Whereas the profile in linear wave equations is usually arbitrary it is important to note that a nonlinear equation will normally describe a restricted class of profiles which ensure persistence of solitons as t — oo. Any theory of ordered structures starts from the assumption that there exist localized states of nonlinear fields and that these states are stable and robust. A one-dimensional soliton is an example of such a stable structure. Rather than identify elementary particles with simple wave packets, a much better assumption is therefore to regard them as solitons. Although no general formulations of stable two or higher dimensional soliton solutions in non-linear field models are known at present, the conceptual construct is sufficiently well founded to anticipate the future development of standing-wave soliton models of elementary particles. [Pg.125]

Problems arise in two situations firstly, if the molecule is linear, no complete set of 3N — 6 internal coordinates is possible. For this case, a method for constructing PES in terms of Cartesian coordinates could be used.56 Secondly, if the molecule is planar, atom-atom distances (or their reciprocals) cannot provide a complete set of internal coordinates, since they cannot describe out-of-plane motion. However, we have found the coordinates Zn so useful that we retain these coordinates and avoid planar geometries (except for three atoms, when only linear geometries are taboo). That is, [Pg.423]

The phase coherence can also be achieved simply by using a linearly phase incremented pulse (PIP) without resorting to additional hardware. Since all the RF pulses utilized for constructing a PIP have the same carrier, no frequency jump is involved. Consequently, phase coherence between the RF pulses applied before and after the PIP is reserved naturally. [Pg.4]

Finally, we point out that further structural assemblies exist in the construction of linear metallic frames (such as Au3 and AU5,50 Pd3 and Pd4,51 Ir4 26), but no pertinent electrochemical investigations on their electron transfer ability have been carried out. [Pg.533]

Viscoelasticity of metal This subject provides an introduction on the viscoelasticity of metals that has no bearing or relationship with viscoelastic properties of plastic materials. The aim is to have the reader recognize that the complex thermodynamic foundations of the theory of viscoplasticity exist with metals. There have been developments in the thermodynamic approach to combined treatment of rheologic and plastic phenomena and to construct a thermodynamic theory non-linear viscoplastic material that may be used to describe the behavior of metals under dynamic loads. [Pg.645]

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