Surface soliton

Fig. 5.9 Schematic representation of a polyacetylene fiber with O2 impurities bonded to the surface. Soliton traps are created on (CH), chains, with trapping energy that is a function of r - ro, the chain-to-surface distance. (From Ref. 56.)...

In this way, we can relate duality to quark-hadron continuity. We considered duality, which is already present at zero chemical potential, between the soliton and the vector mesons a fundamental property of the spectrum of QCD which should persists as we increase the quark chemical potential. Should be noted that differently than in [42] we have not subtracted the energy cost to excite a soliton from the Fermi sea. Since we are already considering the Lagrangian written for the excitations near the Fermi surface we would expect not to consider such a corrections. In any event this is of the order //, [42] and hence negligible with respect to Msoiiton. 

The llrst experimental evidence for a uniaxial soliton reconstruction of the Au(l 11) surface was obtained in 1977 by Miller and Home unfortunately, they missed the significance of the data. They scattered He beams with energies of 11-63 meV from Au(l 11) surfaces. Figure 35 shows a polar He diffraction scan with a beam energy of 11 meV, at a hxed incident angle dj = 80° obtained... 

More advanced mathematical aspects of aromaticity are given in other references [33, 34]. Some alternative methods beyond the scope of this chapter for the study of aromaticity in deltahedral molecules include tensor surface harmonic theory [35-38] and the related Hirsch 2 N -b 1) electron-counting rule for spherical aromaticity [39]. The topological solitons of nonlinear field theory related to the Skyrmions of nuclear physics have also been used to describe aromatic cluster molecules [40]. 

In the representation advanced above, our 3D world is bounded by a hypersurface, whose normal points into our world. This is interpreted as the surface of Dirac s sea of energy momentum. Sources and sinks correspond to punctures on the hypersurface driven by. 1%, identified with particles and antiparticles, respectively. In this way, particles and antiparticles become solitons in the 4D ether. 

Falaco solitons were reported [132] as pairs of solitons that exist on the surface of a fluid (water), and are interconnected through the third spatial dimension. Our model for the photon is a pair of 3D solitons interconnected through the fourth dimension. 

The structure of an usual crystal, or of the perfectly regular chain of a theoretical CP, is specified completely by a small number of parameters, whatever the size of the system. Defects in these perfect structures, such as a dislocation or a soliton, are well defined in the same way. Except for PDAs, which are not considered in this section, this is not true of a real CP sample. It is usually disordered at all scales in a variable way, up to macroscopic dimensions for instance, the morphologies of the two surfaces of a fibrillar PA film are different (see, e.g., Fig. 5 in Ref. 17), or that of an electrochemically synthesized CP film varies continuously along its thick-... 

Bogomolny, E.B., Georgeot, B., Giannoni, M.-J. and Schmit, C. (1995). Quantmn chaos on constant negative curvature surfaces. Chaos Solitons Fractals 5, 1311-1323. 

Surface Waves and Dissipative Solitons Sustained by the Marangoni Effect... 

In the 1990s, this problem of surface structuration was revisited in the light of recent theoretical hndings obtained on nonlinear surface waves. It could be established that the waves sustained by a Marangoni effect, as observed by Linde and Schwarz and Orell and Westwater, are relevant to a nonhnear theory. They have solitonic properties and the patterns that structure the surface are produced by their colhsion. The description and analysis of these nonlinear waves sustained by a solutal Marangoni effect are the subject of this chapter. 

There is also numerical evidence of the above given solitonic properties of nonlinear waves. For the particular case of Equation 4.3 and related two-side propagating wave equations, Christov and Velarde have calculated wave prohles and discussed the kinematics of the collisions of solitonic surface waves in two extreme limiting cases. 

Christov, C.l. and Velarde, M.G., Dissipative solitons, Physica D, 86, 323-347, 1995. Santiago-Rosanne, M., Vignes-Adler, M., and Velarde, M.G., Dissolution of a drop on a liquid surface leading to surface waves and interfacial turbulence, J. Colloid Interface Sci, 191, 65-80, 1997. Santiago-Rosanne, M., Vignes-Adler, M., and Velarde M.G., A pathway to interfacial turbulence, in Fluid Physics, Lecture Notes of Summer Schools, M.G. Velarde and C.l. Christov, Eds., World Scientific, Singapore, 1994, 275. 

Fig. 1. Case 1413, buoy encountered internal wave soliton and slick bands, (a) Mean square curvature, (b) surface water temperature, (c) wind speed, (d) wind direction, and (e) air temperature...

The important role played by solitons in biological transfer remains to be clarified solitons are said to arise from localized disordered regions on, say, a membrane surface in the presence of the transmembrane electric field the local perturbation then tends to spread and to move leading to changes in the orientation of the lipid membrane molecules. The soliton energy is considerably below the energy band gap of a polypeptide chain but may initiate proton transfer in a hydrogen bonded chain in the presence of an electrostatic field. 

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