Nonlinear physics

Materials. NLO materials possess a high degree of optical nonlinearity, physical durabiHty and chemical inertness, and high threshold to optical damage. In addition, it must be possible to process the materials into the form required by the intended appHcation. 

Sagdeev, R. Z., D. A. Usikov, G. M. Zaslavsky. Nonlinear Physics From the Pendulum to Turbulence and Chaos. Harwood Academic Publishers, New York,... 

Process monitoring and analysis a. Virtual sensors Least squares Nonlinear, physically based, steady state, or empirical... 

Nonlinear Physics Coiurol of molecular archiicclure lo produce asymmetric viruciurv- wiih high non-linear coefficients, e.g. in electro-optics. pyroelectric deieeiors. or acousioeleciric devices. 

In multidimensional systems, these intersections would exhibit much more variety than they do in the lower-degrees-of-freedom systems that have been traditionally studied in nonlinear physics. One of the new aspects is tangency , which was found in the predissociation of a van der Waals complex of three bodies [11,12]. The tangency gives birth to transition in chaos [12], which is called a crisis [13]. Then, the extention of the concept of reaction rates to multidimensional chaos, which was first proposed in Ref. 9, breaks down [11,14]. 

Sagdeev, R.Z., Usikov, D.A. and Zaslavsky, G.M. (1988). Nonlinear Physics (Harwood Academic, Chur). 

H.A. Dijkstra Nonlinear Physical Oceanography. A Dynamical Systems Approach to... 

Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion - Israel Institute of Technology, 32000 Haifa, Israel... 

From the standpoint of nonlinear physics, two main themes exist at present in studying chemical reactions One is to reexamine the concept of transition states, the other is to understand the mechanism of IVR. Before studying these topics, let us briefly summarize the present status of nonlinear physics that would be relevant to understanding chemical reactions. 

Having summarized the present status of nonlinear physics, we now go back to chemical reactions. 

Laboratory and field experiments show die presence and interplay of such processes as intrafracture film flow along fracture surfaces, coalescence and divergence of multiple flow paths along fracture surteces, and intrafracture water dripping. The nonlinear dynamics of flow and transport processes in unsaturated fractured porous media arise from die dynamic feedback and conpetition between various nonlinear physical processes along widi the complex geometry of flow paths. The apparent randomness of (he flow field does not prohibit the system s determinism and is, in fact, described by deterministic chaotic models using deterministic differential or difference-differential equations. 

The idea that solitons might play an important role in biopolymers comes from Davydov. In his article [37], he studied alpha-helical proteins and applied some achievements of nonlinear mathematics to biology. As for DNA, the nonlinear physics started in 1980 [10] when the first nonlinear Hamiltonian of DNA, as well as possibility of sohtonic solution, was suggested. A crucial experimental research was explained in Ref. [38], representing victory of nonlinear over linear DNA physics. 

Yakushevich, L.V., Nonlinear Physics of DNA Wiley Series in Nonlinear Science, John Wiley and Sons, Chichester, England, 1998. 

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