). One-dimensional sand piles, cellular automata and related models (E. Goiles and M. Kiwi). Fracture propagation: from time to ensemble averages and back again (L. Limnitz-Adler and G. Martinez-Mekler). Numerical study of a generalized Domany-Kinzel probabilistic one-dimensional cellular automaton (H.F. Verona de Resende et al.). Equilibrium properties of a cellular automaton for thermofluid dynamics (A. Salcido and R. Rechtman). Degree of ultrametricity of fractal sets (C.M. Arizmendi, A.H. Rizzo and J.R. Sanchez). Part 3: Statistical Physics. Commensurate-incommemsurate transitions and area-preserving maps: the Frenkel-Kontorova model (R.B. Griffiths). Atomic and electronic structure of quasicrystals (J.M. Cabrera-Trujillo, F. Mejía-Lira and J.L. Morán-López). Uniqueness and degeneracy of ground states for some quantum spin chains (B. Nachtergaele). Exact versus quantum monte carlo analysis of the groundstate of the one-dimensional Hubbard model for finite lattices (L. Braunstein, R. Deza and A. Mijovilovich). Maximum entropy formalism applied to soap froths (J.R. Iglesias and R.M. de Almeida). Multiscaling structure of the density of states of the Ising Hamiltonian (P. Cordero). Spin-I Ising Ferromagnet in a Random Crystal Field (C.E.I. Carneiro et al.). Noise induced transitions in a bidimensional bistable potential well (E.S. Hernandez). Path integral approach to the Fokker-Planck equation; an improved numerical procedure (G. Abramson, H.S. Wio and L.D. Salem). Maximum entropy principle approach to the degenerate parametric amplifier (J. Aliaga, G. Crespo and A.N. Proto). Unbounded operators in statistical mechanics (D. Ortero and V. Zunino). Spectral characteristics of the nonlinear interaction of a bicromatric field of light with a two-level system (A. Marcano et al.). Part 4: Dynamical Systems, Instabilities and Chaos. Effect of a resonant periodic perturbation on nonlinear processes (J. Rössler, E. Lazo and M. Kiwi). Fractal structure of boundaries in two bistable systems (R. Bulajich and R. Pérez-Pascual). Chaos in billiards of nuclear interest (A.J. Fendrik, J. Vega and C.O. Dorso). Stability of the Coulomb orbits for the hydrogen atom (S. Blanco, A. Costa and L. Romanelli). Nonlinear behaviour in a dripping faucet (H.N. Núñez-Yépez et al.). Author index. Subject index.