Pattern size in Gaussian fields from spinodal decomposition

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Wacker PK, Bianchi LA, Blömker D
Zeitschrift: SIAM Journal on Applied Mathematics
Jahr der Veröffentlichung: 2017
Band: 77
Heftnummer: 4
Seitenbereich: 1292 - 1319
ISSN: 0036-1399


Abstract

We
study the two-dimensional snake-like pattern that arises in phase
separation of alloys described by spinodal decomposition in the
Cahn-Hilliard model. These are somewhat universal patterns due to an
overlay of eigenfunctions of the Laplacian with a similar wave-number.
Similar structures appear in other models like reaction-diffusion
systems describing animal coats' patterns or vegetation patterns in
desertification.
Our main result studies random functions given by cosine Fourier
series with independent Gaussian coefficients, that dominate the
dynamics in the Cahn-Hilliard model. This is not a cosine process, as
the sum is taken over domains in Fourier space that not only grow and
scale with a parameter of order 1/ε,
but also move to infinity. Moreover, the model under consideration is
neither stationary nor isotropic.
To study the pattern size of nodal domains we consider the density of
zeros on any straight line through the spatial domain. Using a theorem
by Edelman and Kostlan and weighted ergodic theorems that ensure the
convergence of the moving sums, we show that the average distance of
zeros is asymptotically of order ε with a precisely given constant.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Wacker, Philipp Konstantin Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Zitierweisen

APA:
Wacker, P.K., Bianchi, L.A., & Blömker, D. (2017). Pattern size in Gaussian fields from spinodal decomposition. SIAM Journal on Applied Mathematics, 77(4), 1292 - 1319. https://dx.doi.org/10.1137/15M1052081

MLA:
Wacker, Philipp Konstantin, Luigi Amedeo Bianchi, and Dirk Blömker. "Pattern size in Gaussian fields from spinodal decomposition." SIAM Journal on Applied Mathematics 77.4 (2017): 1292 - 1319.

BibTeX: 

Zuletzt aktualisiert 2019-26-04 um 13:10