Exploiting aperiodic order in technological devices

2008 ◽  
pp. 299-370
Keyword(s):  
Aperiodic Order

scholarly journals Fixed-Parameter Extrapolation and Aperiodic Order

2018 ◽  
Vol 49 (3) ◽  
pp. 35-47
Author(s):  
Stephen Fenner ◽  
Frederic Green ◽  
Steven Homer
Keyword(s):  
Aperiodic Order ◽  
Fixed Parameter

scholarly journals Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials

2018 ◽  
Vol 98 (19) ◽  
Author(s):  
Marino Coppolaro ◽  
Giuseppe Castaldi ◽  
Vincenzo Galdi
Keyword(s):  
Aperiodic Order

scholarly journals A classification of aperiodic order via spectral metrics and Jarník sets

2018 ◽  
Vol 39 (11) ◽  
pp. 3031-3065 ◽  
Author(s):  
MAIK GRÖGER ◽  
MARC KESSEBÖHMER ◽  
ARNE MOSBACH ◽  
TONY SAMUEL ◽  
MALTE STEFFENS
Keyword(s):  
Hausdorff Dimension ◽  
Level Sets ◽  
Continued Fraction ◽  
Regularity Condition ◽  
Hölder Regularity ◽  
Aperiodic Order ◽  
Holder Regularity

Given an$\unicode[STIX]{x1D6FC}>1$and a$\unicode[STIX]{x1D703}$with unbounded continued fraction entries, we characterize new relations between Sturmian subshifts with slope$\unicode[STIX]{x1D703}$with respect to (i) an$\unicode[STIX]{x1D6FC}$-Hölder regularity condition of a spectral metric, (ii) level sets defined in terms of the Diophantine properties of$\unicode[STIX]{x1D703}$, and (iii) complexity notions which we call$\unicode[STIX]{x1D6FC}$-repetitiveness,$\unicode[STIX]{x1D6FC}$-repulsiveness and$\unicode[STIX]{x1D6FC}$-finiteness—generalizations of the properties known as linear repetitiveness, repulsiveness and power freeness, respectively. We show that the level sets relate naturally to (exact) Jarník sets and prove that their Hausdorff dimension is$2/(\unicode[STIX]{x1D6FC}+1)$.

scholarly journals Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order

2017 ◽  
Vol 370 (3-4) ◽  
pp. 1607-1637 ◽  
Author(s):  
Rostislav Grigorchuk ◽  
Daniel Lenz ◽  
Tatiana Nagnibeda
Keyword(s):  
Schroedinger Operators ◽  
Schreier Graphs ◽  
Aperiodic Order

scholarly journals Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula

2021 ◽  
Vol 281 (12) ◽  
pp. 109265
Author(s):  
Michael Björklund ◽  
Tobias Hartnick ◽  
Felix Pogorzelski
Keyword(s):  
Aperiodic Order
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