Probabilistic estimates of the maximum norm of random Neumann Fourier series

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Wacker PK, Blömker D, Wanner T
Zeitschrift: Communications in Nonlinear Science and Numerical Simulation
Jahr der Veröffentlichung: 2017
Band: 47
Seitenbereich: 348 - 369
ISSN: 1007-5704
Sprache: Englisch


Abstract

We study the maximum norm behavior of L2-normalized
random Fourier cosine series with a prescribed large wave number.
Precise bounds of this type are an important technical tool in estimates
for spinodal decomposition, the celebrated phase separation phenomenon
in metal alloys. We derive rigorous asymptotic results as the wave
number converges to infinity, and shed light on the behavior of the
maximum norm for medium range wave numbers through numerical
simulations. Finally, we develop a simplified model for describing the
magnitude of extremal values of random Neumann Fourier series. The model
describes key features of the development of maxima and can be used to
predict them. This is achieved by decoupling magnitude and sign
distribution, where the latter plays an important role for the study of
the size of the maximum norm. Since we are considering series with
Neumann boundary conditions, particular care has to be placed on
understanding the behavior of the random sums at the boundary.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

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


Zitierweisen

APA:
Wacker, P.K., Blömker, D., & Wanner, T. (2017). Probabilistic estimates of the maximum norm of random Neumann Fourier series. Communications in Nonlinear Science and Numerical Simulation, 47, 348 - 369. https://dx.doi.org/10.1016/j.cnsns.2016.11.023

MLA:
Wacker, Philipp Konstantin, Dirk Blömker, and Thomas Wanner. "Probabilistic estimates of the maximum norm of random Neumann Fourier series." Communications in Nonlinear Science and Numerical Simulation 47 (2017): 348 - 369.

BibTeX: 

Zuletzt aktualisiert 2019-26-04 um 14:10