Expansion in the width and collective dynamics of a domain wall

Arodź, Henryk

doi:10.1016/s0550-3213(97)00497-5

Cited by 15 publications

(16 citation statements)

References 32 publications

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“…We shall see that we can find approximate solutions to the field equations near surfaces of codimension N which have zero extrinsic curvature, and whose other curvature radii are large compared with the width of the defect. These results are well known and have been shown in various ways in [30,31,32], but the approach here is slightly different and worth exhibiting in some detail for the later sections of the paper.…”

Section: Field Equationssupporting

confidence: 53%

Level set method for the evolution of defect and brane networks

Hindmarsh

2003

Phys. Rev. D

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A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, wellknown in other contexts, possesses self-similar "scaling" solutions, for which one can calculate many quantities of interest. Here, the length and area densities of cosmic strings and domain walls are calculated in Minkowski space, and radiation, matter, and curvature-dominated FRW cosmologies with 2 and 3 space dimensions. The scaling exponents agree the naive ones based on dimensional analysis, except for cosmic strings in 3-dimensional Minkowski space, which are predicted to have a logarithmic correction to the naive scaling form. The scaling amplitudes of the length and area densities are a factor of approximately 2 lower than results from numerical simulations of classical field theories. An expression for the length density of strings in the condensed matter literature is corrected.

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Section: Field Equationssupporting

confidence: 53%

Level set method for the evolution of defect and brane networks

Hindmarsh

2003

Phys. Rev. D

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“…The integration with respect to s variable leads to the effective mechanical Lagrangian for the S(t) variable where the constants w and b denote the widths of the dielectric layer in both normal directions. The explicit formula for potential can be obtained for small curvatures K(s) << 1/w ∆U ≈ bw 3 6…”

Section: Long Josephson Junction and Its Possible Technical Applicationsmentioning

confidence: 99%

Curvature Effects in 1-D and 2-D Josephson Junctions

Dobrowolski¹

2016

GIQ

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The gauge invariant phase difference between superconducting electrodes is a dominating dynamical degree of freedom in the Josephson junction. This rapport concerns the influence of the curvature of the junction on the dynamic of this field variable. The effects of curvature are discussed in the long and large area junctions. In particular the dynamics of the fluxion and the kink front are studied.

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“…Our paper is devoted to dynamics of domain walls in uniaxial nematic liquid crystals in an external magnetic field. Static, planar domain walls were discussed for the first time in [5]. We would like to approximately calculate director field of a curved domain wall.…”

Section: Introductionmentioning

confidence: 99%

“…We would like to approximately calculate director field of a curved domain wall. We use a method, called the improved expansion in width, whose general theoretical formulation has been given in [5,6]. Appropriately adapted expansion in width can also be applied to disclination lines [7].…”

Section: Introductionmentioning

confidence: 99%