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Topological phases on non-periodic latticesJha, Mani Chandra 13 May 2024 (has links)
The investigation into topological phases on non-periodic lattices has recently gained wide interest because of the discovery of never-before seen phenomena lacking a counterpart in periodic lattices. In this thesis, I present the results of my work on the lattice Laughlin state on fractal lattices and that of the BHZ model on quasicrystals. I show that the entanglement spectrum has the same topological fingerprint as in periodic lattices, and thus can be used as a probe of topological order in these new environments, where such probes are severely lacking, especially for interacting topological phases. I also show how the entanglement entropy displays precise oscillations as a function of lattice filling in fractal lattices, and is smooth for periodic lattices. I study the on-site particle densities, and anyonic excitations on different kinds of fractal lattices and show how radically different they are from the 2D case.
Finally, I study the BHZ model on the Amman-Beenker tiling and show the different kinds of Bulk Localized Transport(BLT) states, the edge states, and how the latter can be used to pump charge between different kind of BLT states. I couple two layers of the half-BHZ, which are time-reversed partners of each other, with a simple time-reversal symmetric hopping, and show that the BLT and edge states still survive.
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Analysis of Vibration of 2-D Periodic Cellular StructuresJeong, Sang Min 19 May 2005 (has links)
The vibration of and wave propagation in periodic cellular structures
are analyzed. Cellular structures exhibit a number of desirable
multifunctional properties, which make them attractive in a variety of
engineering applications. These include ultra-light structures, thermal
and acoustic insulators, and impact amelioration systems, among others.
Cellular structures with deterministic architecture can be considered
as example of periodic structures. Periodic structures feature unique
wave propagation characteristics, whereby elastic waves propagate only
in specific frequency bands, known as "pass band", while they are
attenuated in all other frequency bands, known as "stop bands". Such
dynamic properties are here exploited to provide cellular structures
with the capability of behaving as directional, pass-band mechanical
filters, thus complementing their well documented multifunctional
characteristics.
This work presents a methodology for the analysis of the dynamic
behavior of periodic cellular structures, which allows the evaluation
of location and spectral width of propagation and attenuation regions.
The filtering characteristics are tested and demonstrated for
structures of various geometry and topology, including cylindrical
grid-like structures, Kagom and eacute; and tetrhedral truss core lattices.
Experimental investigations is done on a 2-D lattice manufactured out
of aluminum. The complete wave field of the specimen at various
frequencies is measured using a Scanning Laser Doppler Vibrometer
(SLDV). Experimental results show good agreement with the methodology
and computational tools developed in this work. The results demonstrate
how wave propagation characteristics are defined by cell geometry and
configuration. Numerical and experimental results show the potential of
periodic cellular structures as mechanical filters and/or isolators of
vibrations.
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Collective dynamics of weakly coupled nonlinear periodic structures / Dynamique collective des structures périodiques non-linéaires faiblement coupléesBitar, Diala 21 February 2017 (has links)
Bien que la dynamique des réseaux périodiques non-linéaires ait été investiguée dans les domainestemporel et fréquentiel, il existe un réel besoin d’identifier des relations pratiques avec lephénomène de la localisation d’énergie en termes d’interactions modales et topologies de bifurcation.L’objectif principal de cette thèse consiste à exploiter le phénomène de la localisation pourmodéliser la dynamique collective d’un réseau périodique de résonateurs non-linéaires faiblementcouplés.Un modèle analytico-numérique a été développé pour étudier la dynamique collective d’unréseau périodique d’oscillateurs non-linéaires couplés sous excitations simultanées primaire et paramétrique,où les interactions modales, les topologies de bifurcations et les bassins d’attraction ontété analysés. Des réseaux de pendules et de nano-poutres couplés électrostatiquement ont étéinvestigués sous excitation extérieure et paramétrique, respectivement. Il a été démontré qu’enaugmentant le nombre d’oscillateurs, le nombre de solutions multimodales et la distribution desbassins d’attraction des branches résonantes augmentent. Ce modèle a été étendu pour investiguerla dynamique collective des réseaux 2D de pendules couplés et de billes sphériques en compressionsous excitation à la base, où la dynamique collective est plus riche avec des amplitudes de vibrationplus importantes et des bandes passantes plus larges. Une deuxième investigation de cettethèse consiste à identifier les solitons associés à la dynamique collective d’un réseau périodique etd’étudier sa stabilité. / Although the dynamics of periodic nonlinear lattices was thoroughly investigated in the frequencyand time-space domains, there is a real need to perform profound analysis of the collectivedynamics of such systems in order to identify practical relations with the nonlinear energy localizationphenomenon in terms of modal interactions and bifurcation topologies. The principal goal ofthis thesis consists in exploring the localization phenomenon for modeling the collective dynamicsof periodic arrays of weakly coupled nonlinear resonators.An analytico-numerical model has been developed in order to study the collective dynamics ofa periodic coupled nonlinear oscillators array under simultaneous primary and parametric excitations,where the bifurcation topologies, the modal interactions and the basins of attraction havebeen analyzed. Arrays of coupled pendulums and electrostatically coupled nanobeams under externaland parametric excitations respectively were considered. It is shown that by increasing thenumber of coupled oscillators, the number of multimodal solutions and the distribution of the basinsof attraction of the resonant solutions increase. The model was extended to investigate the collectivedynamics of periodic nonlinear 2D arrays of coupled pendulums and spherical particles underbase excitation, leading to additional features, mainly larger bandwidth and important vibrationalamplitudes. A second investigation of this thesis consists in identifying the solitons associated tothe collective nonlinear dynamics of the considered arrays of periodic structures and the study oftheir stability.
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