TY - JOUR
T1 - Defects are weak and self-dual solutions of the Cross-Newell phase diffusion equation for natural patterns
AU - Newell, A. C.
AU - Passot, T.
AU - Bowman, C.
AU - Ercolani, N.
AU - Indik, R.
N1 - Funding Information:
We are grateful for support from AFOSR Contract No. F496209410144-DEF and NSF Grant No. DMS-9302013.
PY - 1996
Y1 - 1996
N2 - We show that defects are weak solutions of the phase diffusion equation for the macroscopic order parameter for natural patterns. Further, by exploring a new class of nontrivial solutions for which the graph of the phase function has vanishing Gaussian curvature (in 3D, all sectional curvatures) except at points, we are able to derive explicit expressions which capture the anatomies of point and line (and surface) defects in two and three dimensional patterns, together with their topological characters and energetic constraints.
AB - We show that defects are weak solutions of the phase diffusion equation for the macroscopic order parameter for natural patterns. Further, by exploring a new class of nontrivial solutions for which the graph of the phase function has vanishing Gaussian curvature (in 3D, all sectional curvatures) except at points, we are able to derive explicit expressions which capture the anatomies of point and line (and surface) defects in two and three dimensional patterns, together with their topological characters and energetic constraints.
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U2 - 10.1016/0167-2789(96)00073-5
DO - 10.1016/0167-2789(96)00073-5
M3 - Article
AN - SCOPUS:0000426270
VL - 97
SP - 185
EP - 205
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-3
ER -