Soliton particles

Solitons A mathematically appealing model of real particles is that of solitons. It is known that in a dispersive linear medium, a general wave form changes its shape as it moves. In a nonlinear system, however, shape-preserving solitary solutions exist. 

A typical evolution of a disordered state under a radius r = 3 parity-rule FA, showing a dissolution into, and subsequent soliton-like interaction between, several particles with different velocities, is shown in figure 3.37. 

Radius (r) distinct Particles Range of Speeds distinct d and tt Most Likely Speed % of Collisions That are Soliton... 

Fig. 12.18 Schematic representation of particles built up from a space-time lattice i.e.geometrodynamic solitons.

Solitary waves, especially in shallow water, have been studied for many years[24]. They have the interesting property of interacting with other solitary waves and to separate afterwards as if there had been no interaction at all. This persistence of the wave led to the name soliton, to emphasize the particle-like character of these waves which seem to retain their identities in a collision. 

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. 

C. Particles as Solitons in 4D Ether V. A Charge-Neutral/Mass-Neutral Photon... 

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. 

The mass of a particle (resp. antiparticle) is then proportional to the preonic mass flow into (resp. out of) our 3D-world, which carry a momentum flux q c . Particles (resp. antiparticles) are solitons of steady flow, whose rest mass M ) is the result of a transfer of energy from (resp. into) the u axis during the duration Tm of a measurement inside a 3D volume whose size corresponds to the volume of the particle. Then... 

It appears that a mechanical model for spin must start from extensive particles. It is expected that the 4D solitons will exhibit vorticity in many instances. Let the moment of inertia I associated with a particle be... 

Another important classification of particle dark matter rests upon its production mechanism. Particles that were in thermal equilibrium in the early Universe, like neutrinos, neutralinos, and most other WIMPs (weakly interacting massive particles), are called thermal relics. Particles which were produced by a non-thermal mechanism and that never had the chance of reaching thermal equilibrium in the early Universe are called non-thermal relics. There are several examples of non-thermal relics axions emitted by cosmic strings, solitons produced in phase transitions, WIMPZILLAs produced gravitationally at the end of inflation, etc. 

L. Schimansky-Geier. Effect of the potential shape and of a brownian particle mass on noise-induced transport. Chaos, Solitons ej Fractals, 12 1459-1471, 2001. 

When two trans-polyacetylene chains with different phases are put together, an obvious disturbance occurs in the standard conjugation pattern. The bond alternation defect that appears is known as a neutral soliton (Fig. 1.7). This kind of quasi-particle has an unpaired electron but is electrically neutral and is isoenergetically mobile along the polymer chain in both directions. This soliton gives rise to a state in the middle of the otherwise empty energy gap that can be occupied by zero, one or two electrons (Fig. 1.8). 

A complete understanding of the conduction processes has not yet been obtained. It is clear that at least two types of processes are required charge transport along the chains and charge transport between the chains. Transport along the chains may be possible because of the formation of various kinds of pseudo-particles, such as solitons and polarons, which are localised but mobile excitations (Bower, 2002). 

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