Matches in SemOpenAlex for { <https://semopenalex.org/work/W2893862515> ?p ?o ?g. }
Showing items 1 to 99 of
99
with 100 items per page.
- W2893862515 abstract "The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units whose states are characterized by a scalar angle variable. One such application in which we are interested is the alignment of orientation vectors among members of a swarm. Despite being commonly used for this purpose, the Kuramoto model can only describe swarms in 2 dimensions, and hence the results obtained do not apply to the often relevant situation of swarms in 3 dimensions. Partly based on this motivation, as well as on relevance to the classical, mean-field, zero-temperature Heisenberg model with quenched site disorder, in this paper we study the Kuramoto model generalized to $D$ dimensions. We show that in the important case of 3 dimensions, as well as for any odd number of dimensions, the $D$-dimensional generalized Kuramoto model for heterogeneous units has dynamics that are remarkably different from the dynamics in 2 dimensions. In particular, for odd $D$ the transition to coherence occurs discontinuously as the inter-unit coupling constant $K$ is increased through zero, as opposed to the $D=2$ case (and, as we show, also the case of even $D$) for which the transition to coherence occurs continuously as $K$ increases through a positive critical value $K_c$. We also demonstrate the qualitative applicability of our results to related models constructed specifically to capture swarming and flocking dynamics in three dimensions." @default.
- W2893862515 created "2018-10-05" @default.
- W2893862515 creator A5017906200 @default.
- W2893862515 creator A5068834876 @default.
- W2893862515 creator A5082913931 @default.
- W2893862515 date "2019-01-03" @default.
- W2893862515 modified "2023-09-29" @default.
- W2893862515 title "Continuous versus Discontinuous Transitions in the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math> -Dimensional Generalized Kuramoto Model: Odd <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math> is Different" @default.
- W2893862515 cites W111157985 @default.
- W2893862515 cites W1970464880 @default.
- W2893862515 cites W1989378721 @default.
- W2893862515 cites W2004326222 @default.
- W2893862515 cites W2018314770 @default.
- W2893862515 cites W2019946735 @default.
- W2893862515 cites W2035538683 @default.
- W2893862515 cites W2050040670 @default.
- W2893862515 cites W2085728855 @default.
- W2893862515 cites W2092782423 @default.
- W2893862515 cites W2092812423 @default.
- W2893862515 cites W2106286592 @default.
- W2893862515 cites W2111896942 @default.
- W2893862515 cites W2130518506 @default.
- W2893862515 cites W2135397361 @default.
- W2893862515 cites W2145742480 @default.
- W2893862515 cites W2154344689 @default.
- W2893862515 cites W2158443610 @default.
- W2893862515 cites W2168448159 @default.
- W2893862515 cites W2178920083 @default.
- W2893862515 cites W2557437318 @default.
- W2893862515 cites W2750670530 @default.
- W2893862515 cites W2750743999 @default.
- W2893862515 cites W3037683188 @default.
- W2893862515 cites W3098602446 @default.
- W2893862515 cites W3100825849 @default.
- W2893862515 cites W3100942729 @default.
- W2893862515 cites W3101485430 @default.
- W2893862515 cites W3102551889 @default.
- W2893862515 cites W3103282891 @default.
- W2893862515 cites W3103317772 @default.
- W2893862515 cites W3105553417 @default.
- W2893862515 cites W3125210089 @default.
- W2893862515 cites W612741145 @default.
- W2893862515 doi "https://doi.org/10.1103/physrevx.9.011002" @default.
- W2893862515 hasPublicationYear "2019" @default.
- W2893862515 type Work @default.
- W2893862515 sameAs 2893862515 @default.
- W2893862515 citedByCount "34" @default.
- W2893862515 countsByYear W28938625152019 @default.
- W2893862515 countsByYear W28938625152020 @default.
- W2893862515 countsByYear W28938625152021 @default.
- W2893862515 countsByYear W28938625152022 @default.
- W2893862515 countsByYear W28938625152023 @default.
- W2893862515 crossrefType "journal-article" @default.
- W2893862515 hasAuthorship W2893862515A5017906200 @default.
- W2893862515 hasAuthorship W2893862515A5068834876 @default.
- W2893862515 hasAuthorship W2893862515A5082913931 @default.
- W2893862515 hasBestOaLocation W28938625151 @default.
- W2893862515 hasConcept C114614502 @default.
- W2893862515 hasConcept C121332964 @default.
- W2893862515 hasConcept C121864883 @default.
- W2893862515 hasConcept C184720557 @default.
- W2893862515 hasConcept C2778562939 @default.
- W2893862515 hasConcept C2780042749 @default.
- W2893862515 hasConcept C2781220375 @default.
- W2893862515 hasConcept C33923547 @default.
- W2893862515 hasConcept C37914503 @default.
- W2893862515 hasConcept C62520636 @default.
- W2893862515 hasConceptScore W2893862515C114614502 @default.
- W2893862515 hasConceptScore W2893862515C121332964 @default.
- W2893862515 hasConceptScore W2893862515C121864883 @default.
- W2893862515 hasConceptScore W2893862515C184720557 @default.
- W2893862515 hasConceptScore W2893862515C2778562939 @default.
- W2893862515 hasConceptScore W2893862515C2780042749 @default.
- W2893862515 hasConceptScore W2893862515C2781220375 @default.
- W2893862515 hasConceptScore W2893862515C33923547 @default.
- W2893862515 hasConceptScore W2893862515C37914503 @default.
- W2893862515 hasConceptScore W2893862515C62520636 @default.
- W2893862515 hasFunder F4320337345 @default.
- W2893862515 hasFunder F4320338279 @default.
- W2893862515 hasIssue "1" @default.
- W2893862515 hasLocation W28938625151 @default.
- W2893862515 hasLocation W28938625152 @default.
- W2893862515 hasOpenAccess W2893862515 @default.
- W2893862515 hasPrimaryLocation W28938625151 @default.
- W2893862515 hasRelatedWork W2016925261 @default.
- W2893862515 hasRelatedWork W2093362457 @default.
- W2893862515 hasRelatedWork W2791163263 @default.
- W2893862515 hasRelatedWork W2888394803 @default.
- W2893862515 hasRelatedWork W2971631169 @default.
- W2893862515 hasRelatedWork W3015430560 @default.
- W2893862515 hasRelatedWork W4206311838 @default.
- W2893862515 hasRelatedWork W4295681959 @default.
- W2893862515 hasRelatedWork W3071458276 @default.
- W2893862515 hasRelatedWork W4281670007 @default.
- W2893862515 hasVolume "9" @default.
- W2893862515 isParatext "false" @default.
- W2893862515 isRetracted "false" @default.
- W2893862515 magId "2893862515" @default.
- W2893862515 workType "article" @default.