Matches in SemOpenAlex for { <https://semopenalex.org/work/W2069894184> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2069894184 abstract "In the one-dimensional optical analog to Anderson localization, a periodically layered medium has one or more parameters randomly disordered. Such a randomized system can be modeled by an infinite product of 2x2 random transfer matrices with the upper Lyapunov exponent of the matrix product identified as the localization factor (inverse localization length) for the model. The theorem of Furstenberg allows us, at least theoretically, to calculate this upper Lyapunov exponent. In Furstenberg's formula we not only integrate with respect to the probability measure of the random matrices, but also with respect to the invariant probability measure of the direction of the vector propagated by the random matrices. This invariant measure is difficult to find analytically, and, as a result, the most successful approach is to determine the invariant measure numerically. A Monte Carlo simulation which uses accumulated bin counts to track the direction of the propagated vector through a long chain of random matrices does a good job of estimating the invariant probability measure, but with a level of uncertainty. A potentially more accurate numerical technique by Froyland and Aihara obtains the invariant measure as a left eigenvector of a large sparse matrix containing probability values determined by the action of the random matrices on input vectors. We first apply these two techniques to a random Fibonacci sequence whose Lyapunov exponent was determined by Viswanath. We then demonstrate these techniques on a quarter-wave stack model with binary discrete disorder in layer thickness, and compare results to the continuously disordered counterpart." @default.
- W2069894184 created "2016-06-24" @default.
- W2069894184 creator A5081014047 @default.
- W2069894184 date "2009-02-12" @default.
- W2069894184 modified "2023-09-23" @default.
- W2069894184 title "Discretely disordered photonic bandgap structures: a more accurate invariant measure calculation" @default.
- W2069894184 cites W1635208330 @default.
- W2069894184 cites W1969918410 @default.
- W2069894184 cites W1988116220 @default.
- W2069894184 cites W1997815317 @default.
- W2069894184 cites W1998062690 @default.
- W2069894184 cites W2008254969 @default.
- W2069894184 cites W2018855000 @default.
- W2069894184 cites W2035225015 @default.
- W2069894184 cites W2047354095 @default.
- W2069894184 cites W2059121108 @default.
- W2069894184 cites W2074713445 @default.
- W2069894184 cites W2087583851 @default.
- W2069894184 cites W2092205945 @default.
- W2069894184 cites W2094293203 @default.
- W2069894184 cites W2115814323 @default.
- W2069894184 cites W2133353957 @default.
- W2069894184 cites W2145645384 @default.
- W2069894184 cites W593670694 @default.
- W2069894184 doi "https://doi.org/10.1117/12.809489" @default.
- W2069894184 hasPublicationYear "2009" @default.
- W2069894184 type Work @default.
- W2069894184 sameAs 2069894184 @default.
- W2069894184 citedByCount "1" @default.
- W2069894184 crossrefType "proceedings-article" @default.
- W2069894184 hasAuthorship W2069894184A5081014047 @default.
- W2069894184 hasConcept C105795698 @default.
- W2069894184 hasConcept C115667082 @default.
- W2069894184 hasConcept C121332964 @default.
- W2069894184 hasConcept C121864883 @default.
- W2069894184 hasConcept C122044880 @default.
- W2069894184 hasConcept C133654230 @default.
- W2069894184 hasConcept C134306372 @default.
- W2069894184 hasConcept C158622935 @default.
- W2069894184 hasConcept C158693339 @default.
- W2069894184 hasConcept C190470478 @default.
- W2069894184 hasConcept C191544260 @default.
- W2069894184 hasConcept C19499675 @default.
- W2069894184 hasConcept C2780009758 @default.
- W2069894184 hasConcept C33923547 @default.
- W2069894184 hasConcept C37914503 @default.
- W2069894184 hasConcept C41008148 @default.
- W2069894184 hasConcept C62520636 @default.
- W2069894184 hasConcept C64812099 @default.
- W2069894184 hasConcept C77088390 @default.
- W2069894184 hasConcept C77553402 @default.
- W2069894184 hasConceptScore W2069894184C105795698 @default.
- W2069894184 hasConceptScore W2069894184C115667082 @default.
- W2069894184 hasConceptScore W2069894184C121332964 @default.
- W2069894184 hasConceptScore W2069894184C121864883 @default.
- W2069894184 hasConceptScore W2069894184C122044880 @default.
- W2069894184 hasConceptScore W2069894184C133654230 @default.
- W2069894184 hasConceptScore W2069894184C134306372 @default.
- W2069894184 hasConceptScore W2069894184C158622935 @default.
- W2069894184 hasConceptScore W2069894184C158693339 @default.
- W2069894184 hasConceptScore W2069894184C190470478 @default.
- W2069894184 hasConceptScore W2069894184C191544260 @default.
- W2069894184 hasConceptScore W2069894184C19499675 @default.
- W2069894184 hasConceptScore W2069894184C2780009758 @default.
- W2069894184 hasConceptScore W2069894184C33923547 @default.
- W2069894184 hasConceptScore W2069894184C37914503 @default.
- W2069894184 hasConceptScore W2069894184C41008148 @default.
- W2069894184 hasConceptScore W2069894184C62520636 @default.
- W2069894184 hasConceptScore W2069894184C64812099 @default.
- W2069894184 hasConceptScore W2069894184C77088390 @default.
- W2069894184 hasConceptScore W2069894184C77553402 @default.
- W2069894184 hasLocation W20698941841 @default.
- W2069894184 hasOpenAccess W2069894184 @default.
- W2069894184 hasPrimaryLocation W20698941841 @default.
- W2069894184 hasRelatedWork W1998062690 @default.
- W2069894184 hasRelatedWork W2010077002 @default.
- W2069894184 hasRelatedWork W2012081888 @default.
- W2069894184 hasRelatedWork W2053463234 @default.
- W2069894184 hasRelatedWork W2057776604 @default.
- W2069894184 hasRelatedWork W2069894184 @default.
- W2069894184 hasRelatedWork W2074668627 @default.
- W2069894184 hasRelatedWork W2101908586 @default.
- W2069894184 hasRelatedWork W2768879641 @default.
- W2069894184 hasRelatedWork W4301900775 @default.
- W2069894184 isParatext "false" @default.
- W2069894184 isRetracted "false" @default.
- W2069894184 magId "2069894184" @default.
- W2069894184 workType "article" @default.