Mit 2 Figuren im Text
(Eingegangen an, 4. Mai 1959)As a simple model of c~-decay, a particle in a penetrable sphere is treated and the time behaviour of the wave function discussed. The deviations from the exponential law Ior very small and for very large times cannot be experimentally observed.
Some liquid crystalline phases of bent-core mesogens are known to form stable freely-suspended filaments with length to diameter ratios of 1000 and larger. These structures can behave like thin liquid chords. We study filament oscillations excited with harmonic sound waves. From amplitudes of the filament motion and phase shifts respective to the harmonic excitation signal we develop a model for the filament dynamics. Like in solid chords, the resonance frequency f 0 is inversely proportional to their length. The dependence of f 0 upon the filament radius allows one to draw conclusions on the nature of the filament tension. For thin filaments, this tension can be largely attributed to surface tension, while for thick filaments there must be other, bulk contributions in addition. The decay time of the filament oscillations is proportional to the filament length. This can be explained by the assumption that dissipation is restricted to the two filament ends. An important observation is that thick filaments often deviate significantly from cylindrical shape.
The recently proposed non-local equation of motion for the classical electron is slightly modified so that the resulting differential-difference equation becomes absolutely stable, i.e. any sort of runaway solutions are excluded, no matter which initial conditions are imposed. The electromagnetic part entering the equation of motion appears in the finitedifference form of Caldirola, whereas the non-electromagnetic part is a pure differential form. Further generalizations are discussed, thereby introducing the notion of time-like structure functions for classical charged particles with internal structure.
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