Droplet-shaped wave (original) (raw)
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 motionto 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).
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| dbo: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 motionto 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 form where 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 condition The 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. (en) |
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| dbo:wikiPageRevisionID | 1095010827 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Physics dbr:Tachyon dbr:Wave_equation dbr:Causality_(physics) dbr:Heaviside_step_function dbc:Wave_mechanics dbr:Support_(mathematics) dbr:Dirac_delta_function dbr:Spacetime_triangle_diagram_technique dbr:X-wave |
| dbp:wikiPageUsesTemplate | dbt:= dbt:Math |
| dcterms:subject | dbc:Wave_mechanics |
| rdfs: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 motionto 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). (en) |
| rdfs:label | Droplet-shaped wave (en) |
| owl:sameAs | freebase:Droplet-shaped wave wikidata:Droplet-shaped wave https://global.dbpedia.org/id/fHRk |
| prov:wasDerivedFrom | wikipedia-en:Droplet-shaped_wave?oldid=1095010827&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Droplet-shaped_wave |
| is dbo:wikiPageWikiLink of | dbr:Index_of_wave_articles dbr:Droplets_(disambiguation) dbr:X-wave |
| is foaf:primaryTopic of | wikipedia-en:Droplet-shaped_wave |