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From Dirac Structures to Port-Hamiltonian Partial Differential Equations, a Tutorial Introduction [PDF]
EntropyIn this paper, we discuss the geometric structure, i.e., Dirac structure, underlying port-Hamiltonian systems. The paper has a tutorial character, and thus it contains questions/exercises.
Hans Zwart
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Integration of Coupling Dirac Structures [PDF]
Pacific Journal of Mathematics, 2015 Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure.
Brahic, Olivier, Fernandes, Rui Loja
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Dirac structures of omni-Lie algebroids [PDF]
International Journal of Mathematics, 2011 Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid $\dev E\oplus \jet E$ is necessarily a Lie algebroid together with a representation on $E$.
Chen, Zhuo, Liu, Zhangju, Sheng, Yunhe
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Communications in Mathematical Physics, 2022 We study complex Dirac structures, that is, Dirac structures in the complexified generalized tangent bundle. These include presymplectic foliations, transverse holomorphic structures, CR-related geometries and generalized complex structures. We introduce two invariants, the order and the (normalized) type.
Aguero, Dan, Rubio, Roberto||
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Acoustic Tunneling Study for Hexachiral Phononic Crystals Based on Dirac-Cone Dispersion Properties
Crystals, 2021 Acoustic tunneling is an essential property for phononic crystals in a Dirac-cone state. By analyzing the linear dispersion relations for the accidental degeneracy of Bloch eigenstates, the influence of geometric parameters on opening the Dirac-cone ...
Luyun Chen, Yong Liu, Hui Kong
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Dirac–Nijenhuis structures [PDF]
Journal of Physics A: Mathematical and General, 2004 Summary: In this paper, we study the concept of Dirac-Nijenhuis structures. We consider them to be a pair \((D,{\mathcal N})\) where \(D\) is a Dirac structure, defined with respect to a Lie bialgebroid \((A,A^\ast )\), and \({\mathcal N}\) is a Nijenhuis operator which defines a deformation of the Lie algebroid structure of \(D\) in a compatible way ...
Clemente-Gallardo, J. +1 more
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Dirac Cone Characteristics of Hexachiral Phononic Crystal
Shanghai Jiaotong Daxue xuebao, 2021 The band structure properties of phononic crystal is important to evaluate the vibration and noise reduction of acoustic metamaterials. Taking the 2D hexachiral phononic crystal as an example, the band structure and Dirac cone properties were ...
CHEN Luyun, WANG Jian, CUI Yifeng, KONG Hui
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On Higher Dirac Structures [PDF]
International Mathematics Research Notices, 2017 To appear in ...
Bursztyn, Henrique +2 more
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Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures [PDF]
49th IEEE Conference on Decision and Control (CDC), 2010 Comment: 6 ...
Vankerschaver, Joris +3 more
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Mid-Infrared Sensor Based on Dirac Semimetal Coupling Structure
Sensors, 2022 A multilayer structure based on Dirac semimetals is investigated, where long-range surface plasmon resonance (LRSPR) of a dielectric layer/Dirac semimetal/dielectric layer are coupled with surface plasmon polaritons (SPPs) on graphene to substantially ...
Yuxiao Zou, Ying Liu, Guofeng Song
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