Derivation of the Biot-Savart equation from the Nonlinear Schrödinger equation
|Title:||Derivation of the Biot-Savart equation from the Nonlinear Schrödinger equation||Authors:||Bustamante, Miguel
|Permanent link:||http://hdl.handle.net/10197/7282||Date:||25-Nov-2015||Online since:||2015-12-10T14:14:15Z||Abstract:||We present a systematic derivation of the Biot-Savart equation from the nonlinear Schrödinger equation, in the limit when the curvature radius of vortex lines and the intervortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines, [equation not represented here], with cutoff length [equation not represented here], where ρ0 is the background condensate density far from the vortex lines and κ is the quantum of circulation.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||American Physical Society||Journal:||Physical Review E: Statistical, Nonlinear, and Soft Matter Physics||Volume:||92||Issue:||5||Copyright (published version):||2015 American Physical Society||Keywords:||Superfluid dynamics; Turbulence; Equations; Derivations||DOI:||http://dx.doi.org/10.1103/PhysRevE.92.053019||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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