Imperial College London
Alternate

ProfessorDarrylHolm

Faculty of Natural Sciences, Department of Mathematics

Chair in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8531d.holm Website

 
 
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Location

 

6M27Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Holm:2019:10.1007/s00332-018-9479-5,
author = {Holm, D},
doi = {10.1007/s00332-018-9479-5},
journal = {Journal of Nonlinear Science},
pages = {115--138},
title = {Stochastic evolution of augmented Born–Infeld equations},
url = {http://dx.doi.org/10.1007/s00332-018-9479-5},
volume = {29},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born–Infeld model of nonlinear electromagnetism. The similarities in the results are striking. Namely, the introduction of Stratonovich cylindrical noise into each of their Hamiltonian formulations introduces stochastic Lie transport into their dynamics in the same form for both theories. Moreover, the resulting stochastic partial differential equations retain their unperturbed form, except for an additional term representing induced Lie transport by the set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation for this remarkable similarity lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, which is done via pairing spatial correlation eigenvectors for cylindrical noise with the momentum map for the deterministic motion. This momentum map is responsible for the well-known analogy between hydrodynamics and electromagnetism. The momentum map for the Maxwell and Born–Infeld theories of electromagnetism treated here is the 1-form density known as the Poynting vector. Two appendices treat the Hamiltonian structures underlying these results.
AU  - Holm,D
DO  - 10.1007/s00332-018-9479-5
EP  - 138
PY  - 2019///
SN  - 0938-8974
SP  - 115
TI  - Stochastic evolution of augmented Born–Infeld equations
T2  - Journal of Nonlinear Science
UR  - http://dx.doi.org/10.1007/s00332-018-9479-5
UR  - http://hdl.handle.net/10044/1/66546
VL  - 29
ER  -
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