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Search results for: TOPOLOGICAL PHASES
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Topological Methods in Nonlinear Analysis
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Topological extraordinary optical transmission
PublicationΤhe incumbent technology for bringing light to the nanoscale, the near-field scanning optical microscope, has notoriously small throughput efficiencies of the order of 10^4-10^5 or less. We report on a broadband, topological, unidirectionally guiding structure, not requiring adiabatic tapering and, in principle, enabling near-perfect (∼100%) optical transmission through an unstructured single arbitrarily subdiffraction slit at...
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Construction of phylogenetic trees with topological constraints
PublicationThis paper proposes a method of reconstruction of phylogenetic trees based on heuristic search with topological constraints. Using topological constraints it is possible to reduce the set of solutions as well as to enforce that the result is consistent with a given hypothesis about the evolution process within some group of species. Along with this work a number of algorithms used for phylogenetic analysis were implemented. Those...
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Combinatorial-topological framework for the analysis of global dynamics
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Naval electromagnetic compatibility investigations by use of topological model
PublicationPublikacja przedstawia zagadnienie uwarunkowań kompatybilnościowych na statkach. Ze względu na trudności jakie stwarza analiza EMC dużych obiektów, środowisko elektromagnetyczne okrętów jest zwykle dzielone na fragmenty analizowane oddzielnie. Referat przedstawia topologiczny model środowiska elektromagnetycznego w formie macierzowej, który pozwala na kompleksową analizę zagadnień kompatybilnościowych wielu systemów pracujących...
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On thermal stability of topological qubit in Kitaev's 4D model
PublicationWe analyse stability of the four-dimensional Kitaev model-a candidate for scalable quantum memory - in finite temperature within the weak coupling Markovian limit. It is shown that, below a critical temperature, certain topological qubit observables X and Z possess relaxation times exponentially long in the size of the system. Their construction involves polynomial in system size algorithm which uses as an input the results of...
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Magnetotransport properties of the correlated topological nodal-line semimetal YbCdGe
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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublicationThe grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors...