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- Droplet-shaped_wave abstract "In physics, Droplet-shaped waves are casual localized solutions of the wave equation closely related to the X-shaped waves, but, in contrast, possessing a finite support.A family of the droplet-shaped waves was obtained by extension of the "toy model" of X-wave generation by a superluminal point electric charge (tachyon) at infinite rectilinear motion to the case of a line source pulse started at time t = 0. The pulse front is supposed to propagatewith a constant superluminal velocity v = βc (here c is the speed of light,so β > 1).In the cylindrical spacetime coordinate system τ=ct, ρ, φ, z,originated in the point of pulse generation and oriented along the (given) line of source propagation (direction z),the general expression for such a source pulse takes the formwhere δ(•) and H(•) are, correspondingly, the Dirac delta and Heaviside step functionswhile J(τ, z) is an arbitrary continuous function representing the pulse shape.Notably, H (βτ - z) H (z) = 0 for τ < 0, so s (τ, ρ, z) = 0 for τ < 0 as well.As far as the wave source does not exist prior to the moment τ = 0, a one-time application of the causality principle implies zero wavefunction ψ (τ, ρ, z) for negative values of time.As a consequence, ψ is uniquely defined by the problem for the wave equation withthe time-asymmetric homogeneous initial conditionThe general integral solution for the resulting waves and the analytical description of their finite,droplet-shaped support can be obtained from the above problem using the STTD technique.,,".
- Droplet-shaped_wave wikiPageID "40626819".
- Droplet-shaped_wave wikiPageRevisionID "595997388".
- Droplet-shaped_wave subject Category:Wave_mechanics.
- Droplet-shaped_wave comment "In physics, Droplet-shaped waves are casual localized solutions of the wave equation closely related to the X-shaped waves, but, in contrast, possessing a finite support.A family of the droplet-shaped waves was obtained by extension of the "toy model" of X-wave generation by a superluminal point electric charge (tachyon) at infinite rectilinear motion to the case of a line source pulse started at time t = 0.".
- Droplet-shaped_wave label "Droplet-shaped wave".
- Droplet-shaped_wave sameAs m.0xplb1b.
- Droplet-shaped_wave sameAs Q17009530.
- Droplet-shaped_wave sameAs Q17009530.
- Droplet-shaped_wave wasDerivedFrom Droplet-shaped_wave?oldid=595997388.
- Droplet-shaped_wave isPrimaryTopicOf Droplet-shaped_wave.