Hocking, John G
1988-01-01
""As textbook and reference work, this is a valuable addition to the topological literature."" - Mathematical ReviewsDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff t
Manetti, Marco
2015-01-01
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
An archaebacterial homologue of the essential eubacterial cell division protein FtsZ.
Baumann, P; Jackson, S P
1996-06-25
Life falls into three fundamental domains--Archaea, Bacteria, and Eucarya (formerly archaebacteria, eubacteria, and eukaryotes,. respectively). Though Archaea lack nuclei and share many morphological features with Bacteria, molecular analyses, principally of the transcription and translation machineries, have suggested that Archaea are more related to Eucarya than to Bacteria. Currently, little is known about the archaeal cell division apparatus. In Bacteria, a crucial component of the cell division machinery is FtsZ, a GTPase that localizes to a ring at the site of septation. Interestingly, FtsZ is distantly related in sequence to eukaryotic tubulins, which also interact with GTP and are components of the eukaryotic cell cytoskeleton. By screening for the ability to bind radiolabeled nucleotides, we have identified a protein of the hyperthermophilic archaeon Pyrococcus woesei that interacts tightly and specifically with GTP. Furthermore, through screening an expression library of P. woesei genomic DNA, we have cloned the gene encoding this protein. Sequence comparisons reveal that the P. woesei GTP-binding protein is strikingly related in sequence to eubacterial FtsZ and is marginally more similar to eukaryotic tubulins than are bacterial FtsZ proteins. Phylogenetic analyses reinforce the notion that there is an evolutionary linkage between FtsZ and tubulins. These findings suggest that the archaeal cell division apparatus may be fundamentally similar to that of Bacteria and lead us to consider the evolutionary relationships between Archaea, Bacteria, and Eucarya.
Effect of exercise on patient specific abdominal aortic aneurysm flow topology and mixing.
Arzani, Amirhossein; Les, Andrea S; Dalman, Ronald L; Shadden, Shawn C
2014-02-01
Computational fluid dynamics modeling was used to investigate changes in blood transport topology between rest and exercise conditions in five patient-specific abdominal aortic aneurysm models. MRI was used to provide the vascular anatomy and necessary boundary conditions for simulating blood velocity and pressure fields inside each model. Finite-time Lyapunov exponent fields and associated Lagrangian coherent structures were computed from blood velocity data and were used to compare features of the transport topology between rest and exercise both mechanistically and qualitatively. A mix-norm and mix-variance measure based on fresh blood distribution throughout the aneurysm over time were implemented to quantitatively compare mixing between rest and exercise. Exercise conditions resulted in higher and more uniform mixing and reduced the overall residence time in all aneurysms. Separated regions of recirculating flow were commonly observed in rest, and these regions were either reduced or removed by attached and unidirectional flow during exercise, or replaced with regional chaotic and transiently turbulent mixing, or persisted and even extended during exercise. The main factor that dictated the change in flow topology from rest to exercise was the behavior of the jet of blood penetrating into the aneurysm during systole. Copyright © 2013 John Wiley & Sons, Ltd.
Photoaffinity labeling of the pactamycin binding site on eubacterial ribosomes
International Nuclear Information System (INIS)
Tejedor, F.; Amils, R.; Ballesta, J.P.
1985-01-01
Pactamycin, an inhibitor of the initial steps of protein synthesis, has an acetophenone group in its chemical structure that makes the drug a potentially photoreactive molecule. In addition, the presence of a phenolic residue makes it easily susceptible to radioactive labeling. Through iodination, one radioactive derivative of pactamycin has been obtained with biological activities similar to the unmodified drug when tested on in vivo and cell-free systems. With the use of [ 125 I]iodopactamycin, ribosomes of Escherichia coli have been photolabeled under conditions that preserve the activity of the particles and guarantee the specificity of the binding sites. Under these conditions, RNA is preferentially labeled when free, small ribosomal subunits are photolabeled, but proteins are the main target in the whole ribosome. This indicates that an important conformational change takes place in the binding site on association of the two subunits. The major labeled proteins are S2, S4, S18, S21, and L13. These proteins in the pactamycin binding site are probably related to the initiation step of protein synthesis
Motif formation and industry specific topologies in the Japanese business firm network
Maluck, Julian; Donner, Reik V.; Takayasu, Hideki; Takayasu, Misako
2017-05-01
Motifs and roles are basic quantities for the characterization of interactions among 3-node subsets in complex networks. In this work, we investigate how the distribution of 3-node motifs can be influenced by modifying the rules of an evolving network model while keeping the statistics of simpler network characteristics, such as the link density and the degree distribution, invariant. We exemplify this problem for the special case of the Japanese Business Firm Network, where a well-studied and relatively simple yet realistic evolving network model is available, and compare the resulting motif distribution in the real-world and simulated networks. To better approximate the motif distribution of the real-world network in the model, we introduce both subgraph dependent and global additional rules. We find that a specific rule that allows only for the merging process between nodes with similar link directionality patterns reduces the observed excess of densely connected motifs with bidirectional links. Our study improves the mechanistic understanding of motif formation in evolving network models to better describe the characteristic features of real-world networks with a scale-free topology.
Nucleotide compositional asymmetry between the leading and lagging strands of eubacterial genomes
Qu, Hongzhu; Wu, Hao; Zhang, Tongwu; Zhang, Zhang; Hu, Songnian; Yu, Jun
2010-01-01
Nucleotide compositional asymmetry (NCA) between leading and lagging strands (LeS and LaS) is dynamic and diverse among eubacterial genomes due to different mutation and selection forces. A thorough investigation is needed in order to study the relationship between nucleotide composition dynamics and gene distribution biases. Based on a collection of 364 eubacterial genomes that were grouped according to a DnaE-based scheme (DnaE1-DnaE1, DnaE2-DnaE1, and DnaE3-PolC), we investigated NCA and nucleotide composition gradients at three codon positions and found that there was universal G-enrichment on LeS among all groups. This was due to a strong selection for G-heading (codon position1 or cp1) codons and mutation pressure that led to more G-ending (cp3) codons. Moreover, a slight T-enrichment of LeS due to the mutation of cytosine deamination at cp3 was universal among DnaE1-DnaE1 and DnaE2-DnaE1 genomes, but was not clearly seen among DnaE3-PolC genomes, in which A-enrichment of LeS was proposed to be the effect of selections unique to polC and a mutation bias toward A-richness at cp1 that may be a result of transcription-coupled DNA repair mechanisms. Furthermore, strand-biased gene distribution enhances the purine-richness of LeS for DnaE3-PolC genomes and T-richness of LeS for DnaE1-DnaE1 and DnaE2-dnaE1 genomes. © 2010 Institut Pasteur.
Nucleotide compositional asymmetry between the leading and lagging strands of eubacterial genomes
Qu, Hongzhu
2010-12-01
Nucleotide compositional asymmetry (NCA) between leading and lagging strands (LeS and LaS) is dynamic and diverse among eubacterial genomes due to different mutation and selection forces. A thorough investigation is needed in order to study the relationship between nucleotide composition dynamics and gene distribution biases. Based on a collection of 364 eubacterial genomes that were grouped according to a DnaE-based scheme (DnaE1-DnaE1, DnaE2-DnaE1, and DnaE3-PolC), we investigated NCA and nucleotide composition gradients at three codon positions and found that there was universal G-enrichment on LeS among all groups. This was due to a strong selection for G-heading (codon position1 or cp1) codons and mutation pressure that led to more G-ending (cp3) codons. Moreover, a slight T-enrichment of LeS due to the mutation of cytosine deamination at cp3 was universal among DnaE1-DnaE1 and DnaE2-DnaE1 genomes, but was not clearly seen among DnaE3-PolC genomes, in which A-enrichment of LeS was proposed to be the effect of selections unique to polC and a mutation bias toward A-richness at cp1 that may be a result of transcription-coupled DNA repair mechanisms. Furthermore, strand-biased gene distribution enhances the purine-richness of LeS for DnaE3-PolC genomes and T-richness of LeS for DnaE1-DnaE1 and DnaE2-dnaE1 genomes. © 2010 Institut Pasteur.
1972-01-01
A unified approach to computer vision and manipulation is developed which is called choreographic vision. In the model, objects to be viewed by a projected robot in the Viking missions to Mars are seen as objects to be manipulated within choreographic contexts controlled by a multimoded remote, supervisory control system on Earth. A new theory of context relations is introduced as a basis for choreographic programming languages. A topological vision model is developed for recognizing objects by shape and contour. This model is integrated with a projected vision system consisting of a multiaperture image dissector TV camera and a ranging laser system. System program specifications integrate eye-hand coordination and topological vision functions and an aerospace multiprocessor implementation is described.
Sun, Wei; Jin, Junfei; Xu, Ruijuan; Hu, Wei; Szulc, Zdzislaw M.; Bielawski, Jacek; Obeid, Lina M.; Mao, Cungui
2010-01-01
Human alkaline ceramidase 2 (ACER2) plays an important role in cellular responses by regulating the hydrolysis of ceramides in cells. Here we report its biochemical characterization, membrane topology, and activity regulation. Recombinant ACER2 was expressed in yeast mutant cells (Δypc1Δydc1) that lack endogenous ceramidase activity, and microsomes from ACER2-expressiong yeast cells were used to biochemically characterize ACER2. ACER2 catalyzed the hydrolysis of various ceramides and followed...
Tran, Tam N T; Shelton, Jennifer; Brown, Susan; Durrett, Timothy P
2017-10-01
Euonymus alatus diacylglycerol acetyltransferase (EaDAcT) catalyzes the transfer of an acetyl group from acetyl-CoA to the sn-3 position of diacylglycerol to form 3-acetyl-1,2-diacyl-sn-glycerol (acetyl-TAG). EaDAcT belongs to a small, plant-specific subfamily of the membrane bound O-acyltransferases (MBOAT) that acylate different lipid substrates. Sucrose gradient density centrifugation revealed that EaDAcT colocalizes to the same fractions as an endoplasmic reticulum (ER)-specific marker. By mapping the membrane topology of EaDAcT, we obtained an experimentally determined topology model for a plant MBOAT. The EaDAcT model contains four transmembrane domains (TMDs), with both the N- and C-termini orientated toward the lumen of the ER. In addition, there is a large cytoplasmic loop between the first and second TMDs, with the MBOAT signature region of the protein embedded in the third TMD close to the interface between the membrane and the cytoplasm. During topology mapping, we discovered two cysteine residues (C187 and C293) located on opposite sides of the membrane that are important for enzyme activity. In order to identify additional amino acid residues important for acetyltransferase activity, we isolated and characterized acetyltransferases from other acetyl-TAG-producing plants. Among them, the acetyltransferase from Euonymus fortunei possessed the highest activity in vivo and in vitro. Mutagenesis of conserved amino acids revealed that S253, H257, D258 and V263 are essential for EaDAcT activity. Alteration of residues unique to the acetyltransferases did not alter the unique acyl donor specificity of EaDAcT, suggesting that multiple amino acids are important for substrate recognition. © 2017 The Authors The Plant Journal © 2017 John Wiley & Sons Ltd.
Energy Technology Data Exchange (ETDEWEB)
Larraga, V; Munoz, E [Consejo Superior de Investigaciones Cientificas, Madrid (Spain). Instituto de Biologia Celular
1975-05-01
The paper reports about an investigation into the question of the specific labelling and topological distribution of glycoproteins and proteins in Streptomyces albus membranes. The method of sample preparation is described: Tritium labelling of glycoproteins in protoplasts and membranes, iodination of proteins, trypsin treatment and polyacrylamide gel electrophoresis. The findings suggest an asymmetrical distribution of the glycoproteins in membranes and a weak accessibility to iodine label. A structural model of the plasma membranes of Streptomyces albus is proposed similar to the general 'fluid mosaic' model of Singer and Nicholson.
A family of fluoride-specific ion channels with dual-topology architecture.
Stockbridge, Randy B; Robertson, Janice L; Kolmakova-Partensky, Ludmila; Miller, Christopher
2013-08-27
Fluoride ion, ubiquitous in soil, water, and marine environments, is a chronic threat to microorganisms. Many prokaryotes, archea, unicellular eukaryotes, and plants use a recently discovered family of F(-) exporter proteins to lower cytoplasmic F(-) levels to counteract the anion's toxicity. We show here that these 'Fluc' proteins, purified and reconstituted in liposomes and planar phospholipid bilayers, form constitutively open anion channels with extreme selectivity for F(-) over Cl(-). The active channel is a dimer of identical or homologous subunits arranged in antiparallel transmembrane orientation. This dual-topology assembly has not previously been seen in ion channels but is known in multidrug transporters of the SMR family, and is suggestive of an evolutionary antecedent of the inverted repeats found within the subunits of many membrane transport proteins. DOI:http://dx.doi.org/10.7554/eLife.01084.001.
Free Boolean Topological Groups
Directory of Open Access Journals (Sweden)
Ol’ga Sipacheva
2015-11-01
Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.
The Impact of DNA Topology and Guide Length on Target Selection by a Cytosine-Specific Cas9.
Tsui, Tsz Kin Martin; Hand, Travis H; Duboy, Emily C; Li, Hong
2017-06-16
Cas9 is an RNA-guided DNA cleavage enzyme being actively developed for genome editing and gene regulation. To be cleaved by Cas9, a double stranded DNA, or the protospacer, must be complementary to the guide region, typically 20-nucleotides in length, of the Cas9-bound guide RNA, and adjacent to a short Cas9-specific element called Protospacer Adjacent Motif (PAM). Understanding the correct juxtaposition of the protospacer- and PAM-interaction with Cas9 will enable development of versatile and safe Cas9-based technology. We report identification and biochemical characterization of Cas9 from Acidothermus cellulolyticus (AceCas9). AceCas9 depends on a 5'-NNNCC-3' PAM and is more efficient in cleaving negative supercoils than relaxed DNA. Kinetic as well as in vivo activity assays reveal that AceCas9 achieves optimal activity when combined with a guide RNA containing a 24-nucleotide complementarity region. The cytosine-specific, DNA topology-sensitive, and extended guide-dependent properties of AceCas9 may be explored for specific genome editing applications.
Nomura, Yurika; Ito, Shota; Teranishi, Miwako; Ono, Hikaru; Inoue, Keiichi; Kandori, Hideki
2018-01-31
Light-driven H + , Na + and Cl - pumps have been found in eubacteria, which convert light energy into a transmembrane electrochemical potential. A recent mutation study revealed asymmetric functional conversion between the two pumps, where successful functional conversions are achieved exclusively when mutagenesis reverses the evolutionary amino acid sequence changes. Although this fact suggests that the essential structural mechanism of an ancestral function is retained even after gaining a new function, questions regarding the essential structural mechanism remain unanswered. Light-induced difference FTIR spectroscopy was used to monitor the presence of strongly hydrogen-bonded water molecules for all eubacterial H + , Na + and Cl - pumps, including a functionally converted mutant. This fact suggests that the strongly hydrogen-bonded water molecules are maintained for these new functions during evolution, which could be the reason for successful functional conversion from Na + to H + , and from Cl - to H + pumps. This also explains the successful conversion of the Cl - to the H + pump only for eubacteria, but not for archaea. It is concluded that water-containing hydrogen-bonding networks constitute one of the essential structural mechanisms in eubacterial light-driven ion pumps.
Foundations of topological racks and quandles
Mohamed Moutuou, El-Kaioum; Elhamdadi, Mohamed
2016-01-01
We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step towards a general continuous cohomology theory for topological racks and quandles
Silva-Santiago, Evangelina; Pardo, Juan Pablo; Hernández-Muñoz, Rolando; Aranda-Anzaldo, Armando
2017-01-15
During the interphase the nuclear DNA of metazoan cells is organized in supercoiled loops anchored to constituents of a nuclear substructure or compartment known as the nuclear matrix. The stable interactions between DNA and the nuclear matrix (NM) correspond to a set of topological relationships that define a nuclear higher-order structure (NHOS). Current evidence suggests that the NHOS is cell-type-specific. Biophysical evidence and theoretical models suggest that thermodynamic and structural constraints drive the actualization of DNA-NM interactions. However, if the topological relationships between DNA and the NM were the subject of any biological constraint with functional significance then they must be adaptive and thus be positively selected by natural selection and they should be reasonably conserved, at least within closely related species. We carried out a coarse-grained, comparative evaluation of the DNA-NM topological relationships in primary hepatocytes from two closely related mammals: rat and mouse, by determining the relative position to the NM of a limited set of target sequences corresponding to highly-conserved genomic regions that also represent a sample of distinct chromosome territories within the interphase nucleus. Our results indicate that the pattern of topological relationships between DNA and the NM is not conserved between the hepatocytes of the two closely related species, suggesting that the NHOS, like the karyotype, is species-specific. Copyright © 2016 Elsevier B.V. All rights reserved.
Willard, Stephen
2004-01-01
Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: ""continuous topology,"" represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and ""geometric topology,"" covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340
Ferrarini, Luca; Veer, Ilya M; van Lew, Baldur; Oei, Nicole Y L; van Buchem, Mark A; Reiber, Johan H C; Rombouts, Serge A R B; Milles, J
2011-06-01
In recent years, graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain. Most of these networks have shown small-world topological characteristics: high efficiency in long distance communication between nodes, combined with highly interconnected local clusters of nodes. Moreover, functional studies performed at high resolutions have presented convincing evidence that resting-state functional connectivity networks exhibits (exponentially truncated) scale-free behavior. Such evidence, however, was mostly presented qualitatively, in terms of linear regressions of the degree distributions on log-log plots. Even when quantitative measures were given, these were usually limited to the r(2) correlation coefficient. However, the r(2) statistic is not an optimal estimator of explained variance, when dealing with (truncated) power-law models. Recent developments in statistics have introduced new non-parametric approaches, based on the Kolmogorov-Smirnov test, for the problem of model selection. In this work, we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest. The analysis, performed at voxel level and in a subject-specific fashion, confirmed the superiority of a truncated power-law model, showing high consistency across subjects. Moreover, the most highly connected voxels were found to be consistently part of the default mode network. Our results provide statistically sound support to the evidence previously presented in literature for a truncated power-law model of resting-state functional connectivity. Copyright © 2010 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Rishi Das Roy
2014-06-01
Full Text Available Eubacterial genomes vary considerably in their nucleotide composition. The percentage of genetic material constituted by guanosine and cytosine (GC nucleotides ranges from 20% to 70%. It has been posited that GC-poor organisms are more dependent on protein folding machinery. Previous studies have ascribed this to the accumulation of mildly deleterious mutations in these organisms due to population bottlenecks. This phenomenon has been supported by protein folding simulations, which showed that proteins encoded by GC-poor organisms are more prone to aggregation than proteins encoded by GC-rich organisms. To test this proposition using a genome-wide approach, we classified different eubacterial proteomes in terms of their aggregation propensity and chaperone-dependence using multiple machine learning models. In contrast to the expected decrease in protein aggregation with an increase in GC richness, we found that the aggregation propensity of proteomes increases with GC content. A similar and even more significant correlation was obtained with the GroEL-dependence of proteomes: GC-poor proteomes have evolved to be less dependent on GroEL than GC-rich proteomes. We thus propose that a decrease in eubacterial GC content may have been selected in organisms facing proteostasis problems.
Topological insulators and topological superconductors
Bernevig, Andrei B
2013-01-01
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topolo...
Topological Methods for Visualization
Energy Technology Data Exchange (ETDEWEB)
Berres, Anne Sabine [Los Alamos National Lab. (LANL), Los Alamos, NM (United Stat
2016-04-07
This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.
Goodman, Sue E
2009-01-01
Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while i
Buchin, K.; Buchin, M.; Wagner, D.; Wattenhofer, R.
2007-01-01
Information between two nodes in a network is sent based on the network topology, the structure of links connecting pairs of nodes of a network. The task of topology control is to choose a connecting subset from all possible links such that the overall network performance is good. For instance, a
Wang, Lei; Luo, Hubin; Deng, Shenghua; Sun, Ying; Wang, Cong
2017-12-18
The well-known idea of "structure determines properties" can be understood profoundly in the case of hexagonal zinc dicyanometalate. Using density functional theory (DFT) calculations, we show the uniaxial negative thermal expansion (NTE) and negative linear compressibility (NLC) properties of Zn[Au(CN) 2 ] 2 . The temperature dependence of phonon frequencies within the quasi-harmonic approximation (QHA) is investigated. The abnormal phonon hardening (frequency increase on heating) is detected in the ranges of 0-225, 320-345, and 410-430 cm -1 , which can be indicative of the unusual physical properties of Zn[Au(CN) 2 ] 2 . Due to the significance of low-energy phonon frequencies in Zn[Au(CN) 2 ] 2 , in this work, the corresponding vibrational mode of the lowest-frequency optical phonon at the zone center is analyzed. The specific topology of a springlike framework that will produce the effects of a compressed spring on heating and an extended spring under hydrostatic pressure is identified and leads to the coexistence of uniaxial-NTE and NLC behaviors in Zn[Au(CN) 2 ] 2 . The distinguishing phonon group velocity along the a axis and c axis facilitates different responses for both the axes under temperature and hydrostatic pressure field. Through an analysis and visualization of the spatial dependence of elastic tensors, it is found that a negative Poisson's ratio (NPR) is presented in all projection planes due to the specific topology.
Buchstaber, Victor M
2015-01-01
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v
Franz, Marcel
2013-01-01
Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was
Directory of Open Access Journals (Sweden)
Yu-Ling Shih
Full Text Available Pole-to-pole oscillations of the Min proteins in Escherichia coli are required for the proper placement of the division septum. Direct interaction of MinE with the cell membrane is critical for the dynamic behavior of the Min system. In vitro, this MinE-membrane interaction led to membrane deformation; however, the underlying mechanism remained unclear. Here we report that MinE-induced membrane deformation involves the formation of an amphipathic helix of MinE(2-9, which, together with the adjacent basic residues, function as membrane anchors. Biochemical evidence suggested that the membrane association induces formation of the helix, with the helical face, consisting of A2, L3, and F6, inserted into the membrane. Insertion of this helix into the cell membrane can influence local membrane curvature and lead to drastic changes in membrane topology. Accordingly, MinE showed characteristic features of protein-induced membrane tubulation and lipid clustering in in vitro reconstituted systems. In conclusion, MinE shares common protein signatures with a group of membrane trafficking proteins in eukaryotic cells. These MinE signatures appear to affect membrane curvature.
Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile
2015-03-01
The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.
Luminet, Jean-Pierre
2015-08-01
Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.
Schmidt, Gunther
2018-01-01
This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
DEFF Research Database (Denmark)
A. Kristensen, Anders Schmidt; Damkilde, Lars
2007-01-01
. A way to solve the initial design problem namely finding a form can be solved by so-called topology optimization. The idea is to define a design region and an amount of material. The loads and supports are also fidefined, and the algorithm finds the optimal material distribution. The objective function...... dictates the form, and the designer can choose e.g. maximum stiness, maximum allowable stresses or maximum lowest eigenfrequency. The result of the topology optimization is a relatively coarse map of material layout. This design can be transferred to a CAD system and given the necessary geometrically...... refinements, and then remeshed and reanalysed in other to secure that the design requirements are met correctly. The output of standard topology optimization has seldom well-defined, sharp contours leaving the designer with a tedious interpretation, which often results in less optimal structures. In the paper...
Arnold, Vladimir; Zorich, Anton
1999-01-01
This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors … have done much to s
Warner, S
1993-01-01
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn''s Lemma, is also expected.
Kostov, Ivan
2010-01-01
We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and show their equivalence. The CFT approach reformulates the problem in terms of a conformal field theory on a Riemann surface, while the topological recursion is based on a recurrence equation for the observables representing symplectic invariants on the complex curve. The two approaches lead to two different graph expansions, one of which can be obtained as a partial resummation of the other.
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
DEFF Research Database (Denmark)
Bendsøe, Martin P.; Sigmund, Ole
2007-01-01
Taking as a starting point a design case for a compliant mechanism (a force inverter), the fundamental elements of topology optimization are described. The basis for the developments is a FEM format for this design problem and emphasis is given to the parameterization of design as a raster image...
Manufacturing tolerant topology optimization
DEFF Research Database (Denmark)
Sigmund, Ole
2009-01-01
In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick...... (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization...... approach, under- and over-etching is modelled by image processing-based "erode" and "dilate" operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show...
Lin, Wen-Hsien; Liu, Wei-Chung; Hwang, Ming-Jing
2009-03-11
Human cells of various tissue types differ greatly in morphology despite having the same set of genetic information. Some genes are expressed in all cell types to perform house-keeping functions, while some are selectively expressed to perform tissue-specific functions. In this study, we wished to elucidate how proteins encoded by human house-keeping genes and tissue-specific genes are organized in human protein-protein interaction networks. We constructed protein-protein interaction networks for different tissue types using two gene expression datasets and one protein-protein interaction database. We then calculated three network indices of topological importance, the degree, closeness, and betweenness centralities, to measure the network position of proteins encoded by house-keeping and tissue-specific genes, and quantified their local connectivity structure. Compared to a random selection of proteins, house-keeping gene-encoded proteins tended to have a greater number of directly interacting neighbors and occupy network positions in several shortest paths of interaction between protein pairs, whereas tissue-specific gene-encoded proteins did not. In addition, house-keeping gene-encoded proteins tended to connect with other house-keeping gene-encoded proteins in all tissue types, whereas tissue-specific gene-encoded proteins also tended to connect with other tissue-specific gene-encoded proteins, but only in approximately half of the tissue types examined. Our analysis showed that house-keeping gene-encoded proteins tend to occupy important network positions, while those encoded by tissue-specific genes do not. The biological implications of our findings were discussed and we proposed a hypothesis regarding how cells organize their protein tools in protein-protein interaction networks. Our results led us to speculate that house-keeping gene-encoded proteins might form a core in human protein-protein interaction networks, while clusters of tissue-specific gene
Directory of Open Access Journals (Sweden)
Tiago Simas
Full Text Available The human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (metric, such that there is no alternative path that is accumulatively stronger, or indirect (semi-metric, where one or more alternative paths exist that have greater strength than the direct edge. The sensitivity and specificity of this method of analysis is illustrated by two case-control analyses with independent, matched groups of adolescents with autism spectrum conditions (ASC and major depressive disorder (MDD.Significance differences in the global percentage of semi-metric edges was observed in both groups, with increases in ASC and decreases in MDD relative to controls. Furthermore, MDD was associated with regional differences in left frontal and temporal lobes, the right limbic system and cerebellum. In contrast, ASC had a broadly increased percentage of semi-metric edges with a more generalised distribution of effects and some areas of reduction. In summary, MDD was characterised by localised, large reductions in the percentage of semi-metric edges, whilst ASC is characterised by more generalised, subtle increases. These differences were corroborated in greater detail by inspection of the semi-metric backbone for each group; that is, the sub-graph of semi-metric edges present in >90% of participants, and by nodal degree differences in the semi-metric connectome.These encouraging results, in what we believe is the first application of semi-metric analysis to neuroimaging data, raise confidence in the methodology as potentially capable of detection and characterisation of a range of neurodevelopmental and psychiatric disorders.
Fomenko, Anatoly
2016-01-01
This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role ...
Topological Aspects of Information Retrieval.
Egghe, Leo; Rousseau, Ronald
1998-01-01
Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)
Guillemin, Victor
2010-01-01
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main
Topological strength of magnetic skyrmions
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Ramos, J.G.G.S.; Rodrigues, E.I.B.
2017-02-01
This work deals with magnetic structures that attain integer and half-integer skyrmion numbers. We model and solve the problem analytically, and show how the solutions appear in materials that engender distinct, very specific physical properties, and use them to describe their topological features. In particular, we found a way to model skyrmion with a large transition region correlated with the presence of a two-peak skyrmion number density. Moreover, we run into the issue concerning the topological strength of a vortex-like structure and suggest an experimental realization, important to decide how to modify and measure the topological strength of the magnetic structure.
Topology Optimization of Nanophotonic Devices
DEFF Research Database (Denmark)
Yang, Lirong
This thesis explores the various aspects of utilizing topology optimization in designing nanophotonic devices. Either frequency-domain or time-domain methods is used in combination with the optimization algorithms, depending on various aims of the designing problems. The frequency-domain methods...... lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses....
Emerging Trends in Topological Insulators and Topological ...
Indian Academy of Sciences (India)
/fulltext/reso/022/08/0787-0800. Keywords. Superconductor, quantum Hall effect, topological insulator, Majorana fermions. Abstract. Topological insulators are new class of materials which arecharacterized by a bulk band gap like ordinary ...
Margalef-Roig, J
1992-01-01
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Induced topological pressure for topological dynamical systems
International Nuclear Information System (INIS)
Xing, Zhitao; Chen, Ercai
2015-01-01
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure
DEFF Research Database (Denmark)
Alexiadis, V; Waldmann, T; Andersen, Jens S.
2000-01-01
The structure of chromatin regulates the genetic activity of the underlying DNA sequence. We report here that the protein encoded by the proto-oncogene DEK, which is involved in acute myelogenous leukemia, induces alterations of the superhelical density of DNA in chromatin. The change in topology...
DEFF Research Database (Denmark)
Marcussen, Lars
2003-01-01
Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum.......Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum....
Topological superconductors: a review.
Sato, Masatoshi; Ando, Yoichi
2017-07-01
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
Gamelin, Theodore W
1999-01-01
A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations. Index. 51 illustrations.
Topological hierarchy matters — topological matters with superlattices of defects
International Nuclear Information System (INIS)
He Jing; Kou Su-Peng
2016-01-01
Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states. In this paper, we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters. We find that both topological defects (quantized vortices) and non topological defects (vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects. These topological mid-gap states have nontrivial topological properties, including the nonzero Chern number and the gapless edge states. Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters. (topical review)
Introduction to topological quantum matter & quantum computation
Stanescu, Tudor D
2017-01-01
What is -topological- about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-know...
Topologically Massive Higher Spin Gravity
Bagchi, A.; Lal, S.; Saha, A.; Sahoo, B.
2011-01-01
We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the
Book Review: Computational Topology
DEFF Research Database (Denmark)
Raussen, Martin
2011-01-01
Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5......Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5...
Topological massive sigma models
International Nuclear Information System (INIS)
Lambert, N.D.
1995-01-01
In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the manifold to admit a Killing vector. We use the topological massive sigma model constructed here to simplify the calculation of the observables. Lastly it is noted that this model can be viewed as interpolating between topological massless sigma models and topological Landau-Ginzburg models. ((orig.))
Topological Strings and Integrable Hierarchies
Aganagic, M; Klemm, A D; Marino, M; Vafa, C; Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2006-01-01
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how A-model topological string on P^1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.
Energy Technology Data Exchange (ETDEWEB)
Kalb, Jeffrey L.; Lee, David S.
2008-01-01
Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.
Topological Characterization of Fractured Coal
Jing, Yu; Armstrong, Ryan T.; Ramandi, Hamed L.; Mostaghimi, Peyman
2017-12-01
Coal transport properties are highly dependent on the underlying fractured network, known as cleats, which are characterized by geometrical and topological properties. X-ray microcomputed tomography (micro-CT) has been widely applied to obtain 3-D digital representations of the cleat network. However, segmentation of 3-D data is often problematic due to image noise, which will result in inaccurate estimation of coal properties (e.g., porosity and specific surface area). To circumvent this issue, a discrete fracture network (DFN) model is proposed. We develop a characterization framework to determine if the developed DFN models can preserve the topological properties of the coal cleat network found in micro-CT data. We compute the Euler characteristic, fractal dimension, and percolation quantities to analyze the topology locally and globally and compare the results between micro-CT data (before denoising), filtered micro-CT data (after denoising), and the DFN model. We find that micro-CT data with noise have extensive connectivity while filtered micro-CT data and DFN models have similar topology both globally and locally. It is concluded that the topology of the DFN models are closer to that of the realistic cleat network that do not have segmentation-induced pores. In addition, micro-CT imaging always struggles with the trade-off between sample size and resolution, while the presented DFN models are not restricted by imaging resolution and thus can be constructed with extended domain size. Overall, the presented DFN model is a reliable alternative with realistic cleat topology, extended domain size and favorable data format for direct numerical simulations.
Tamura, Itiro
1992-01-01
This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds.
International Nuclear Information System (INIS)
Eberhart, M.
1996-01-01
A systematic study of the charge density topologies corresponding to a number of transition metal aluminides with the B2 structure indicates that unstable crystal structures are sometimes associated with uncharacteristic topologies. This observation invites the speculation that the distance to a topological instability might relate to a metals phase behavior. Following this speculation, a metric is imposed on the topological theory of Bader, producing a geometrical theory, where it is now possible to assign a distance from a calculated charge density topology to a topological instability. For the cubic transition metals, these distances are shown to correlate with single crystal elastic constants, where the metals that are furthest from an instability are observed to be the stiffest. (author). 16 refs., 1 tab., 9 figs
Topological mirror superconductivity.
Zhang, Fan; Kane, C L; Mele, E J
2013-08-02
We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.
Interactive Topology Optimization
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten
Interactivity is the continuous interaction between the user and the application to solve a task. Topology optimization is the optimization of structures in order to improve stiffness or other objectives. The goal of the thesis is to explore how topology optimization can be used in applications...... on theory of from human-computer interaction which is described in Chapter 2. Followed by a description of the foundations of topology optimization in Chapter 3. Our applications for topology optimization in 2D and 3D are described in Chapter 4 and a game which trains the human intuition of topology...... optimization is presented in Chapter 5. Topology optimization can also be used as an interactive modeling tool with local control which is presented in Chapter 6. Finally, Chapter 7 contains a summary of the findings and concludes the dissertation. Most of the presented applications of the thesis are available...
Clay, Adam
2016-01-01
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Topological Foundations of Electromagnetism
Barrett, Terrence W
2008-01-01
Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic field
Siino, Masaru
1997-01-01
The topologies of event horizons are investigated. Considering the existence of the endpoint of the event horizon, it cannot be differentiable. Then there are the new possibilities of the topology of the event horizon though they are excluded in smooth event horizons. The relation between the topology of the event horizon and the endpoint of it is revealed. A torus event horizon is caused by two-dimensional endpoints. One-dimensional endpoints provide the coalescence of spherical event horizo...
Gulamsarwar, Syazwani; Salleh, Zabidin
2017-08-01
The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.
Decorrelating topology with HMC
International Nuclear Information System (INIS)
Lippert, Th.; Alles, B.; Bali, G.; D'Elia, M.; Di Giacomo, A.; Eicker, N.; Guesken, S.; Schilling, K.; Spitz, A.; Struckmann, T.; Ueberholz, P.; Viehoff, J.
1999-01-01
The investigation of the decorrelation efficiency of the HMC algorithm with respect to vacuum topology is a prerequisite for trustworthy full QCD simulations, in particular for the computation of topology sensitive quantities. We demonstrate that for ((m π )/(m ρ ))-ratios ≥ 0.69 sufficient tunneling between the topological sectors can be achieved, for two flavours of dynamical Wilson fermions close to the scaling region (β 5.6). Our results are based on time series of length 5000 trajectories
Directory of Open Access Journals (Sweden)
Ali Bajravani
2018-04-01
Full Text Available By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively.
Singh, Tej Bahadur
2013-01-01
Topological SpacesMetric Spaces Topologies Derived Concepts Bases Subspaces Continuity and ProductsContinuityProduct TopologyConnectednessConnected Spaces Components Path-Connected Spaces Local ConnectivityConvergence Sequences Nets Filters Hausdorff SpacesCountability Axioms 1st and 2nd Countable Spaces Separable and Lindelöf SpacesCompactnessCompact Spaces Countably Compact Spaces Compact Metric Spaces Locally Compact Spaces Proper Maps Topological Constructions Quotient Spaces Identification Maps Cones, Suspensions and Joins Wedge Sums and Smash Products Adjunction Spaces Coherent Topologie
Topological Gyroscopic Metamaterials
Nash, Lisa Michelle
Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.
Morita, K
1989-01-01
Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.
QCD as a topologically ordered system
International Nuclear Information System (INIS)
Zhitnitsky, Ariel R.
2013-01-01
We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1) A problem where the would be η ′ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1) A problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations. -- Highlights: •QCD may belong to a topologically ordered phase similar to condensed matter (CM) systems. •We identify the non-propagating topological field in deformed QCD with the Veneziano ghost. •Relation between “string-net” condensates in CM systems and the “skeletons” in QCD lattice simulations is studied
Global monopoles can change Universe's topology
International Nuclear Information System (INIS)
Marunović, Anja; Prokopec, Tomislav
2016-01-01
If the Universe undergoes a phase transition, at which global monopoles are created or destroyed, topology of its spatial sections can change. More specifically, by making use of Myers' theorem, we show that, after a transition in which global monopoles form, spatial sections of a spatially flat, infinite Universe becomes finite and closed. This implies that global monopoles can change the topology of Universe's spatial sections (from infinite and open to finite and closed). Global monopoles cannot alter the topology of the space-time manifold.
General Topology of the Universe
Pandya, Aalok
2002-01-01
General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded.
The topological filtration of gamma-structures
DEFF Research Database (Denmark)
Li, Thomas; Reidys, Christian
2013-01-01
In this paper we study gamma-structures filtered by topological genus. gamma-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A gamma-structure is composed by specific building blocks, that have...... topological genus less than or equal to gamma, where composition means concatenation and nesting of such blocks. Our main results are the derivation of a new bivariate generating function for gamma-structures via symbolic methods, the singularity analysis of the solutions and a central limit theorem...... for the distribution of topological genus in gamma-structures of given length. In our derivation specific bivariate polynomials play a central role. Their coefficients count particular motifs of fixed topological genus and they are of relevance in the context of genus recursion and novel folding algorithms....
A topological derivative method for topology optimization
DEFF Research Database (Denmark)
Norato, J.; Bendsøe, Martin P.; Haber, RB
2007-01-01
resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void......We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric...... regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures....
The nature of the topological intuition
Sultanova L. B.
2016-01-01
The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-ca...
Topology optimization approaches
DEFF Research Database (Denmark)
Sigmund, Ole; Maute, Kurt
2013-01-01
Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary...
Mendelson, Bert
1990-01-01
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.
Modeling Internet Topology Dynamics
Haddadi, H.; Uhlig, S.; Moore, A.; Mortier, R.; Rio, M.
Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements,
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-12-01
If to each element x of a set X there corresponds a set B(x of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x is the set of neighborhoods of x in this topology.
Reconfigurable topological photonic crystal
Shalaev, Mikhail I.; Desnavi, Sameerah; Walasik, Wiktor; Litchinitser, Natalia M.
2018-02-01
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topology of the band structure. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals (PCs) can serve as a platform for realizing a scatter-free propagation of light waves. In conventional PCs, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological PCs and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals (LCs), which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a LC background medium. Background index is changed depending on the orientation of a LC, while preserving the topology of the system. This results in a change of the spectral position of the photonic bandgap and the topological edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.
How to model wireless mesh networks topology
International Nuclear Information System (INIS)
Sanni, M L; Hashim, A A; Anwar, F; Ali, S; Ahmed, G S M
2013-01-01
The specification of network connectivity model or topology is the beginning of design and analysis in Computer Network researches. Wireless Mesh Networks is an autonomic network that is dynamically self-organised, self-configured while the mesh nodes establish automatic connectivity with the adjacent nodes in the relay network of wireless backbone routers. Researches in Wireless Mesh Networks range from node deployment to internetworking issues with sensor, Internet and cellular networks. These researches require modelling of relationships and interactions among nodes including technical characteristics of the links while satisfying the architectural requirements of the physical network. However, the existing topology generators model geographic topologies which constitute different architectures, thus may not be suitable in Wireless Mesh Networks scenarios. The existing methods of topology generation are explored, analysed and parameters for their characterisation are identified. Furthermore, an algorithm for the design of Wireless Mesh Networks topology based on square grid model is proposed in this paper. The performance of the topology generated is also evaluated. This research is particularly important in the generation of a close-to-real topology for ensuring relevance of design to the intended network and validity of results obtained in Wireless Mesh Networks researches
Topological Acoustic Delay Line
Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Wei, Qi; Liu, Xiaojun; Christensen, Johan
2018-03-01
Topological protected wave engineering in artificially structured media is at the frontier of ongoing metamaterials research that is inspired by quantum mechanics. Acoustic analogues of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation with strikingly unconventional acoustic edge modes immune to backscattering. Earlier fabrications of topological insulators are characterized by an unreconfigurable geometry and a very narrow frequency response, which severely hinders the exploration and design of useful devices. Here we establish topologically protected sound in reconfigurable phononic crystals that can be switched on and off simply by rotating its three-legged "atoms" without altering the lattice structure. In particular, we engineer robust phase delay defects that take advantage of the ultrabroadband reflection-free sound propagation. Such topological delay lines serve as a paradigm in compact acoustic devices, interconnects, and electroacoustic integrated circuits.
Machine learning topological states
Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
2017-11-01
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.
Emerging Trends in Topological Insulators and Topological ...
Indian Academy of Sciences (India)
tems can lead to a state that supports zero energy Majorana fermions .... orbital motion is a relativistic effect most pronounced in heavy ... 1D helical edge states appear within the gap with a linear disper- ... free fermion in 1D. .... less, and electrically neutral. ... to be used as a building block for the next generation topological.
Topology Optimization for Additive Manufacturing
DEFF Research Database (Denmark)
Clausen, Anders
This PhD thesis deals with the combination of topology optimization and additive man-ufacturing (AM, also known as 3D-printing). In addition to my own works, the thesis contains a broader review and assessment of the literature within the field. The thesis first presents a classification...... of the various AM technologies, a review of relevant manufacturing materials, the properties of these materials in the additively manufactured part, as well as manufacturing constraints with a potential for design optimization. Subsequently, specific topology optimization formulations relevant for the most im...... for scalable manufacturing. In relation to interface problems it is shown how a flexible void area may be included into a standard minimum compliance problem by employing an additional design variable field and a sensitivity filter. Furthermore, it is shown how the design of coated structures may be modeled...
Signatures of topological superconductivity
Energy Technology Data Exchange (ETDEWEB)
Peng, Yang
2017-07-19
The prediction and experimental discovery of topological insulators brought the importance of topology in condensed matter physics into the limelight. Topology hence acts as a new dimension along which more and more new states of matter start to emerge. One of these topological states of matter, namely topological superconductors, comes into the focus because of their gapless excitations. These gapless excitations, especially in one dimensional topological superconductors, are Majorana zero modes localized at the ends of the superconductor and exhibit exotic nonabelian statistics, which can be potentially applied to fault-tolerant quantum computation. Given their highly interesting physical properties and potential applications to quantum computation, both theorists and experimentalists spend great efforts to realize topological supercondoctors and to detect Majoranas. In two projects within this thesis, we investigate the properties of Majorana zero modes in realistic materials which are absent in simple theoretical models. We find that the superconducting proximity effect, an essential ingredient in all existing platforms for topological superconductors, plays a significant role in determining the localization property of the Majoranas. Strong proximity coupling between the normal system and the superconducting substrate can lead to strongly localized Majoranas, which can explain the observation in a recent experiment. Motivated by experiments in Molenkamp's group, we also look at realistic quantum spin Hall Josephson junctions, in which charge puddles acting as magnetic impurities are coupled to the helical edge states. We find that with this setup, the junction generically realizes an exotic 8π periodic Josephson effect, which is absent in a pristine Josephson junction. In another two projects, we propose more pronounced signatures of Majoranas that are accessible with current experimental techniques. The first one is a transport measurement, which uses
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Topologically massive supergravity
Directory of Open Access Journals (Sweden)
S. Deser
1983-01-01
Full Text Available The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The system's energy, as well as that of the original topological gravity, is therefore positive.
Sacramento, P. D.; Vieira, V. R.
2018-04-01
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.
Algebraic topology and concurrency
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric
2006-01-01
We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...
Chatterjee, D
2007-01-01
About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the
Topological pregauge-pregeometry
International Nuclear Information System (INIS)
Akama, Keiichi; Oda, Ichiro.
1990-12-01
The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions is investigated from the viewpoint of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale. (author)
Elementary topology problem textbook
Viro, O Ya; Netsvetaev, N Yu; Kharlamov, V M
2008-01-01
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the pr
Topology optimized microbioreactors
DEFF Research Database (Denmark)
Schäpper, Daniel; Lencastre Fernandes, Rita; Eliasson Lantz, Anna
2011-01-01
This article presents the fusion of two hitherto unrelated fields—microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein...
Real topological string amplitudes
Energy Technology Data Exchange (ETDEWEB)
Narain, K.S. [The Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Piazzalunga, N. [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794-3636 (United States); International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy); Tanzini, A. [International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy)
2017-03-15
We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G{sub χ}, at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g{sup ′}=−χ+1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F{sub g}.
Topological Susceptibility from Slabs
Bietenholz, Wolfgang; Gerber, Urs
2015-01-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.
Topological susceptibility from slabs
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Forcrand, Philippe de [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); CERN, Physics Department, TH Unit, CH-1211 Geneva 23 (Switzerland); Gerber, Urs [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Apdo. Postal 2-82, Morelia, Michoacán, C.P. 58040 (Mexico)
2015-12-14
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ{sub t}. In principle it seems straightforward to measure χ{sub t} by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ{sub t} even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ{sub t}, as we demonstrate with numerical results for non-linear σ-models.
Contact and symplectic topology
Colin, Vincent; Stipsicz, András
2014-01-01
Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
Wilansky, Albert
2008-01-01
Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.
Fall Foliage Topology Seminars
1990-01-01
This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. Many of the ideas presented are still in their infancy, and it is hoped that the work here will spur others to new and exciting developments. Among the many techniques disussed are the use of obstruction groups to distinguish certain exact sequences and several graph theoretic techniques with applications to the theory of groups.
Tunable Topological Phononic Crystals
Chen, Zeguo; Wu, Ying
2016-01-01
Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.
Tunable Topological Phononic Crystals
Chen, Zeguo
2016-05-27
Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.
Sampling Algorithms of Pure Network Topologies: Stability and Separability of Metric Embeddings
National Research Council Canada - National Science Library
Airoldi, Edoardo M
2005-01-01
... has become a central theme for KDD. The intuition behind the plethora of approaches relies upon a few basic types of networks, which are identified by specific local and global topological properties, and which the authors term "pure" topology types...
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
Directory of Open Access Journals (Sweden)
Apu Kumar Saha
2015-06-01
Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.
LHCb Topological Trigger Reoptimization
International Nuclear Information System (INIS)
Likhomanenko, Tatiana; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Ilten, Philip; Williams, Michael
2015-01-01
The main b-physics trigger algorithm used by the LHCb experiment is the so- called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all ’interesting” decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. Methods studied include cascading, ensembling and blending techniques. Furthermore, novel boosting techniques have been implemented that will help reduce systematic uncertainties in Run 2 measurements. We demonstrate that the reoptimized topological trigger is expected to significantly improve on the Run 1 performance for a wide range of b-hadron decays. (paper)
p-topological Cauchy completions
Directory of Open Access Journals (Sweden)
J. Wig
1999-01-01
Full Text Available The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular, p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and only if it is “cushioned,” meaning that each equivalence class of nonconvergent Cauchy filters contains a smallest filter. For a Cauchy space allowing a p-topological completion, it is shown that a certain class of Reed completions preserve the p-topological property, including the Wyler and Kowalsky completions, which are, respectively, the finest and the coarsest p-topological completions. However, not all p-topological completions are Reed completions. Several extension theorems for p-topological completions are obtained. The most interesting of these states that any Cauchy-continuous map between Cauchy spaces allowing p-topological and p′-topological completions, respectively, can always be extended to a θ-continuous map between any p-topological completion of the first space and any p′-topological completion of the second.
Aganagic, M; Marino, M; Vafa, C; Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2005-01-01
We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of Calabi-Yau. We interpret this result as an operator computation of the amplitudes in the B-model mirror which is the Kodaira-Spencer quantum theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.
Riemann, topology, and physics
Monastyrsky, Michael I
2008-01-01
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...
International Nuclear Information System (INIS)
Zou, L.P.; Zhang, P.M.; Pak, D.G.
2013-01-01
We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N) (N=2,3) under the action of maximal Abelian stability group. Starting with explicit vacuum knot configurations we study possible exact classical solutions. Exact analytic non-static knot solution in a simple CP 1 model in Euclidean space–time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new solutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space–time can be naturally obtained from knot solitons in integrable CP 1 models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is proposed
Sadun, Lorenzo
2008-01-01
Aperiodic tilings are interesting to mathematicians and scientists for both theoretical and practical reasons. The serious study of aperiodic tilings began as a solution to a problem in logic. Simpler aperiodic tilings eventually revealed hidden "symmetries" that were previously considered impossible, while the tilings themselves were quite striking. The discovery of quasicrystals showed that such aperiodicity actually occurs in nature and led to advances in materials science. Many properties of aperiodic tilings can be discerned by studying one tiling at a time. However, by studying families of tilings, further properties are revealed. This broader study naturally leads to the topology of tiling spaces. This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to ...
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Deo, Satya
2018-01-01
This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...
Topological and non-topological soliton solutions to some time
Indian Academy of Sciences (India)
Topological and non-topological soliton solutions to some time-fractional differential equations ... These equations have been widely applied in many branches of nonlinear ... Department of Engineering Sciences, Faculty of Technology and ...
International Nuclear Information System (INIS)
Carroll, S.M.; Trodden, M.
1998-01-01
We propose a class of field theories featuring solitonic solutions in which topological defects can end when they intersect other defects of equal or higher dimensionality. Such configurations may be termed open-quotes Dirichlet topological defects,close quotes in analogy with the D-branes of string theory. Our discussion focuses on defects in scalar field theories with either gauge or global symmetries, in 3+1 dimensions; the types of defects considered include walls ending on walls, strings on walls, and strings on strings. copyright 1998 The American Physical Society
Filters in topology optimization
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...
Coghetto Roland
2015-01-01
Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods of x ...
Monastyrsky, M I
2006-01-01
This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.
Free topological vector spaces
Gabriyelyan, Saak S.; Morris, Sidney A.
2016-01-01
We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...
Topological superconductivity, topological confinement, and the vortex quantum Hall effect
International Nuclear Information System (INIS)
Diamantini, M. Cristina; Trugenberger, Carlo A.
2011-01-01
Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
Photoinduced Topological Phase Transitions in Topological Magnon Insulators.
Owerre, S A
2018-03-13
Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagomé ferromagnet Cu(1-3, bdc), and they also possess protected magnon edge modes. These topological magnetic materials can transport heat as well as spin currents, hence they can be useful for spintronic applications. Moreover, as magnons are charge-neutral spin-1 bosonic quasiparticles with a magnetic dipole moment, topological magnon materials can also interact with electromagnetic fields through the Aharonov-Casher effect. In this report, we study photoinduced topological phase transitions in intrinsic topological magnon insulators in the kagomé ferromagnets. Using magnonic Floquet-Bloch theory, we show that by varying the light intensity, periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with different sign of the Berry curvatures and the thermal Hall conductivity. We further show that, under certain conditions, periodically driven gapped topological magnon insulators can also be tuned to synthetic gapless topological magnon semimetals with Dirac-Weyl magnon cones. We envision that this work will pave the way for interesting new potential practical applications in topological magnetic materials.
Topological field theories and duality
International Nuclear Information System (INIS)
Stephany, J.; Universidad Simon Bolivar, Caracas
1996-05-01
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs
Wireless sensor network topology control
Zuk, Olexandr; Romanjuk, Valeriy; Sova, Oleg
2010-01-01
Topology control process for the wireless sensor network is considered. In this article the use of rule base for making decision on the search of optimum network topology is offered for the realization of different aims of network management.
Topology optimization of viscoelastic rectifiers
DEFF Research Database (Denmark)
Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin
2012-01-01
An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...
Towards topological quantum computer
Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.
2018-01-01
Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
Slope constrained Topology Optimization
DEFF Research Database (Denmark)
Petersson, J.; Sigmund, Ole
1998-01-01
The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density-energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing...
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
Meldgaard, Morten
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture of ...
LHCb Topological Trigger Reoptimization
INSPIRE-00400931; Ilten, Philip; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Williams, Michael
2015-12-23
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. ...
International Nuclear Information System (INIS)
Marmo, G.; Morandi, G.
1995-01-01
In this lecture some mathematical problems that arise when one deals with low-dimensional field theories, such as homotopy and topological invariants, differential calculus on Lie groups and coset spaces, fiber spaces and parallel transport, differential calculus on fiber bundles, sequences on principal bundles and Chern-Simons terms are discussed
Rendering the Topological Spines
Energy Technology Data Exchange (ETDEWEB)
Nieves-Rivera, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
Coherence Multiplex System Topologies
Meijerink, Arjan; Taniman, R.O.; Heideman, G.H.L.M.; van Etten, Wim
2007-01-01
Coherence multiplexing is a potentially inexpensive form of optical code-division multiple access, which is particularly suitable for short-range applications with moderate bandwidth requirements, such as access networks, LANs, or interconnects. Various topologies are known for constructing an
Topological Trigger Developments
Likhomanenko, Tatiana
2015-01-01
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger utilized a custom boosted decision tree algorithm, selected an almost 100% pure sample of b-hadrons with a typical efficiency of 60-70%, and its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and uBoost. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. These inclu...
Towards topological quantum computer
Directory of Open Access Journals (Sweden)
D. Melnikov
2018-01-01
Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
Topology of Document Retrieval Systems.
Everett, Daniel M.; Cater, Steven C.
1992-01-01
Explains the use of a topological structure to examine the closeness between documents in retrieval systems and analyzes the topological structure of a vector-space model, a fuzzy-set model, an extended Boolean model, a probabilistic model, and a TIRS (Topological Information Retrieval System) model. Proofs for the results are appended. (17…
Comparing topological charge definitions using topology fixing actions
International Nuclear Information System (INIS)
Bruckmann, Falk; Gruber, Florian; Jansen, Karl; Marinkovic, Marina; Urbach, Carsten; Wagner, Marc
2009-05-01
We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge - the field theoretic and the index definition - is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite volume effects arising in the static potential and related quantities due to topology fixing. (orig.)
Fine topology and locally Minkowskian manifolds
Agrawal, Gunjan; Sinha, Soami Pyari
2018-05-01
Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.
Quasi-topological Ricci polynomial gravities
Li, Yue-Zhou; Liu, Hai-Shan; Lü, H.
2018-02-01
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.
Topological effects on the mechanical properties of polymer knots
Zhao, Yani; Ferrari, Franco
2017-11-01
The mechanical properties of knotted polymer rings under stretching in a bad or good solvent are investigated by applying a force F to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer conformations is performed on a simple cubic lattice using the Wang-Landau algorithm. The specific energy, specific heat capacity, gyration radius and the force-elongation curves are computed for several knot topologies with lengths up to 120 lattice units. The common features of the mechanical and thermal behavior of stretched short polymer rings forming knots of a given topological type are analyzed as well as the differences arising due to topology and size effects. It is found that these systems admit three different phases depending on the values of the tensile force F and the temperature T. The transitions from one phase to the other are well characterized by the peaks of the specific heat capacity and by the data of the gyration radius and specific energy. At very low temperatures the force-elongation curves show that the stretching of a knot is a stepwise process, which becomes smooth at higher temperatures. Criteria for distinguishing topological and size effects are provided. It turns out from our study that the behavior of short polymer rings is strongly influenced by topological effects. In particular, the swelling and the swelling rate of knots are severely limited by the topological constraints. Several other properties that are affected by topology, like the decay of the specific energy at high tensile forces, are discussed. The fading out of the influences of topological origin with increasing knot lengths has been verified. Some anomalies detected in the plots of the specific heat capacity of very short and complex knots have been explained by the limitations in the number of accessible energy states due to the topological constraints.
Topology optimized permanent magnet systems
Bjørk, R.; Bahl, C. R. H.; Insinga, A. R.
2017-09-01
Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a Λcool figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.
Undergraduate topology a working textbook
McCluskey, Aisling
2014-01-01
This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp i
Topology optimized permanent magnet systems
DEFF Research Database (Denmark)
Bjørk, Rasmus; Bahl, Christian; Insinga, Andrea Roberto
2017-01-01
Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron...... and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a ΛcoolΛcool figure of merit of 0...
Nobel Lecture: Topological quantum matter*
Haldane, F. Duncan M.
2017-10-01
Nobel Lecture, presented December 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter."
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Ultrafilters and topologies on groups
Zelenyuk, Yevhen
2011-01-01
This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results aboutultrafilters. Topics covered include: topological and left topological groups, ultrafilter semigroups, local homomorphisms and automorphisms, subgroups and ideal structure of ßG, almost maximal spaces and projectives of finite semigroups, resolvability of groups. This is a self-contained book aimed at graduate students and researchers working in to
The Optimizer Topology Characteristics in Seismic Hazards
Sengor, T.
2015-12-01
The characteristic data of the natural phenomena are questioned in a topological space approach to illuminate whether there is an algorithm behind them bringing the situation of physics of phenomena to optimized states even if they are hazards. The optimized code designing the hazard on a topological structure mashes the metric of the phenomena. The deviations in the metric of different phenomena push and/or pull the fold of the other suitable phenomena. For example if the metric of a specific phenomenon A fits to the metric of another specific phenomenon B after variation processes generated with the deviation of the metric of previous phenomenon A. Defining manifold processes covering the metric characteristics of each of every phenomenon is possible for all the physical events; i.e., natural hazards. There are suitable folds in those manifold groups so that each subfold fits to the metric characteristics of one of the natural hazard category at least. Some variation algorithms on those metric structures prepare a gauge effect bringing the long time stability of Earth for largely scaled periods. The realization of that stability depends on some specific conditions. These specific conditions are called optimized codes. The analytical basics of processes in topological structures are developed in [1]. The codes are generated according to the structures in [2]. Some optimized codes are derived related to the seismicity of NAF beginning from the quakes of the year 1999. References1. Taner SENGOR, "Topological theory and analytical configuration for a universal community model," Procedia- Social and Behavioral Sciences, Vol. 81, pp. 188-194, 28 June 2013, 2. Taner SENGOR, "Seismic-Climatic-Hazardous Events Estimation Processes via the Coupling Structures in Conserving Energy Topologies of the Earth," The 2014 AGU Fall Meeting, Abstract no.: 31374, ABD.
Advanced Topology Optimization Methods for Conceptual Architectural Design
DEFF Research Database (Denmark)
Aage, Niels; Amir, Oded; Clausen, Anders
2015-01-01
This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...
Advanced Topology Optimization Methods for Conceptual Architectural Design
DEFF Research Database (Denmark)
Aage, Niels; Amir, Oded; Clausen, Anders
2014-01-01
This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...
ELeaRNT: Evolutionary Learning of Rich Neural Network Topologies
National Research Council Canada - National Science Library
Matteucci, Matteo
2006-01-01
In this paper we present ELeaRNT an evolutionary strategy which evolves rich neural network topologies in order to find an optimal domain specific non linear function approximator with a good generalization performance...
Multiple topological phase transitions in a gyromagnetic photonic crystal
Chen, Zeguo; Mei, Jun; Sun, Xiao Cheng; Zhang, Xiujuan; Zhao, Jiajun; Wu, Ying
2017-01-01
reveals that the topological property is associated with the pseudospin orientations and that it is characterized by the spin Chern number. The emerging quantum anomalous Hall phase features a single helical edge state that is locked by a specific
Floquet topological insulators for sound
Fleury, Romain; Khanikaev, Alexander B.; Alù, Andrea
2016-06-01
The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential of topological acoustics. Here we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. We show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.
Quist, Daniel A [Los Alamos, NM; Gavrilov, Eugene M [Los Alamos, NM; Fisk, Michael E [Jemez, NM
2008-01-15
A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.
Robinson, Michael
2014-01-01
Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
Monastyrsky, Michail Ilych
2007-01-01
The book presents a class of new results in molecular biology for which topological methods and ideas are important. These include: the large-scale conformation properties of DNA; computational methods (Monte Carlo) allowing the simulation of large-scale properties of DNA; the tangle model of DNA recombination and other applications of Knot theory; dynamics of supercoiled DNA and biocatalitic properties of DNA; the structure of proteins; and other very recent problems in molecular biology. The text also provides a short course of modern topology intended for the broad audience of biologists and physicists. The authors are renowned specialists in their fields and some of the new results presented here are documented for the first time in monographic form.
DNA topology and transcription
Kouzine, Fedor; Levens, David; Baranello, Laura
2014-01-01
Chromatin is a complex assembly that compacts DNA inside the nucleus while providing the necessary level of accessibility to regulatory factors conscripted by cellular signaling systems. In this superstructure, DNA is the subject of mechanical forces applied by variety of molecular motors. Rather than being a rigid stick, DNA possesses dynamic structural variability that could be harnessed during critical steps of genome functioning. The strong relationship between DNA structure and key genomic processes necessitates the study of physical constrains acting on the double helix. Here we provide insight into the source, dynamics, and biology of DNA topological domains in the eukaryotic cells and summarize their possible involvement in gene transcription. We emphasize recent studies that might inspire and impact future experiments on the involvement of DNA topology in cellular functions. PMID:24755522
DEFF Research Database (Denmark)
Blok, Anders
2010-01-01
Climate change is quickly becoming a ubiquitous socionatural reality, mediating extremes of sociospatial scale from the bodily to the planetary. Although environmentalism invites us to ‘think globally and act locally', the meaning of these scalar designations remains ambiguous. This paper explores...... the topological presuppositions of social theory in the context of global climate change, asking how carbon emissions ‘translate' into various sociomaterial forms. Staging a meeting between Tim Ingold's phenomenology of globes and spheres and the social topologies of actor-network theory (ANT), the paper advances...... a ‘relational-scalar' analytics of spatial practices, technoscience, and power. As technoscience gradually constructs a networked global climate, this ‘grey box' comes to circulate within fluid social spaces, taking on new shades as it hybridizes knowledges, symbols, and practices. Global climates thus come...
Topological confinement and superconductivity
Energy Technology Data Exchange (ETDEWEB)
Al-hassanieh, Dhaled A [Los Alamos National Laboratory; Batista, Cristian D [Los Alamos National Laboratory
2008-01-01
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in aID-system.
DEFF Research Database (Denmark)
Schwerdtfeger, Peter; Wirz, Lukas; Avery, James Emil
2014-01-01
Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar g....... In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems....
Technologies for converter topologies
Zhou, Yan; Zhang, Haiyu
2017-02-28
In some embodiments of the disclosed inverter topologies, an inverter may include a full bridge LLC resonant converter, a first boost converter, and a second boost converter. In such embodiments, the first and second boost converters operate in an interleaved manner. In other disclosed embodiments, the inverter may include a half-bridge inverter circuit, a resonant circuit, a capacitor divider circuit, and a transformer.
Operator algebras and topology
International Nuclear Information System (INIS)
Schick, T.
2002-01-01
These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)
Topology-function conservation in protein-protein interaction networks.
Davis, Darren; Yaveroğlu, Ömer Nebil; Malod-Dognin, Noël; Stojmirovic, Aleksandar; Pržulj, Nataša
2015-05-15
Proteins underlay the functioning of a cell and the wiring of proteins in protein-protein interaction network (PIN) relates to their biological functions. Proteins with similar wiring in the PIN (topology around them) have been shown to have similar functions. This property has been successfully exploited for predicting protein functions. Topological similarity is also used to guide network alignment algorithms that find similarly wired proteins between PINs of different species; these similarities are used to transfer annotation across PINs, e.g. from model organisms to human. To refine these functional predictions and annotation transfers, we need to gain insight into the variability of the topology-function relationships. For example, a function may be significantly associated with specific topologies, while another function may be weakly associated with several different topologies. Also, the topology-function relationships may differ between different species. To improve our understanding of topology-function relationships and of their conservation among species, we develop a statistical framework that is built upon canonical correlation analysis. Using the graphlet degrees to represent the wiring around proteins in PINs and gene ontology (GO) annotations to describe their functions, our framework: (i) characterizes statistically significant topology-function relationships in a given species, and (ii) uncovers the functions that have conserved topology in PINs of different species, which we term topologically orthologous functions. We apply our framework to PINs of yeast and human, identifying seven biological process and two cellular component GO terms to be topologically orthologous for the two organisms. © The Author 2015. Published by Oxford University Press.
Topological Substituent Descriptors
Directory of Open Access Journals (Sweden)
Mircea V. DIUDEA
2002-12-01
Full Text Available Motivation. Substituted 1,3,5-triazines are known as useful herbicidal substances. In view of reducing the cost of biological screening, computational methods are carried out for evaluating the biological activity of organic compounds. Often a class of bioactives differs only in the substituent attached to a basic skeleton. In such cases substituent descriptors will give the same prospecting results as in case of using the whole molecule description, but with significantly reduced computational time. Such descriptors are useful in describing steric effects involved in chemical reactions. Method. Molecular topology is the method used for substituent description and multi linear regression analysis as a statistical tool. Results. Novel topological descriptors, XLDS and Ws, based on the layer matrix of distance sums and walks in molecular graphs, respectively, are proposed for describing the topology of substituents linked on a chemical skeleton. They are tested for modeling the esterification reaction in the class of benzoic acids and herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino-1,3,5-triazines. Conclusions. Ws substituent descriptor, based on walks in graph, satisfactorily describes the steric effect of alkyl substituents behaving in esterification reaction, with good correlations to the Taft and Charton steric parameters, respectively. Modeling the herbicidal activity of the seo of 1,3,5-triazines exceeded the models reported in literature, so far.
A role for chromatin topology in imprinted domain regulation.
MacDonald, William A; Sachani, Saqib S; White, Carlee R; Mann, Mellissa R W
2016-02-01
Recently, many advancements in genome-wide chromatin topology and nuclear architecture have unveiled the complex and hidden world of the nucleus, where chromatin is organized into discrete neighbourhoods with coordinated gene expression. This includes the active and inactive X chromosomes. Using X chromosome inactivation as a working model, we utilized publicly available datasets together with a literature review to gain insight into topologically associated domains, lamin-associated domains, nucleolar-associating domains, scaffold/matrix attachment regions, and nucleoporin-associated chromatin and their role in regulating monoallelic expression. Furthermore, we comprehensively review for the first time the role of chromatin topology and nuclear architecture in the regulation of genomic imprinting. We propose that chromatin topology and nuclear architecture are important regulatory mechanisms for directing gene expression within imprinted domains. Furthermore, we predict that dynamic changes in chromatin topology and nuclear architecture play roles in tissue-specific imprint domain regulation during early development and differentiation.
Transportation Network Topologies
Holmes, Bruce J.; Scott, John
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21st thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which
Decoherence patterns of topological qubits from Majorana modes
International Nuclear Information System (INIS)
Ho, Shih-Hao; Chao, Sung-Po; Chou, Chung-Hsien; Lin, Feng-Li
2014-01-01
We investigate the decoherence patterns of topological qubits in contact with the environment using a novel way of deriving the open system dynamics, rather than using the Feynman–Vernon approach. Each topological qubit is made up of two Majorana modes of a 1D Kitaev chain. These two Majorana modes interact with the environment in an incoherent way which yields peculiar decoherence patterns of the topological qubit. More specifically, we consider the open system dynamics of topological qubits which are weakly coupled to fermionic/bosonic Ohmic-like environments. We find atypical patterns of quantum decoherence. In contrast to the case for non-topological qubits—which always decohere completely in all Ohmic-like environments—topological qubits decohere completely in Ohmic and sub-Ohmic environments but not in super-Ohmic ones. Moreover, we find that the fermion parities of the topological qubits, though they cannot prevent the qubit states from exhibiting decoherence in sub-Ohmic environments, can prevent thermalization turning the state into a Gibbs state. We also study the cases in which each Majorana mode can couple to different Ohmic-like environments, and the time dependence of concurrence for two topological qubits. (paper)
Tunable topological phases in photonic and phononic crystals
Chen, Zeguo
2018-02-18
Topological photonics/phononics, inspired by the discovery of topological insulators, is a prosperous field of research, in which remarkable one-way propagation edge states are robust against impurities or defect without backscattering. This dissertation discusses the implementation of multiple topological phases in specific designed photonic and phononic crystals. First, it reports a tunable quantum Hall phase in acoustic ring-waveguide system. A new three-band model focused on the topological transitions at the Γ point is studied, which gives the functionality that nontrivial topology can be tuned by changing the strengths of the couplings and/or the broken time-reversal symmetry. The resulted tunable topological edge states are also numerically verified. Second, based on our previous studied acoustic ring-waveguide system, we introduce anisotropy by tuning the couplings along different directions. We find that the bandgap topology is related to the frequency and directions. We report our proposal on a frequency filter designed from such an anisotropic topological phononic crystal. Third, motivated by the recent progress on quantum spin Hall phases, we propose a design of time-reversal symmetry broken quantum spin Hall insulators in photonics, in which a new quantum anomalous Hall phase emerges. It supports a chiral edge state with certain spin orientations, which is robust against the magnetic impurities. We also report the realization of the quantum anomalous Hall phase in phononics.
Topological imprint for periodic orbits
International Nuclear Information System (INIS)
Martín, Jesús San; Moscoso, Ma José; Gómez, A González
2012-01-01
The more self-crossing points an orbit has the more complex it is. We introduce the topological imprint to characterize crossing points and focus on the period-doubling cascade. The period-doubling cascade topological imprint determines the topological imprint for orbits in chaotic bands. In addition, there is a closer link between this concept and the braids studied by Lettelier et al (2000 J. Phys. A: Math. Gen. 33 1809–25). (paper)
Intuitionistic supra fuzzy topological spaces
International Nuclear Information System (INIS)
Abbas, S.E.
2004-01-01
In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space
Lynch, Mark
2012-01-01
We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Manipulating topological-insulator properties using quantum confinement
International Nuclear Information System (INIS)
Kotulla, M; Zülicke, U
2017-01-01
Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron–hole asymmetry are disentangled and their respective physical consequences elucidated. (paper)
OPTIMAL NETWORK TOPOLOGY DESIGN
Yuen, J. H.
1994-01-01
This program was developed as part of a research study on the topology design and performance analysis for the Space Station Information System (SSIS) network. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. It is intended that this new design technique consider all important performance measures explicitly and take into account the constraints due to various technical feasibilities. In the current program, technical constraints are taken care of by the user properly forming the starting set of candidate components (e.g. nonfeasible links are not included). As subsets are generated, they are tested to see if they form an acceptable network by checking that all requirements are satisfied. Thus the first acceptable subset encountered gives the cost-optimal topology satisfying all given constraints. The user must sort the set of "feasible" link elements in increasing order of their costs. The program prompts the user for the following information for each link: 1) cost, 2) connectivity (number of stations connected by the link), and 3) the stations connected by that link. Unless instructed to stop, the program generates all possible acceptable networks in increasing order of their total costs. The program is written only to generate topologies that are simply connected. Tests on reliability, delay, and other performance measures are discussed in the documentation, but have not been incorporated into the program. This program is written in PASCAL for interactive execution and has been implemented on an IBM PC series computer operating under PC DOS. The disk contains source code only. This program was developed in 1985.
International Nuclear Information System (INIS)
Hudetz, T.
1989-01-01
As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)
Topologically nontrivial quantum layers
International Nuclear Information System (INIS)
Carron, G.; Exner, P.; Krejcirik, D.
2004-01-01
Given a complete noncompact surface Σ embedded in R 3 , we consider the Dirichlet Laplacian in the layer Ω that is defined as a tubular neighborhood of constant width about Σ. Using an intrinsic approach to the geometry of Ω, we generalize the spectral results of the original paper by Duclos et al. [Commun. Math. Phys. 223, 13 (2001)] to the situation when Σ does not possess poles. This enables us to consider topologically more complicated layers and state new spectral results. In particular, we are interested in layers built over surfaces with handles or several cylindrically symmetric ends. We also discuss more general regions obtained by compact deformations of certain Ω
International Nuclear Information System (INIS)
Schultz, J.H.
1981-01-01
The use of limiter pumps as the principle plasma exhaust system of a magnetic confinement fusion device promises significant simplification, when compared to previously investigating divertor based systems. Further simplifications, such as the integration of the exhaust system with a radio frequency heating system and with the main reactor shield and structure are investigated below. The integrity of limiters in a reactor environment is threatened by many mechanisms, the most severe of which may be erosion by sputtering. Two novel topologies are suggested which allow high erosion without limiter failure
Foundations of combinatorial topology
Pontryagin, L S
2015-01-01
Hailed by The Mathematical Gazette as ""an extremely valuable addition to the literature of algebraic topology,"" this concise but rigorous introductory treatment focuses on applications to dimension theory and fixed-point theorems. The lucid text examines complexes and their Betti groups, including Euclidean space, application to dimension theory, and decomposition into components; invariance of the Betti groups, with consideration of the cone construction and barycentric subdivisions of a complex; and continuous mappings and fixed points. Proofs are presented in a complete, careful, and eleg
DEFF Research Database (Denmark)
Ekman, Ulrik
2015-01-01
that increasingly develop mixed reality environments with context-aware out-of-the-box computing as well as the soci-ocultural and experiental horizon of a virtually and physically mobile citizenry. Design here must meet an ongoing and exceedingly complex interactivity among environmental, technical, social...... and personal multiplicities of urban nodes on the move. This chapter focuses on the design of a busy traffic intersection in the South Korean u-city Songdo. Hence, the discussion whether and how Songdo may be approached via design as topology primarily considers the situation, event, and experience in which...
Nagata, J-I
1985-01-01
This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first edition appeared.The reader will find many new topics in chapters IV-VIII, e.g. theory of Wallmann-Shanin's compactification, realcompact space, various generalizations of paracompactness, generalized metric spaces, Dugundji type extension theory, linearly ordered topolo
Descriptive Topology in Selected Topics of Functional Analysis
Kakol, J; Pellicer, Manuel Lopez
2011-01-01
"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Frechet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical set
Visualizing vector field topology in fluid flows
Helman, James L.; Hesselink, Lambertus
1991-01-01
Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.
Graph topology and gap topology for unstable systems
Zhu, S.Q.
1989-01-01
A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the
1997-01-01
The origins of this volume can be traced back to a conference on "Ethics, Economic and Business" organized by Columbia Busi ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana. Preliminary versions of several of the papers were presented at that meeting. In July 1994 the Fields Institute of Mathematical Sciences sponsored a workshop on "Geometry, Topology and Markets": additional papers and more refined versions of the original papers were presented there. They were published in their present versions in Social Choice and Wel fare, volume 14, number 2, 1997. The common aim of these workshops and this volume is to crystallize research in an area which has emerged rapidly in the last fifteen years, the area of topological approaches to social choice and the theory of games. The area is attracting increasing interest from social choice theorists, game theorists, mathematical econ omists and mathematicians, yet there is no authoritative collection of papers in the a...
Topology with applications topological spaces via near and far
Naimpally, Somashekhar A
2013-01-01
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces. This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising. It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and...
Topology optimized RF MEMS switches
DEFF Research Database (Denmark)
Philippine, M. A.; Zareie, H.; Sigmund, Ole
2013-01-01
Topology optimization is a rigorous and powerful method that should become a standard MEMS design tool - it can produce unique and non-intuitive designs that meet complex objectives and can dramatically improve the performance and reliability of MEMS devices. We present successful uses of topology...
Topology optimization of turbulent flows
DEFF Research Database (Denmark)
Dilgen, Cetin B.; Dilgen, Sumer B.; Fuhrman, David R.
2018-01-01
The aim of this work is to present a fast and viable approach for taking into account turbulence in topology optimization of complex fluid flow systems, without resorting to any simplifying assumptions in the derivation of discrete adjoints. Topology optimization is an iterative gradient...
Coverings, Networks and Weak Topologies
Czech Academy of Sciences Publication Activity Database
Dow, A.; Junnila, H.; Pelant, Jan
2006-01-01
Roč. 53, č. 2 (2006), s. 287-320 ISSN 0025-5793 R&D Projects: GA ČR GA201/97/0216 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * weak topologies * networks topologies Subject RIV: BA - General Mathematics
Observational modeling of topological spaces
International Nuclear Information System (INIS)
Molaei, M.R.
2009-01-01
In this paper a model for a multi-dimensional observer by using of the fuzzy theory is presented. Relative form of Tychonoff theorem is proved. The notion of topological entropy is extended. The persistence of relative topological entropy under relative conjugate relation is proved.
Topological strings from Liouville gravity
International Nuclear Information System (INIS)
Ishibashi, N.; Li, M.
1991-01-01
We study constrained SU(2) WZW models, which realize a class of two-dimensional conformal field theories. We show that they give rise to topological gravity coupled to the topological minimal models when they are coupled to Liouville gravity. (orig.)
Novel topological invariants and anomalies
International Nuclear Information System (INIS)
Hirayama, M.; Sugimasa, N.
1987-01-01
It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional
On Neutrosophic Soft Topological Space
Directory of Open Access Journals (Sweden)
Tuhin Bera
2018-03-01
Full Text Available In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also. Then, the notion of neutrosophic soft continuous mapping on a neutrosophic soft topological space and it’s properties are developed here.
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
Combined Shape and Topology Optimization
DEFF Research Database (Denmark)
Christiansen, Asger Nyman
Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable...... Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface...... representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead...
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....
Chiral topological insulator of magnons
Li, Bo; Kovalev, Alexey A.
2018-05-01
We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters, the system can be tuned between the chiral topological insulator, three-dimensional magnon anomalous Hall, and Weyl magnon phases.
Transportation Network Topologies
Alexandrov, Natalia (Editor)
2004-01-01
The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.
International Nuclear Information System (INIS)
Gregoire, Thomas; Wacker, Jay G.
2002-01-01
New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking. (author)
Cultural Topology of Creativity
Directory of Open Access Journals (Sweden)
L. M. Andryukhina
2015-02-01
Full Text Available The man in the modern culture faces the challenge of either being creative or forced to leave the stage, which reflects the essential basics of life. The price of lost opportunities, caused by mental stereotypes and encapsulation, is gradually rising. The paper reveals the socio-cultural conditions and the necessary cultural topology of creativity development, as well as the man’s creative potential in the 21st century. The content of the creativity concept is specified along with the phenomenon of its fast expansion in the modern discourse. That results from the global spreading of numerous creative practices in various spheres of life, affecting the progress directions in economics, business, industrial technologies, labor, employment and social stratification. The author emphasizes the social features of creativity, the rising number of, so called, creative class, and outlines the two opposing strategies influencing the topology modification of the social and cultural environment. The first one, applied by the developed countries, facilitates the development of the creative human potential, whereas the other one, inherent in our country, holds that a creative person is able to make progress by himself. However, for solving the urgent problem of innovative development, the creative potential of modern Russia is not sufficient, and following the second strategy will result in unrealized social opportunities and ever lasting social and cultural situation demanding further investment. According to the author, to avoid such a perspective, it is necessary to overcome the three deeply rooted archetypes: the educational disciplinary centrism, organizational absolutism and cultural ostracism.
Cultural Topology of Creativity
Directory of Open Access Journals (Sweden)
L. M. Andryukhina
2012-01-01
Full Text Available The man in the modern culture faces the challenge of either being creative or forced to leave the stage, which reflects the essential basics of life. The price of lost opportunities, caused by mental stereotypes and encapsulation, is gradually rising. The paper reveals the socio-cultural conditions and the necessary cultural topology of creativity development, as well as the man’s creative potential in the 21st century. The content of the creativity concept is specified along with the phenomenon of its fast expansion in the modern discourse. That results from the global spreading of numerous creative practices in various spheres of life, affecting the progress directions in economics, business, industrial technologies, labor, employment and social stratification. The author emphasizes the social features of creativity, the rising number of, so called, creative class, and outlines the two opposing strategies influencing the topology modification of the social and cultural environment. The first one, applied by the developed countries, facilitates the development of the creative human potential, whereas the other one, inherent in our country, holds that a creative person is able to make progress by himself. However, for solving the urgent problem of innovative development, the creative potential of modern Russia is not sufficient, and following the second strategy will result in unrealized social opportunities and ever lasting social and cultural situation demanding further investment. According to the author, to avoid such a perspective, it is necessary to overcome the three deeply rooted archetypes: the educational disciplinary centrism, organizational absolutism and cultural ostracism.
Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens; von Oppen, Felix
2017-07-01
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall-superconductor hybrids.
Directory of Open Access Journals (Sweden)
Daniel Litinski
2017-09-01
Full Text Available We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall–superconductor hybrids.
Equivariant topological quantum field theory and symmetry protected topological phases
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [Division of Physics, California Institute of Technology,1200 E California Blvd, Pasadena, CA, 91125 (United States); Turzillo, Alex [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794 (United States)
2017-03-01
Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.
Topology optimization and lattice Boltzmann methods
DEFF Research Database (Denmark)
Nørgaard, Sebastian Arlund
This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...
Partial Actions, Paradoxicality and Topological full Groups
DEFF Research Database (Denmark)
Scarparo, Eduardo
uniform Roe algebra is finite. In Article C, we analyze the C*-algebra generated by the Koopman representation of a topological full group, showing, in particular, that it is not AF andhas real rank zero. We also prove that if G is a finitely generated, elementary amenable group, and C*(G) has real rank......We study how paradoxicality properties affect the way groups partially acton topological spaces and C*-algebras. We also investigate the real rank zero and AF properties for certain classes of group C*-algebras. Specifically, in article A, we characterize supramenable groups in terms of existence...... of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a C*-algebra by a semidirect product of groups as two iterated...
Analysis of Membrane Protein Topology in the Plant Secretory Pathway.
Guo, Jinya; Miao, Yansong; Cai, Yi
2017-01-01
Topology of membrane proteins provides important information for the understanding of protein function and intermolecular associations. Integrate membrane proteins are generally transported from endoplasmic reticulum (ER) to Golgi and downstream compartments in the plant secretory pathway. Here, we describe a simple method to study membrane protein topology along the plant secretory pathway by transiently coexpressing a fluorescent protein (XFP)-tagged membrane protein and an ER export inhibitor protein, ARF1 (T31N), in tobacco BY-2 protoplast. By fractionation, microsome isolation, and trypsin digestion, membrane protein topology could be easily detected by either direct confocal microscopy imaging or western-blot analysis using specific XFP antibodies. A similar strategy in determining membrane protein topology could be widely adopted and applied to protein analysis in a broad range of eukaryotic systems, including yeast cells and mammalian cells.
Topological semimetal in honeycomb lattice LnSI
Nie, Simin; Xu, Gang; Prinz, Fritz B.; Zhang, Shou-cheng
2017-10-01
Recognized as elementary particles in the standard model, Weyl fermions in condensed matter have received growing attention. However, most of the previously reported Weyl semimetals exhibit rather complicated electronic structures that, in turn, may have raised questions regarding the underlying physics. Here, we report promising topological phases that can be realized in specific honeycomb lattices, including ideal Weyl semimetal structures, 3D strong topological insulators, and nodal-line semimetal configurations. In particular, we highlight a semimetal featuring both Weyl nodes and nodal lines. Guided by this model, we showed that GdSI, the long-perceived ideal Weyl semimetal, has two pairs of Weyl nodes residing at the Fermi level and that LuSI (YSI) is a 3D strong topological insulator with the right-handed helical surface states. Our work provides a mechanism to study topological semimetals and proposes a platform for exploring the physics of Weyl semimetals as well as related device designs.
Topological Rankings in Communication Networks
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard; Træholt, Chresten
2015-01-01
In the theory of communication the central problem is to study how agents exchange information. This problem may be studied using the theory of connected spaces in topology, since a communication network can be modelled as a topological space such that agents can communicate if and only...... if they belong to the same path connected component of that space. In order to study combinatorial properties of such a communication network, notions from algebraic topology are applied. This makes it possible to determine the shape of a network by concrete invariants, e.g. the number of connected components...
Topology optimization for coated structures
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik; Sigmund, Ole
2015-01-01
This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....
Topology optimised wavelength dependent splitters
DEFF Research Database (Denmark)
Hede, K. K.; Burgos Leon, J.; Frandsen, Lars Hagedorn
A photonic crystal wavelength dependent splitter has been constructed by utilising topology optimisation1. The splitter has been fabricated in a silicon-on-insulator material (Fig. 1). The topology optimised wavelength dependent splitter demonstrates promising 3D FDTD simulation results....... This complex photonic crystal structure is very sensitive against small fabrication variations from the expected topology optimised design. A wavelength dependent splitter is an important basic building block for high-performance nanophotonic circuits. 1J. S. Jensen and O. Sigmund, App. Phys. Lett. 84, 2022...
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
The ABCD of topological recursion
DEFF Research Database (Denmark)
Andersen, Jorgen Ellegaard; Borot, Gaëtan; Chekhov, Leonid O.
Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial data a quantum Airy structure...... the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a Z2-invariant version of the latter. This Z2-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of math-ph/0702045....
Irrational Charge from Topological Order
Moessner, R.; Sondhi, S. L.
2010-10-01
Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice models, the three-dimensional resonating valence bond liquid on bipartite lattices as well as water and spin ice. By contrast, the gauge charges of the quasiparticles retain their quantized values.
Reconstructing Topological Graphs and Continua
Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf
2015-01-01
The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...
Focus on topological quantum computation
International Nuclear Information System (INIS)
Pachos, Jiannis K; Simon, Steven H
2014-01-01
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This ‘focus on’ collection brings together several of the latest developments in the field and facilitates the synergy between different approaches. (editorial)
When quantum optics meets topology
Amo, Alberto
2018-02-01
Routing photons at the micrometer scale remains one of the greatest challenges of integrated quantum optics. The main difficulty is the scattering losses at bends and splitters in the photonic circuit. Current approaches imply elaborate designs, quite sensitive to fabrication details (1). Inspired by the physics underlying the one-way transport of electrons in topological insulators, on page 666 of this issue, Barik et al. (2) report a topological photonic crystal in which single photons are emitted and routed through bends with negligible loss. The marriage between quantum optics and topology promises new opportunities for compact quantum optics gating and manipulation.
Topological susceptibility from the overlap
DEFF Research Database (Denmark)
Del Debbio, Luigi; Pica, Claudio
2003-01-01
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge....... Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study...
Site and strain-specific variation in gut microbiota profiles and metabolism in experimental mice.
Directory of Open Access Journals (Sweden)
Melissa K Friswell
2010-01-01
Full Text Available The gastrointestinal tract microbiota (GTM of mammals is a complex microbial consortium, the composition and activities of which influences mucosal development, immunity, nutrition and drug metabolism. It remains unclear whether the composition of the dominant GTM is conserved within animals of the same strain and whether stable GTMs are selected for by host-specific factors or dictated by environmental variables.The GTM composition of six highly inbred, genetically distinct strains of mouse (C3H, C57, GFEC, CD1, CBA nu/nu and SCID was profiled using eubacterial -specific PCR-DGGE and quantitative PCR of feces. Animals exhibited strain-specific fecal eubacterial profiles that were highly stable (c. >95% concordance over 26 months for C57. Analyses of mice that had been relocated before and after maturity indicated marked, reproducible changes in fecal consortia and that occurred only in young animals. Implantation of a female BDF1 mouse with genetically distinct (C57 and Agoutie embryos produced highly similar GTM profiles (c. 95% concordance between mother and offspring, regardless of offspring strain, which was also reflected in urinary metabolite profiles. Marked institution-specific GTM profiles were apparent in C3H mice raised in two different research institutions.Strain-specific data were suggestive of genetic determination of the composition and activities of intestinal symbiotic consortia. However, relocation studies and uterine implantation demonstrated the dominance of environmental influences on the GTM. This was manifested in large variations between isogenic adult mice reared in different research institutions.
Electrical impedance tomography: topology optimization
International Nuclear Information System (INIS)
Miranda, Lenine Campos
2013-01-01
The Electrical Impedance Tomography (EIT) is a study of body parts who use electric current. Is studied through computers resistance or conductivity of these parts, producing an image used for medical diagnosis. A body is wrapped in a blanket placed with small electrodes and receivers of electric current, potential difference. Based on data obtained from a series of measurements at the electrodes, one by one, sending and receiving, you can perform a numerical phantom, where each 'voxel' of the image formed computationally represents the impedance of biological tissue. In Brazil, studies on electrical impedance tomography (EIT) has not yet started. Such equipment are measured tensions - potential difference - between each electrode / sensor one by one, as a way to Simple Combinatorial Analysis. The sequence and the way it is measured strains are in the final image quality. Finite Element Method Interactive, whose algorithm is based on Dialectical Method. We use an initial function with the objective of maximizing the data quantitatively, for better qualitative analysis. Topology Optimization methods are used to improve the image reconstruction. Currently the study is quite primitive related to the theory that shows how to power the new science studied. The high quality images requires a difficulty in obtaining. This work is not intended for detailed for analysis in any tissue or organ specific, but in general terms. And the formation of the 2D image. 3D need a reconstructor to part. (author)
Formation of topological defects
International Nuclear Information System (INIS)
Vachaspati, T.
1991-01-01
We consider the formation of point and line topological defects (monopoles and strings) from a general point of view by allowing the probability of formation of a defect to vary. To investigate the statistical properties of the defects at formation we give qualitative arguments that are independent of any particular model in which such defects occur. These arguments are substantiated by numerical results in the case of strings and for monopoles in two dimensions. We find that the network of strings at formation undergoes a transition at a certain critical density below which there are no infinite strings and the closed-string (loop) distribution is exponentially suppressed at large lengths. The results are contrasted with the results of statistical arguments applied to a box of strings in dynamical equilibrium. We argue that if point defects were to form with smaller probability, the distance between monopoles and antimonopoles would decrease while the monopole-to-monopole distance would increase. We find that monopoles are always paired with antimonopoles but the pairing becomes clean only when the number density of defects is small. A similar reasoning would also apply to other defects
International Nuclear Information System (INIS)
Rome, J.A.; Peng, Y.K.M.
1978-09-01
Guiding center orbits in noncircular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, zeta, psi/sub m/). Here, v is the particle speed, zeta is the pitch angle with respect to the parallel equilibrium current, J/sub parallels/, and psi/sub m/ is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding center orbit. Two D-shaped equilibria in a flux-conserving tokamak having β's of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point and different types of orbits (e.g., circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher β (7.7%) equilibrium results in a dramatically different orbit topology from that of the lower β case. The differences indicate the confinement of additional high energy (v → c, within the guiding center approximation) trapped, co- and countercirculating particles whose orbit psi/sub m/ falls within the absolute B well
Renormalization of topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.; Thompson, G.
1988-11-01
One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs
Topology optimized electrothermal polysilicon microgrippers
DEFF Research Database (Denmark)
Sardan Sukas, Özlem; Petersen, Dirch Hjorth; Mølhave, Kristian
2008-01-01
This paper presents the topology optimized design procedure and fabrication of electrothermal polysilicon microgrippers for nanomanipulation purposes. Performance of the optimized microactuators is compared with a conventional three-beam microactuator design through finite element analysis...
Cartography – morphology – topology
DEFF Research Database (Denmark)
Dinesen, Cort Ross; Peder Pedersen, Claus
I 2004 a Summer School was established on the Greek island of Hydra. The was to be the basis of research-based morphological and topological studies, which have since taken place for 4 weeks of every year. Starting with Hydra’s topography different ways of considering topology were developed....... The work was approached from a new angle every year through a series of associated questions, resulting in an extensive body of drawings describing the various discourses raised. The developed observational forms reflected in the collected body of drawings constitute a topological landscape with a great...... and developing topological emergence as a passage between cartographic appropriation and creative becoming while simultaneously lifting the material out of its mimetic reference, makes room for the of a movement towards a production of meaning as well as a basis for initiating architectonic practices. We seek...
Topological Insulator Nanowires and Nanoribbons
Kong, Desheng; Randel, Jason C.; Peng, Hailin; Cha, Judy J.; Meister, Stefan; Lai, Keji; Chen, Yulin; Shen, Zhi-Xun; Manoharan, Hari C.; Cui, Yi
2010-01-01
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive
Topology of helical fluid flow
DEFF Research Database (Denmark)
Andersen, Morten; Brøns, Morten
2014-01-01
function for the topology of the streamline pattern in incompressible flows. On this basis, we perform a comprehensive study of the topology of the flow field generated by a helical vortex filament in an ideal fluid. The classical expression for the stream function obtained by Hardin (Hardin, J. C. 1982...... the zeroes of a single real function of one variable, and we show that three different flow topologies can occur, depending on a single dimensionless parameter. By including the self-induced velocity on the vortex filament by a localised induction approximation, the stream function is slightly modified...... and an extra parameter is introduced. In this setting two new flow topologies arise, but not more than two critical points occur for any combination of parameters....
A topological quantum optics interface.
Barik, Sabyasachi; Karasahin, Aziz; Flower, Christopher; Cai, Tao; Miyake, Hirokazu; DeGottardi, Wade; Hafezi, Mohammad; Waks, Edo
2018-02-09
The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored. We demonstrate a strong interface between single quantum emitters and topological photonic states. Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals. We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends. This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
Topology Based Domain Search (TBDS)
National Research Council Canada - National Science Library
Manning, William
2002-01-01
This effort will explore radical changes in the way Domain Name System (DNS) is used by endpoints in a network to improve the resilience of the endpoint and its applications in the face of dynamically changing infrastructure topology...
Two-dimensional topological photonics
Khanikaev, Alexander B.; Shvets, Gennady
2017-12-01
Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.
Topological gravity with minimal matter
International Nuclear Information System (INIS)
Li Keke
1991-01-01
Topological minimal matter, obtained by twisting the minimal N = 2 supeconformal field theory, is coupled to two-dimensional topological gravity. The free field formulation of the coupled system allows explicit representations of BRST charge, physical operators and their correlation functions. The contact terms of the physical operators may be evaluated by extending the argument used in a recent solution of topological gravity without matter. The consistency of the contact terms in correlation functions implies recursion relations which coincide with the Virasoro constraints derived from the multi-matrix models. Topological gravity with minimal matter thus provides the field theoretic description for the multi-matrix models of two-dimensional quantum gravity. (orig.)
Classical topology and quantum states
Indian Academy of Sciences (India)
structures) can be reconstructed using Gel'fand–Naimark theory and its ..... pair production and annihilation [23], quantum gravity too can be expected to become ..... showed their utility for research of current interest such as topology change ...
Topological objects in hadron physics
International Nuclear Information System (INIS)
Rho, M.
1988-01-01
The notion of topological objects in hadronic physics is discussed, with emphasis on the role of the Wess-Zumino term and induced transmutation of quantum numbers in chiral bag models. Some applications to nuclear systems are given
Intuitive concepts in elementary topology
Arnold, BH
2011-01-01
Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Elements of mathematics general topology
Bourbaki, Nicolas
1995-01-01
This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover.
Topological interpretation of Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-01-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...
The topology of galaxy clustering.
Coles, P.; Plionis, M.
The authors discuss an objective method for quantifying the topology of the galaxy distribution using only projected galaxy counts. The method is a useful complement to fully three-dimensional studies of topology based on the genus by virtue of the enormous projected data sets available. Applying the method to the Lick counts they find no evidence for large-scale non-gaussian behaviour, whereas the small-scale distribution is strongly non-gaussian, with a shift in the meatball direction.
Symmetry and topology in evolution
International Nuclear Information System (INIS)
Lukacs, B.; Berczi, S.; Molnar, I.; Paal, G.
1991-10-01
This volume contains papers of an interdisciplinary symposium on evolution. The aim of this symposium, held in Budapest, Hungary, 28-29 May 1991, was to clear the role of symmetry and topology at different levels of the evolutionary processes. 21 papers were presented, their topics included evolution of the Universe, symmetry of elementary particles, asymmetry of the Earth, symmetry and asymmetry of biomolecules, symmetry and topology of lining objects, human asymmetry etc. (R.P.)
Topological excitations in semiconductor heterostructures
International Nuclear Information System (INIS)
Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.
2013-01-01
Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements
Topology Optimized Photonic Wire Splitters
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Borel, Peter Ingo; Jensen, Jakob Søndergaard
2006-01-01
Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm.......Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm....
Topological surface states in nodal superconductors.
Schnyder, Andreas P; Brydon, Philip M R
2015-06-24
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.
Dynamical topological invariant after a quantum quench
Yang, Chao; Li, Linhu; Chen, Shu
2018-02-01
We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.
Topological orders in rigid states
International Nuclear Information System (INIS)
Wen, X.G.
1990-01-01
The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. The authors show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90 degrees rotation
Topological Photonics for Continuous Media
Silveirinha, Mario
Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.
Topology change and quantum physics
International Nuclear Information System (INIS)
Balachandran, A.P.; Marmo, G.; Simoni, A.
1995-01-01
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Examples are presented where classical topology is changed by smoothly altering the boundary conditions. When the parameters labelling the latter are treated as quantum variables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies. An existing argument of Sorkin based on the spin-statistics connection and indicating the necessity of topology change in quantum gravity is recalled. It is suggested therefrom and our results here that Einstein gravity and its minor variants are effective theories of a deeper description with additional novel degrees of freedom. Other reasons for suspecting such a microstructure are also summarized. (orig.)
Relativity of topology and dynamics
International Nuclear Information System (INIS)
Finkelstein, D.; Rodriguez, E.
1984-01-01
Recent developments in quantum set theory are used to formulate a program for quantum topological physics. The world is represented in Hilbert space whose psi vectors represent abstract complexes generated from the null set by one bracket operator and the usual Grassmann (or Clifford) product. Such a theory may be more basic than field theory, in that it may generate its own natural topology, time, kinematics and dynamics, without benefit of an absolute time-space dimension, topology, or Hamiltonian. For example there is a natural expression for the quantum gravitational field in terms of quantum topological operators. In such a theory the usual spectrum of possible dimensions describes only one of an indefinite hierarchy of levels, each with a similar spectrum, describing nonspatial infrastructure. While c simplices have no continuous symmetry, the q simplex has an orthogonal group (O(m,n). Because quantum theory cannot take the universe as physical system, a ''third relativity'' is proposed. The division between observer and observed is arbitrary. Then it is wrong to ask for ''the'' topology and dynamics of a system, in the same sense that it is wrong to ask for the ''the'' psi vectors of a system; topology and dynamics, like psi vectors, are not absolute but relative to the observer. (author)
Topology change and quantum physics
International Nuclear Information System (INIS)
Balachandran, A.P.; Marmo, G.; Simoni, A.
1995-03-01
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Several examples are presented where classical topology is changed by smoothly altering the boundary conditions. When the parameters labelling the latter are treated as quantum variables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies. An existing argument of Sorkin based on the spin-statistics connection and indicating the necessity of topology change in quantum gravity is recalled. It is suggested therefrom and our results here that Einstein gravity and its minor variants are effective theories of a deeper description with additional novel degrees of freedom. Other reasons for suspecting such a microstructure are also summarized. (author). 22 refs, 3 figs
Topological BF field theory description of topological insulators
International Nuclear Information System (INIS)
Cho, Gil Young; Moore, Joel E.
2011-01-01
Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
The application of molecular topology for ulcerative colitis drug discovery.
Bellera, Carolina L; Di Ianni, Mauricio E; Talevi, Alan
2018-01-01
Although the therapeutic arsenal against ulcerative colitis has greatly expanded (including the revolutionary advent of biologics), there remain patients who are refractory to current medications while the safety of the available therapeutics could also be improved. Molecular topology provides a theoretic framework for the discovery of new therapeutic agents in a very efficient manner, and its applications in the field of ulcerative colitis have slowly begun to flourish. Areas covered: After discussing the basics of molecular topology, the authors review QSAR models focusing on validated targets for the treatment of ulcerative colitis, entirely or partially based on topological descriptors. Expert opinion: The application of molecular topology to ulcerative colitis drug discovery is still very limited, and many of the existing reports seem to be strictly theoretic, with no experimental validation or practical applications. Interestingly, mechanism-independent models based on phenotypic responses have recently been reported. Such models are in agreement with the recent interest raised by network pharmacology as a potential solution for complex disorders. These and other similar studies applying molecular topology suggest that some therapeutic categories may present a 'topological pattern' that goes beyond a specific mechanism of action.
Quantum transport in topological semimetals under magnetic fields
Lu, Hai-Zhou; Shen, Shun-Qing
2017-06-01
Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.
Optical and Casimir effects in topological materials
Wilson, Justin H.
Two major electromagnetic phenomena, magneto-optical effects and the Casimir effect, have seen much theoretical and experimental use for many years. On the other hand, recently there has been an explosion of theoretical and experimental work on so-called topological materials, and a natural question to ask is how such electromagnetic phenomena change with these novel materials. Specifically, we will consider are topological insulators and Weyl semimetals. When Dirac electrons on the surface of a topological insulator are gapped or Weyl fermions in the bulk of a Weyl semimetal appear due to time-reversal symmetry breaking, there is a resulting quantum anomalous Hall effect (2D in one case and bulk 3D in the other, respectively). For topological insulators, we investigate the role of localized in-gap states which can leave their own fingerprints on the magneto-optics and can therefore be probed. We have shown that these states resonantly contribute to the Hall conductivity and are magneto-optically active. For Weyl semimetals we investigate the Casimir force and show that with thickness, chemical potential, and magnetic field, a repulsive and tunable Casimir force can be obtained. Additionally, various values of the parameters can give various combinations of traps and antitraps. We additionally probe the topological transition called a Lifshitz transition in the band structure of a material and show that in a Casimir experiment, one can observe a non-analytic "kink'' in the Casimir force across such a transition. The material we propose is a spin-orbit coupled semiconductor with large g-factor that can be magnetically tuned through such a transition. Additionally, we propose an experiment with a two-dimensional metal where weak localization is tuned with an applied field in order to definitively test the effect of diffusive electrons on the Casimir force---an issue that is surprisingly unresolved to this day. Lastly, we show how the time-continuous coherent state
Topology optimization under stochastic stiffness
Asadpoure, Alireza
Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations
Ledder, Ruth G; Sreenivasan, Prem K; DeVizio, William; McBain, Andrew J
2010-12-01
The microbiological effects of biocidal products used for the enhancement of oral hygiene relate to the active compound(s) as well as other formulation components. Here, we test the specificities of selected actives in the absence of multiple excipients. Salivary ecosystems were maintained in tissue culture plate-based hydroxyapatite disc models (HDMs) and modified drip-flow biofilm reactors (MDFRs). Test compounds stannous fluoride (SF), SDS, triclosan (TCS), zinc lactate (ZL) and ZL with SF in combination (ZLSF) were delivered to the HDMs once and four times daily for 6 days to MDFRs. Plaques were characterized by differential viable counting and PCR-denaturing gradient gel electrophoresis (DGGE). TCS and SDS were the most effective compounds against HDM plaques, significantly reducing total viable counts (P<0.05), whilst SF, ZL and ZLSF were comparatively ineffective. TCS exhibited specificity for streptococci (P<0.01) and Gram-negative anaerobes (P<0.01) following a single dosing and also on repeated dosing in MDFRs. In contrast to single exposures, multiple dosing with ZLSF also significantly reduced all bacterial groups, whilst SF and ZL caused significant but transient reductions. According to PCR-DGGE analyses, significant (P<0.05) reductions in eubacterial diversity occurred following 6 day dosing with both TCS and ZLSF. Concordance of MDFR eubacterial profiles with salivary inocula ranged between 58 and 97%. TCS and ZL(SF) exhibited similar specificities to those reported for formulations. TCS was the most potent antibacterial, after single and multiple dosage regimens.
Topology Optimization of Active Transport Flows
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe
2017-01-01
Fluid flows with particle transport are common in many industrial processes and components. The design of components for addition or removal of particles as well as mixing or stratification is of great importance in the specific processes. This work presents a methodology to apply topology....... The paper present the design and optimization of a particle separator and the important interpolation for modeling both solids, fluids and particles with a monolithic problem formulation. The interplay with the physics behind the model are discussed and the influence of parameters are demonstrated....
Propagation of optical vortices with fractional topological charge in free space
Ali, Tamelia; Kreminska, Liubov; Golovin, Andrii B.; Crouse, David T.
2014-10-01
The behavior of the optical vortices with fractional topological charges in the far-field is assessed through numerical modeling and confirmed by experimental results. The generation of fractional topological charge variations of the phase within a Gaussian beam was achieved by using a liquid crystal spatial light modulator (LCoS SLM). It is shown that a laser beam carrying an optical vortex with a fractional topological charge evolves into a beam with a topological charge of integer value, specifically an integer value closer to the fractional number in the far field. A potential application of this work is for data transmission within optical telecommunication systems.
Novel Topology of Three-Phase Electric Spring and Its Control
DEFF Research Database (Denmark)
Wang, Qingsong; Cheng, Ming; Jiang, Yunlei
2017-01-01
A novel topology is proposed for three-phase electric spring (TPES) to achieve specific functionalities. With respect to the existing one, the novel topology contains an additional three-phase transformer with the primaries located at the position of the non-critical three-phase load (NCL......) of the existing topology and its secondaries connected to the new three-phase NCL, thus forming a new three-phase smart load (SL). To control the novel topology, the so-called modified δ control utilized for the single-phase electric springs is extended to the three-phase case. Thanks to these solutions, TPES...
Braiding knots with topological strings
International Nuclear Information System (INIS)
Gu, Jie
2015-08-01
For an arbitrary knot in a three-sphere, the Ooguri-Vafa conjecture associates to it a unique stack of branes in type A topological string on the resolved conifold, and relates the colored HOMFLY invariants of the knot to the free energies on the branes. For torus knots, we use a modified version of the topological recursion developed by Eynard and Orantin to compute the free energies on the branes from the Aganagic-Vafa spectral curves of the branes, and find they are consistent with the known colored HOMFLY knot invariants a la the Ooguri-Vafa conjecture. In addition our modified topological recursion can reproduce the correct closed string free energies, which encode the information of the background geometry. We conjecture the modified topological recursion is applicable for branes associated to hyperbolic knots as well, encouraged by the observation that the modified topological recursion yields the correct planar closed string free energy from the Aganagic-Vafa spectral curves of hyperbolic knots. This has implications for the knot theory concerning distinguishing mutant knots with colored HOMFLY invariants. Furthermore, for hyperbolic knots, we present methods to compute colored HOMFLY invariants in nonsymmetric representations of U(N). The key step in this computation is computing quantum 6j-symbols in the quantum group U q (sl N ).
Topological strings from quantum mechanics
International Nuclear Information System (INIS)
Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki
2014-12-01
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Topological susceptibility from the overlap
International Nuclear Information System (INIS)
Del Debbio, Luigi; Pica, Claudio
2004-01-01
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge. Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high statistics (500 to 1000 independent configurations) yield an extrapolated continuum limit with errors that are comparable with other methods. Our current value from the overlap is χ 1/4 = 188±12±5MeV (author)
Driving protocol for a Floquet topological phase without static counterpart
Quelle, A.; Weitenberg, C.; Sengstock, K.; Morais Smith, C.
2017-11-01
Periodically driven systems play a prominent role in optical lattices. In these ultracold atomic systems, driving is used to create a variety of interesting behaviours, of which an important example is provided by topological states of matter. Such Floquet topological phases have a richer classification than their equilibrium counterparts. Although there exist analogues of the equilibrium topological phases that are characterised by a Chern number, the corresponding Hall conductivity, and protected edge states, there is an additional possibility. This is a phase that has a vanishing Chern number and no Hall conductivity, but nevertheless hosts anomalous topological edge states (Rudner et al (2013 Phys. Rev. X 3 031005)). Due to experimental difficulties associated with the observation of such a phase, it has not been experimentally realised in optical lattices so far. In this paper, we show that optical lattices prove to be a good candidate for its realisation and observation, because they can be driven in a controlled manner. Specifically, we present a simple shaking protocol that serves to realise this special Floquet phase, discuss the specific properties that it has, and propose a method to experimentally detect this fascinating topological phase that has no counterpart in equilibrium systems.
Topological Derivatives in Shape Optimization
Novotny, Antonio André
2013-01-01
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intende...
Wave Manipulation by Topology Optimization
DEFF Research Database (Denmark)
Andkjær, Jacob Anders
topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable...... for the cloak is to delay the waves in regions of higher permittivity than the background and subsequently phase match them to the waves outside. Directional acoustic cloaks can also be designed using the topology optimization method. Aluminum cylinders constitutes the design and their placement and size...... concerns the design of planar Fresnel zone plate lenses for focusing electromagnetic waves. The topology optimized zone plates improve the focusing performance compared to results known from the literature....
Aeroelastic Wingbox Stiffener Topology Optimization
Stanford, Bret K.
2017-01-01
This work considers an aeroelastic wingbox model seeded with run-out blade stiffeners along the skins. Topology optimization is conducted within the shell webs of the stiffeners, in order to add cutouts and holes for mass reduction. This optimization is done with a global-local approach in order to moderate the computational cost: aeroelastic loads are computed at the wing-level, but the topology and sizing optimization is conducted at the panel-level. Each panel is optimized separately under stress, buckling, and adjacency constraints, and periodically reassembled to update the trimmed aeroelastic loads. The resulting topology is baselined against a design with standard full-depth solid stiffener blades, and found to weigh 7.43% less.
Topological analysis of metabolic control.
Sen, A K
1990-12-01
A topological approach is presented for the analysis of control and regulation in metabolic pathways. In this approach, the control structure of a metabolic pathway is represented by a weighted directed graph. From an inspection of the topology of the graph, the control coefficients of the enzymes are evaluated in a heuristic manner in terms of the enzyme elasticities. The major advantage of the topological approach is that it provides a visual framework for (1) calculating the control coefficients of the enzymes, (2) analyzing the cause-effect relationships of the individual enzymes, (3) assessing the relative importance of the enzymes in metabolic regulation, and (4) simplifying the structure of a given pathway, from a regulatory viewpoint. Results are obtained for (a) an unbranched pathway in the absence of feedback the feedforward regulation and (b) an unbranched pathway with feedback inhibition. Our formulation is based on the metabolic control theory of Kacser and Burns (1973) and Heinrich and Rapoport (1974).
Topological setting of Bessel functions
International Nuclear Information System (INIS)
Mekhfi, M.
1995-11-01
We start from the topology of the punctured plane encoded within its homotopy group which is isomorphic to the set of integers Z. We then realize group elements Π(n), n is an element of Z as differential operators on the space of analytic functions. Using plausible physical arguments we select a subset of functions which we identify with integer orders reduced Bessel functions. On the other hand we propose a unifying new formula of topological origin, generating real orders Bessel functions out of integers orders ones, the generator being an operator built entirely out of the Π s . We thus have shown that the topology (of the puntured plane) is underlying the inner structure of Bessel functions, in addition it unifies them independently of the orders being integers or reals. (author). 4 refs
Optimal Network-Topology Design
Li, Victor O. K.; Yuen, Joseph H.; Hou, Ting-Chao; Lam, Yuen Fung
1987-01-01
Candidate network designs tested for acceptability and cost. Optimal Network Topology Design computer program developed as part of study on topology design and analysis of performance of Space Station Information System (SSIS) network. Uses efficient algorithm to generate candidate network designs consisting of subsets of set of all network components, in increasing order of total costs and checks each design to see whether it forms acceptable network. Technique gives true cost-optimal network and particularly useful when network has many constraints and not too many components. Program written in PASCAL.
Topological insulators fundamentals and perspectives
Ortmann, Frank; Valenzuela, Sergio O
2015-01-01
There are only few discoveries and new technologies in physical sciences that have the potential to dramatically alter and revolutionize our electronic world. Topological insulators are one of them. The present book for the first time provides a full overview and in-depth knowledge about this hot topic in materials science and condensed matter physics. Techniques such as angle-resolved photoemission spectrometry (ARPES), advanced solid-state Nuclear Magnetic Resonance (NMR) or scanning-tunnel microscopy (STM) together with key principles of topological insulators such as spin-locked electronic
Acoustic design by topology optimization
DEFF Research Database (Denmark)
Dühring, Maria Bayard; Jensen, Jakob Søndergaard; Sigmund, Ole
2008-01-01
To bring down noise levels in human surroundings is an important issue and a method to reduce noise by means of topology optimization is presented here. The acoustic field is modeled by Helmholtz equation and the topology optimization method is based on continuous material interpolation functions...... in the density and bulk modulus. The objective function is the squared sound pressure amplitude. First, room acoustic problems are considered and it is shown that the sound level can be reduced in a certain part of the room by an optimized distribution of reflecting material in a design domain along the ceiling...
International Nuclear Information System (INIS)
Tellis, D.R.
2000-01-01
Full text: Instantons in pure Yang-Mills gauge theory have been studied extensively by physicists and mathematicians alike. The surprisingly rich topological structure plays an important role in hadron structure. A crucial role is played by how the boundary conditions on the gauge fields are imposed. While the topology of gauge fields in pure Yang-Mills gauge theory is understood for the compact manifold of the 4-sphere, the manifold of the 4-torus remains an active area of study. The latter is particularly important in the study of Lattice QCD
Topological vector spaces and distributions
Horvath, John
2012-01-01
""The most readable introduction to the theory of vector spaces available in English and possibly any other language.""-J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition o
International Conference on Algebraic Topology
Cohen, Ralph; Miller, Haynes; Ravenel, Douglas
1989-01-01
These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in part to mark the 25th anniversary of the journal Topology and 60th birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and was conceived as a successor to the Aarhus conferences of 1978 and 1982. Some thirty papers are included in this volume, mostly at a research level. Subjects include cyclic homology, H-spaces, transformation groups, real and rational homotopy theory, acyclic manifolds, the homotopy theory of classifying spaces, instantons and loop spaces, and complex bordism.
Topological entropy of continuous functions on topological spaces
International Nuclear Information System (INIS)
Liu Lei; Wang Yangeng; Wei Guo
2009-01-01
Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems
Topological phases of topological-insulator thin films
Asmar, Mahmoud M.; Sheehy, Daniel E.; Vekhter, Ilya
2018-02-01
We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as a function of both the film thickness and the momentum in the plane of the film for Bi2Se3 and Bi2Te3 . As a result, while the magnitude of the matrix element at the center of the surface Brillouin zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and nontopological phases, separated by semimetallic states, as the film thickness varies. In the topological phase, the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi2Se3 , making Bi2Te3 , where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators.
Non-perturbative topological strings and conformal blocks
Cheng, M.C.N.; Dijkgraaf, R.; Vafa, C.
2011-01-01
We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to
Multiscale topology optimization of solid and fluid structures
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe
This thesis considers the application of the topology optimization method to multiscale problems, specifically the fluid-structure interaction problem. By multiple-scale methods the governing equations, the Navier-Cauchy and the incompressible Navier-Stokes equations are expanded and separated...
Topological phases: Wormholes in quantum matter
Schoutens, K.
2009-01-01
Proliferation of so-called anyonic defects in a topological phase of quantum matter leads to a critical state that can be visualized as a 'quantum foam', with topology-changing fluctuations on all length scales.
In-surface confinement of topological insulator nanowire surface states
International Nuclear Information System (INIS)
Chen, Fan W.; Jauregui, Luis A.; Tan, Yaohua; Manfra, Michael; Klimeck, Gerhard; Chen, Yong P.; Kubis, Tillmann
2015-01-01
The bandstructures of [110] and [001] Bi 2 Te 3 nanowires are solved with the atomistic 20 band tight binding functionality of NEMO5. The theoretical results reveal: The popular assumption that all topological insulator (TI) wire surfaces are equivalent is inappropriate. The Fermi velocity of chemically distinct wire surfaces differs significantly which creates an effective in-surface confinement potential. As a result, topological insulator surface states prefer specific surfaces. Therefore, experiments have to be designed carefully not to probe surfaces unfavorable to the surface states (low density of states) and thereby be insensitive to the TI-effects
Broadband Control of Topological Nodes in Electromagnetic Fields
Song, Alex Y.; Catrysse, Peter B.; Fan, Shanhui
2018-05-01
We study topological nodes (phase singularities) in electromagnetic wave interactions with structures. We show that, when the nodes exist, it is possible to bind certain nodes to a specific plane in the structure by a combination of mirror and time-reversal symmetry. Such binding does not rely on any resonances in the structure. As a result, the nodes persist on the plane over a wide wavelength range. As an implication of such broadband binding, we demonstrate that the topological nodes can be used for hiding of metallic objects over a broad wavelength range.
In-surface confinement of topological insulator nanowire surface states
Energy Technology Data Exchange (ETDEWEB)
Chen, Fan W., E-mail: fanchen@purdue.edu [Department of Physics and Astronomy, Purdue, West Lafayette, Indiana 47907 (United States); Network for Computational Nanotechnology, Purdue, West Lafayette, Indiana 47907 (United States); Jauregui, Luis A. [School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); Tan, Yaohua [Network for Computational Nanotechnology, Purdue, West Lafayette, Indiana 47907 (United States); School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Manfra, Michael [Department of Physics and Astronomy, Purdue, West Lafayette, Indiana 47907 (United States); School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Klimeck, Gerhard [Network for Computational Nanotechnology, Purdue, West Lafayette, Indiana 47907 (United States); School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); Chen, Yong P. [Department of Physics and Astronomy, Purdue, West Lafayette, Indiana 47907 (United States); School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); Kubis, Tillmann [Network for Computational Nanotechnology, Purdue, West Lafayette, Indiana 47907 (United States)
2015-09-21
The bandstructures of [110] and [001] Bi{sub 2}Te{sub 3} nanowires are solved with the atomistic 20 band tight binding functionality of NEMO5. The theoretical results reveal: The popular assumption that all topological insulator (TI) wire surfaces are equivalent is inappropriate. The Fermi velocity of chemically distinct wire surfaces differs significantly which creates an effective in-surface confinement potential. As a result, topological insulator surface states prefer specific surfaces. Therefore, experiments have to be designed carefully not to probe surfaces unfavorable to the surface states (low density of states) and thereby be insensitive to the TI-effects.
In-surface confinement of topological insulator nanowire surface states
Chen, Fan W.; Jauregui, Luis A.; Tan, Yaohua; Manfra, Michael; Klimeck, Gerhard; Chen, Yong P.; Kubis, Tillmann
2015-09-01
The bandstructures of [110] and [001] Bi2Te3 nanowires are solved with the atomistic 20 band tight binding functionality of NEMO5. The theoretical results reveal: The popular assumption that all topological insulator (TI) wire surfaces are equivalent is inappropriate. The Fermi velocity of chemically distinct wire surfaces differs significantly which creates an effective in-surface confinement potential. As a result, topological insulator surface states prefer specific surfaces. Therefore, experiments have to be designed carefully not to probe surfaces unfavorable to the surface states (low density of states) and thereby be insensitive to the TI-effects.
Rule-based topology system for spatial databases to validate complex geographic datasets
Martinez-Llario, J.; Coll, E.; Núñez-Andrés, M.; Femenia-Ribera, C.
2017-06-01
A rule-based topology software system providing a highly flexible and fast procedure to enforce integrity in spatial relationships among datasets is presented. This improved topology rule system is built over the spatial extension Jaspa. Both projects are open source, freely available software developed by the corresponding author of this paper. Currently, there is no spatial DBMS that implements a rule-based topology engine (considering that the topology rules are designed and performed in the spatial backend). If the topology rules are applied in the frontend (as in many GIS desktop programs), ArcGIS is the most advanced solution. The system presented in this paper has several major advantages over the ArcGIS approach: it can be extended with new topology rules, it has a much wider set of rules, and it can mix feature attributes with topology rules as filters. In addition, the topology rule system can work with various DBMSs, including PostgreSQL, H2 or Oracle, and the logic is performed in the spatial backend. The proposed topology system allows users to check the complex spatial relationships among features (from one or several spatial layers) that require some complex cartographic datasets, such as the data specifications proposed by INSPIRE in Europe and the Land Administration Domain Model (LADM) for Cadastral data.
Topology optimization of microfluidic mixers
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe; Gersborg, Allan Roulund; Sigmund, Ole
2009-01-01
This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering...
Magnetic Field Topology in Jets
Gardiner, T. A.; Frank, A.
2000-01-01
We present results on the magnetic field topology in a pulsed radiative. jet. For initially helical magnetic fields and periodic velocity variations, we find that the magnetic field alternates along the, length of the jet from toroidally dominated in the knots to possibly poloidally dominated in the intervening regions.
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Topological freeness for Hilbert bimodules
DEFF Research Database (Denmark)
Kwasniewski, Bartosz
2014-01-01
It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description...
Topological interpretation of multiquark states
International Nuclear Information System (INIS)
Nicolescu, B.
1980-12-01
In this talk we discuss the topological selection rules which govern the physics of multiquark states in the framework in the DTU theory. These new selection rules lead us to expect that narrow multiquark hadrons are rare, are strongly coupled only to some particular channels, and appear only in some restricted mass regions
Topological methods in Euclidean spaces
Naber, Gregory L
2000-01-01
Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem, the Lefschetz Fixed Point Theorem, the Stone-Weierstrass Theorem, and Morse functions. Includes new section of solutions to selected problems.
Topological Order in Silicon Photonics
2017-02-07
photonic edge states and quantum emitters [ S. Barik , H. Miyake, W. DeGottardi, E. Waks and M. Hafezi, New J. Phys., 18, 11301 (2016) ]. Entanglement... Barik , H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi “Two-Dimensionally Confined Topological Edge States in Photonic Crystals”, New J. Phys., 18
Algebraic topology of spin glasses
International Nuclear Information System (INIS)
Koma, Tohru
2011-01-01
We study the topology of frustration in d-dimensional Ising spin glasses with d ≥ 2 with nearest-neighbor interactions. We prove the following. For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the (d - 1)-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three- or higher-dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global topological effect of the frustrations.
Independent Study Project, Topic: Topology.
Notre Dame High School, Easton, PA.
Using this guide and the four popular books noted in it, a student, working independently, will learn about some of the classical ideas and problems of topology: the Meobius strip and Klein bottle, the four color problem, genus of a surface, networks, Euler's formula, and the Jordan Curve Theorem. The unit culminates in a project of the students'…
Topology of molecular interaction networks
Winterbach, W.; Van Mieghem, P.; Reinders, M.; Wang, H.; De Ridder, D.
2013-01-01
Molecular interactions are often represented as network models which have become the common language of many areas of biology. Graphs serve as convenient mathematical representations of network models and have themselves become objects of study. Their topology has been intensively researched over
Nuclear Pasta: Topology and Defects
da Silva Schneider, Andre; Horowitz, Charles; Berry, Don; Caplan, Matt; Briggs, Christian
2015-04-01
A layer of complex non-uniform phases of matter known as nuclear pasta is expected to exist at the base of the crust of neutron stars. Using large scale molecular dynamics we study the topology of some pasta shapes, the formation of defects and how these may affect properties of neutron star crusts.
Topology optimization for acoustic problems
DEFF Research Database (Denmark)
Dühring, Maria Bayard
2006-01-01
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
Topological domain walls in helimagnets
Schoenherr, P.; Müller, J.; Köhler, L.; Rosch, A.; Kanazawa, N.; Tokura, Y.; Garst, M.; Meier, D.
2018-05-01
Domain walls naturally arise whenever a symmetry is spontaneously broken. They interconnect regions with different realizations of the broken symmetry, promoting structure formation from cosmological length scales to the atomic level1,2. In ferroelectric and ferromagnetic materials, domain walls with unique functionalities emerge, holding great promise for nanoelectronics and spintronics applications3-5. These walls are usually of Ising, Bloch or Néel type and separate homogeneously ordered domains. Here we demonstrate that a wide variety of new domain walls occurs in the presence of spatially modulated domain states. Using magnetic force microscopy and micromagnetic simulations, we show three fundamental classes of domain walls to arise in the near-room-temperature helimagnet iron germanium. In contrast to conventional ferroics, the domain walls exhibit a well-defined inner structure, which—analogous to cholesteric liquid crystals—consists of topological disclination and dislocation defects. Similar to the magnetic skyrmions that form in the same material6,7, the domain walls can carry a finite topological charge, permitting an efficient coupling to spin currents and contributions to a topological Hall effect. Our study establishes a new family of magnetic nano-objects with non-trivial topology, opening the door to innovative device concepts based on helimagnetic domain walls.
Spacetime representation of topological phononics
Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.
2018-05-01
Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.
Lateral topological crystalline insulator heterostructure
Sun, Qilong; Dai, Ying; Niu, Chengwang; Ma, Yandong; Wei, Wei; Yu, Lin; Huang, Baibiao
2017-06-01
The emergence of lateral heterostructures fabricated by two-dimensional building blocks brings many exciting realms in material science and device physics. Enriching available nanomaterials for creating such heterostructures and enabling the underlying new physics is highly coveted for the integration of next-generation devices. Here, we report a breakthrough in lateral heterostructure based on the monolayer square transition-metal dichalcogenides MX2 (M = W, X = S/Se) modules. Our results reveal that the MX2 lateral heterostructure (1S-MX2 LHS) can possess excellent thermal and dynamical stability. Remarkably, the highly desired two-dimensional topological crystalline insulator phase is confirmed by the calculated mirror Chern number {{n}\\text{M}}=-1 . A nontrivial band gap of 65 meV is obtained with SOC, indicating the potential for room-temperature observation and applications. The topologically protected edge states emerge at the edges of two different nanoribbons between the bulk band gap, which is consistent with the mirror Chern number. In addition, a strain-induced topological phase transition in 1S-MX2 LHS is also revealed, endowing the potential utilities in electronics and spintronics. Our predictions not only introduce new member and vitality into the studies of lateral heterostructures, but also highlight the promise of lateral heterostructure as appealing topological crystalline insulator platforms with excellent stability for future devices.
Topological excitations in magnetic materials
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D., E-mail: bazeia@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Doria, M.M. [Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro (Brazil); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Rodrigues, E.I.B. [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil)
2016-05-20
In this work we propose a new route to describe topological excitations in magnetic systems through a single real scalar field. We show here that spherically symmetric structures in two spatial dimensions, which map helical excitations in magnetic materials, admit this formulation and can be used to model skyrmion-like structures in magnetic materials.
Asymptotically optimal load balancing topologies
Mukherjee, D.; Borst, S.C.; van Leeuwaarden, J.S.H.
2017-01-01
We consider a system of N servers inter-connected by some underlying graph topology G N . Tasks arrive at the various servers as independent Poisson processes of rate λ . Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears
A Macdonald refined topological vertex
Foda, Omar; Wu, Jian-Feng
2017-07-01
We consider the refined topological vertex of Iqbal et al (2009 J. High Energy Phys. JHEP10(2009)069), as a function of two parameters ≤ft\\lgroup x, y \\right\\rgroup , and deform it by introducing the Macdonald parameters ≤ft\\lgroup q, t \\right\\rgroup , as in the work of Vuletić on plane partitions (Vuletić M 2009 Trans. Am. Math. Soc. 361 2789-804), to obtain ‘a Macdonald refined topological vertex’. In the limit q → t , we recover the refined topological vertex of Iqbal et al and in the limit x → y , we obtain a qt-deformation of the original topological vertex of Aganagic et al (2005 Commun. Math. Phys. 25 425-78). Copies of the vertex can be glued to obtain qt-deformed 5D instanton partition functions that have well-defined 4D limits and, for generic values of ≤ft\\lgroup q, t\\right\\rgroup , contain infinite-towers of poles for every pole present in the limit q → t .
Deformations of topological open strings
Hofman, C.; Ma, Whee Ky
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra - the complex of multilinear maps on the boundary Hilbert space.
Lectures on cosmic topological defects
Energy Technology Data Exchange (ETDEWEB)
Vachaspati, T [Department of Astronomy and Astrophysics, Colaba, Mumbai (India) and Physics Department, Case Western Reserve University, Cleveland (United States)
2001-11-15
These lectures review certain topological defects and aspects of their cosmology. Unconventional material includes brief descriptions of electroweak defects, the structure of domain walls in non-Abelian theories, and the spectrum of magnetic monopoles in SU(5) Grand Unified theory. (author)
Topological Insulator Nanowires and Nanoribbons
Kong, Desheng
2010-01-13
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi2Se5 nanomaterials with a variety of morphologies. The synthesis of Bi 2Se5 nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [1120] direction with a rectangular cross-section and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with ∼ 1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitais to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states. © 2010 American Chemical Society.
Topological visual mapping in robotics.
Romero, Anna; Cazorla, Miguel
2012-08-01
A key problem in robotics is the construction of a map from its environment. This map could be used in different tasks, like localization, recognition, obstacle avoidance, etc. Besides, the simultaneous location and mapping (SLAM) problem has had a lot of interest in the robotics community. This paper presents a new method for visual mapping, using topological instead of metric information. For that purpose, we propose prior image segmentation into regions in order to group the extracted invariant features in a graph so that each graph defines a single region of the image. Although others methods have been proposed for visual SLAM, our method is complete, in the sense that it makes all the process: it presents a new method for image matching; it defines a way to build the topological map; and it also defines a matching criterion for loop-closing. The matching process will take into account visual features and their structure using the graph transformation matching (GTM) algorithm, which allows us to process the matching and to remove out the outliers. Then, using this image comparison method, we propose an algorithm for constructing topological maps. During the experimentation phase, we will test the robustness of the method and its ability constructing topological maps. We have also introduced new hysteresis behavior in order to solve some problems found building the graph.
Topological Properties of Spatial Coherence Function
International Nuclear Information System (INIS)
Ji-Rong, Ren; Tao, Zhu; Yi-Shi, Duan
2008-01-01
The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures (coherence vortices) of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function
Jakob Nielsen and His Contributions to Topology
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
1999-01-01
The Danish mathematician Jakob Nielsen won international recognition as one of the developers of combinatorial group theory and the topology of surfaces. This article describes the life and work of Jakob Nielsen with emphasis on his contributions to topology.......The Danish mathematician Jakob Nielsen won international recognition as one of the developers of combinatorial group theory and the topology of surfaces. This article describes the life and work of Jakob Nielsen with emphasis on his contributions to topology....
Topological Analysis of Wireless Networks (TAWN)
2016-05-31
19b. TELEPHONE NUMBER (Include area code) 31-05-2016 FINAL REPORT 12-02-2015 -- 31-05-2016 Topological Analysis of Wireless Networks (TAWN) Robinson...Release, Distribution Unlimited) N/A The goal of this project was to develop topological methods to detect and localize vulnerabilities of wireless... topology U U U UU 32 Michael Robinson 202-885-3681 Final Report: May 2016 Topological Analysis of Wireless Networks Principal Investigator: Prof. Michael
SATA II - Stochastic Algebraic Topology and Applications
2017-01-30
AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications... Topology and Applications Continuation of, and associated with SATA: Stochastic Algebraic Topology and Applications FA8655-11-1-3039, 09/1/2011–08/31/2014
Topology Discovery Using Cisco Discovery Protocol
Rodriguez, Sergio R.
2009-01-01
In this paper we address the problem of discovering network topology in proprietary networks. Namely, we investigate topology discovery in Cisco-based networks. Cisco devices run Cisco Discovery Protocol (CDP) which holds information about these devices. We first compare properties of topologies that can be obtained from networks deploying CDP versus Spanning Tree Protocol (STP) and Management Information Base (MIB) Forwarding Database (FDB). Then we describe a method of discovering topology ...
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces
Directory of Open Access Journals (Sweden)
A. A. Salama
2014-03-01
Full Text Available In this paper, we generalize the crisp topological spaces to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.
Generalized Mathai-Quillen Topological Sigma Models
Llatas, Pablo M.
1995-01-01
A simple field theoretical approach to Mathai-Quillen topological field theories of maps $X: M_I \\to M_T$ from an internal space to a target space is presented. As an example of applications of our formalism we compute by applying our formulas the action and Q-variations of the fields of two well known topological systems: Topological Quantum Mechanics and type-A topological Sigma Model.
Finite volume QCD at fixed topological charge
Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya
2007-01-01
In finite volume the partition function of QCD with a given $\\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of...
Topological Higgs mechanism with ordinary Higgs mechanism
International Nuclear Information System (INIS)
Oda Ichiro; Yahikozawa Shigeaki.
1989-12-01
Topological Higgs mechanism in higher dimensions is analyzed when ordinary Higgs potential exists. It is shown that if one-form B-field becomes massive by the ordinary Higgs mechanism, another D-2 form C-field also becomes massive through topological term in addition to the topological mass generation by the topological Higgs mechanism. Moreover we investigate this mechanism in three dimensional theories, that is to say, Chern-Simons theory and more general theory. (author). 10 refs
On a complete topological inverse polycyclic monoid
Directory of Open Access Journals (Sweden)
S. O. Bardyla
2016-12-01
Full Text Available We give sufficient conditions when a topological inverse $\\lambda$-polycyclic monoid $P_{\\lambda}$ is absolutely $H$-closed in the class of topological inverse semigroups. For every infinite cardinal $\\lambda$ we construct the coarsest semigroup inverse topology $\\tau_{mi}$ on $P_\\lambda$ and give an example of a topological inverse monoid $S$ which contains the polycyclic monoid $P_2$ as a dense discrete subsemigroup.
Deciphering the imprint of topology on nonlinear dynamical network stability
International Nuclear Information System (INIS)
Nitzbon, J; Schultz, P; Heitzig, J; Kurths, J; Hellmann, F
2017-01-01
Coupled oscillator networks show complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrised to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields. (paper)
Multiple topological phase transitions in a gyromagnetic photonic crystal
Chen, Zeguo
2017-04-19
We present the design of a tunable two-dimensional photonic crystal that exhibits multiple topological phases, including a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase under different combinations of geometric parameters and external magnetic fields. Our photonic crystal enables a platform to study the topology evolution attributed to the interplay between crystalline symmetry and time-reversal symmetry. A four-band tight-binding model unambiguously reveals that the topological property is associated with the pseudospin orientations and that it is characterized by the spin Chern number. The emerging quantum anomalous Hall phase features a single helical edge state that is locked by a specific pseudospin. Simulation results demonstrate that the propagation of such a single helical edge state is robust against magnetic impurities. Potential applications, such as spin splitters, are described.
Adiabatic photo-steering theory in topological insulators
Inoue, Jun-ichi
2014-12-01
Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane-Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.
Macroscopic Floquet topological crystalline steel and superconductor pump
Rossi, Anna M. E. B.; Bugase, Jonas; Fischer, Thomas M.
2017-08-01
The transport of a macroscopic steel sphere and a superconducting sphere on top of two-dimensional periodic magnetic patterns is studied experimentally and compared with the theory and with experiments on topological transport of magnetic colloids. Transport of the steel and superconducting sphere is achieved by moving an external permanent magnet on a closed loop around the two-dimensional crystal. The transport is topological, i.e., the spheres are transported by a primitive unit vector of the lattice when the external magnet loop winds around specific directions. We experimentally determine the set of directions the loops must enclose for nontrivial transport of the spheres into various directions. We show that the loops can be used to sort steel and superconducting spheres. We show that the topological transport is robust with respect to the scale of the system and therefore speculate on its down scalability to the molecular scale.
The Volatility of Data Space: Topology Oriented Sensitivity Analysis
Du, Jing; Ligmann-Zielinska, Arika
2015-01-01
Despite the difference among specific methods, existing Sensitivity Analysis (SA) technologies are all value-based, that is, the uncertainties in the model input and output are quantified as changes of values. This paradigm provides only limited insight into the nature of models and the modeled systems. In addition to the value of data, a potentially richer information about the model lies in the topological difference between pre-model data space and post-model data space. This paper introduces an innovative SA method called Topology Oriented Sensitivity Analysis, which defines sensitivity as the volatility of data space. It extends SA into a deeper level that lies in the topology of data. PMID:26368929
International Nuclear Information System (INIS)
Goncharov, Yu.P.
1982-01-01
In a spacetime having a nontrivial topology QCD may have properties which are absent for QCD in Minkowski spacetime. Two new possibilities for QCD are discussed by the example of spacetime with topology R x (S 1 ) 3 and flat metric: the topological origin of flavours and topological gluon mass generation. (orig.)
Topological Insulators and Superconductors for Innovative Devices
2015-03-20
Final 3. DATES COVERED (From - To) 20120321 - 20150320 4. TITLE AND SUBTITLE Topological insulators and superconductors for innovative...locking, which hold promise for various innovative devices. Similarly, topological superconductors are associated with exotic surface states, which...298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18 Final Report Title: Topological Insulators and Superconductors for Innovative Devices
On the topology of generalized quotients
Directory of Open Access Journals (Sweden)
Józef Burzyk
2008-10-01
Full Text Available Generalized quotients are defined as equivalence classes of pairs (x, f, where x is an element of a nonempty set X and f is an element of a commutative semigroup G acting on X. Topologies on X and G induce a natural topology on B(X,G, the space of generalized quotients. Separation properties of this topology are investigated.
2017-01-01
Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969
Constructing a logical, regular axis topology from an irregular topology
Faraj, Daniel A.
2014-07-01
Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
Thermodynamics of the topological Kondo model
Directory of Open Access Journals (Sweden)
Francesco Buccheri
2015-07-01
Full Text Available Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.
Thermodynamics of the topological Kondo model
Energy Technology Data Exchange (ETDEWEB)
Buccheri, Francesco, E-mail: buccheri@iip.ufrn.br [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); Babujian, Hrachya [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); Yerevan Physics Institute, Alikhanian Brothers 2, Yerevan, 375036 (Armenia); Korepin, Vladimir E. [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); C. N. Yang Institute for Theoretical Physics, Stony Brook University, NY 11794 (United States); Sodano, Pasquale [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); Departemento de Fisíca Teorica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Trombettoni, Andrea [CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste (Italy); SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste (Italy)
2015-07-15
Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.
Topological data analysis for scientific visualization
Tierny, Julien
2017-01-01
Combining theoretical and practical aspects of topology, this book delivers a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a thorough but intuitive manner, with many high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in details, and their application is carefully illustrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis, for lecturers, students and researchers.
Chemistry explained by topology: an alternative approach.
Galvez, Jorge; Villar, Vincent M; Galvez-Llompart, Maria; Amigó, José M
2011-05-01
Molecular topology can be considered an application of graph theory in which the molecular structure is characterized through a set of graph-theoretical descriptors called topological indices. Molecular topology has found applications in many different fields, particularly in biology, chemistry, and pharmacology. The first topological index was introduced by H. Wiener in 1947 [1]. Although its very first application was the prediction of the boiling points of the alkanes, the Wiener index has demonstrated since then a predictive capability far beyond that. Along with the Wiener index, in this paper we focus on a few pioneering topological indices, just to illustrate the connection between physicochemical properties and molecular connectivity.
Converting topological insulators into topological metals within the tetradymite family
Chen, K.-W.; Aryal, N.; Dai, J.; Graf, D.; Zhang, S.; Das, S.; Le Fèvre, P.; Bertran, F.; Yukawa, R.; Horiba, K.; Kumigashira, H.; Frantzeskakis, E.; Fortuna, F.; Balicas, L.; Santander-Syro, A. F.; Manousakis, E.; Baumbach, R. E.
2018-04-01
We report the electronic band structures and concomitant Fermi surfaces for a family of exfoliable tetradymite compounds with the formula T2C h2P n , obtained as a modification to the well-known topological insulator binaries Bi2(Se,Te ) 3 by replacing one chalcogen (C h ) with a pnictogen (P n ) and Bi with the tetravalent transition metals T = Ti, Zr, or Hf. This imbalances the electron count and results in layered metals characterized by relatively high carrier mobilities and bulk two-dimensional Fermi surfaces whose topography is well-described by first-principles calculations. Intriguingly, slab electronic structure calculations predict Dirac-like surface states. In contrast to Bi2Se3 , where the surface Dirac bands are at the Γ point, for (Zr,Hf ) 2Te2 (P,As) there are Dirac cones of strong topological character around both the Γ ¯ and M ¯ points, which are above and below the Fermi energy, respectively. For Ti2Te2P , the surface state is predicted to exist only around the M ¯ point. In agreement with these predictions, the surface states that are located below the Fermi energy are observed by angle-resolved photoemission spectroscopy measurements, revealing that they coexist with the bulk metallic state. Thus this family of materials provides a foundation upon which to develop novel phenomena that exploit both the bulk and surface states (e.g., topological superconductivity).
Topological surface states in nodal superconductors
International Nuclear Information System (INIS)
Schnyder, Andreas P; Brydon, Philip M R
2015-01-01
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states. (topical review)
Topological Insulators Dirac Equation in Condensed Matters
Shen, Shun-Qing
2012-01-01
Topological insulators are insulating in the bulk, but process metallic states around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, Topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological in...
Universe as a topological defect
International Nuclear Information System (INIS)
Anabalon, Andres; Willison, Steven; Zanelli, Jorge
2008-01-01
Four-dimensional Einstein's general relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a manifold with a four-dimensional topological defect. The resulting action is a four-dimensional theory defined by a gauged Wess-Zumino-Witten term. An ansatz is found which reduces the full set of field equations to those of Einstein's general relativity. When the same ansatz is replaced in the action, the gauged WZW term reduces to the Einstein-Hilbert action. Furthermore, the unique coupling constant in the action can be shown to take integer values if the fields are allowed to be analytically continued to complex values
Topological quantization of gravitational fields
International Nuclear Information System (INIS)
Patino, Leonardo; Quevedo, Hernando
2005-01-01
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes values in the Lie algebra of the Lorentz group. This result is generalized to include the case of gauge matter fields in multiple principal fiber bundles. We present several examples of gravitational configurations that include a gravitomagnetic monopole in linearized gravity, the C-energy of cylindrically symmetric fields, the Reissner-Nordstroem and the Kerr-Newman black holes. As a result of the application of the topological quantization procedure, in all the analyzed examples we obtain conditions implying that the parameters entering the metric in each case satisfy certain discretization relationships
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
This thesis investigates how to apply topology optimization using the material distribution technique to steady-state viscous incompressible flow problems. The target design applications are fluid devices that are optimized with respect to minimizing the energy loss, characteristic properties...... transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the thesis gives a proof-of-concept for the application of the method within fluid dynamic problems and it remains of interest for the design of microfluidic devices. Furthermore, the thesis contributes...... at the Technical University of Denmark. Large topology optimization problems with 2D and 3D Stokes flow modeling are solved with direct and iterative strategies employing the parallelized Sun Performance Library and the OpenMP parallelization technique, respectively....
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
Time-Space Topology Optimization
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2008-01-01
A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young......’s modulus and is subjected to a transient load. In the example an optimized dynamic structure is demonstrated that compresses a propagating Gauss pulse....
Topological 2-dimensional quantum mechanics
International Nuclear Information System (INIS)
Dasnieres de Veigy, A.; Ouvry, S.
1992-12-01
A Chern-Simons Lagrangian is defined for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. Exact N-body eigenstates are proposed and a perturbative algorithm is set up. The case where some particles are fixed on a lattice, is discussed, and curved manifolds are considered. (author) 14 refs
Hopf algebras and topological recursion
International Nuclear Information System (INIS)
Esteves, João N
2015-01-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)
Topological defects in extended inflation
International Nuclear Information System (INIS)
Copeland, E.J.; Kolb, E.W.; Chicago Univ., IL; Liddle, A.R.
1990-04-01
We consider the production of topological defects, especially cosmic strings, in extended inflation models. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large-scale structure via cosmic strings. 18 refs
Topological sigma models on supermanifolds
Energy Technology Data Exchange (ETDEWEB)
Jia, Bei, E-mail: beijia@physics.utexas.edu
2017-02-15
This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of “superinstantons”. The language of supergeometry is used extensively throughout this paper.
Membrane topology of hedgehog acyltransferase.
Matevossian, Armine; Resh, Marilyn D
2015-01-23
Hedgehog acyltransferase (Hhat) is a multipass transmembrane enzyme that mediates the covalent attachment of the 16-carbon fatty acid palmitate to the N-terminal cysteine of Sonic Hedgehog (Shh). Palmitoylation of Shh by Hhat is critical for short and long range signaling. Knowledge of the topological organization of Hhat transmembrane helices would enhance our understanding of Hhat-mediated Shh palmitoylation. Bioinformatics analysis of transmembrane domains within human Hhat using 10 different algorithms resulted in highly consistent predictions in the C-terminal, but not in the N-terminal, region of Hhat. To empirically determine the topology of Hhat, we designed and exploited Hhat constructs containing either terminal or 12 different internal epitope tags. We used selective permeabilization coupled with immunofluorescence as well as a protease protection assay to demonstrate that Hhat contains 10 transmembrane domains and 2 re-entrant loops. The invariant His and highly conserved Asp residues within the membrane-bound O-acyltransferase (MBOAT) homology domain are segregated on opposite sides of the endoplasmic reticulum membrane. The localization of His-379 on the lumenal membrane surface is consistent with a role for this invariant residue in catalysis. Analysis of the activity and stability of the Hhat constructs revealed that the C-terminal MBOAT domain is especially sensitive to manipulation. Moreover, there was remarkable similarity in the overall topological organization of Hhat and ghrelin O-acyltransferase, another MBOAT family member. Knowledge of the topological organization of Hhat could serve as an important tool for further design of selective Hhat inhibitors. © 2015 by The American Society for Biochemistry and Molecular Biology, Inc.
Dual topological unitarization -- phenomenological aspect
International Nuclear Information System (INIS)
Tan, C.I.
1978-01-01
An assessment is provided on the viability of dual topological unitarization as a practical scheme for organizing and interpreting hadronic phenomena at current machine energies. Previous detailed reviews are complemented, with emphasis on phenomenological aspects and more recent developments. Diffraction scattering, a test of P--f identity hypothesis, the flavor model, the P--f identity versus the Veneziano two-jet picture, and an illustration of the new phenomenology are included. 24 references
Topological K-Kolmogorov groups
International Nuclear Information System (INIS)
Abd El-Sattar, A. Dabbour.
1987-07-01
The idea of the K-groups was used to define K-Kolmogorov homology and cohomology (over pairs of coefficient groups) which are descriptions of certain modifications of the Kolmogorov groups. The present work is devoted to the study of the topological properties of the K-Kolmogorov groups which lie at the root of the group duality based essentially upon Pontrjagin's concept of group multiplication. 14 refs
Topological methods in gauge theory
International Nuclear Information System (INIS)
Sarukkai, S.R.
1992-01-01
The author begins with an overview of the important topological methods used in gauge theory. In the first chapter, the author discusses the general structure of fiber bundles and associated mathematical concepts and briefly discuss their application in gauge theory. The second chapter deals with the study of instantons in both gauge and gravity theories. These self-dual solutions are presented. This chapter is also a broad introduction to certain topics in gravitational physics. Gravity and gauge theory are unified in Kaluza-Klein theory as discussed in the third chapter. Of particular interest is the physics of the U(1) bundles over non-trivial manifolds. The radius of the fifth dimension is undetermined classically in the Kaluza-Klein theory. A mechanism is described using topological information to derive the functional form of the radius of the fifth dimension and show that it is possible classically to derive expressions for the radius as a consequence of topology. The behavior of the radius is dependent on the information present in the base metric. Results are computed for three gravitational instantons. Consequences of this mechanism are discussed. The description is studied of instantons in terms of projector valued fields and universal bundles. The results of the previous chapter and this are connected via the study of universal bundles. Projector valued transformations are defined and their consequences discussed. With the solutions of instantons in this formalism, it is shown explicitly that there can be solutions which allow for a Sp(n) instanton to be transformed to a Sp(k) instanton, thus showing that there can be interpolations which carry one instanton with a rank n to another characterized by rank k with different topological numbers
Topological defects in extended inflation
International Nuclear Information System (INIS)
Copeland, E.J.; Kolb, E.W.; Liddle, A.R.
1990-01-01
We consider the production of topological defects, especially cosmic strings, in extended-inflation models. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of the bubbles when they collide. This mechanism allows a natural combination of inflation and large-scale structure via cosmic strings
Lectures on the Topological Vertex
Mariño, M
2008-01-01
In this lectures, I will summarize the approach to Gromov–Witten invariants on toric Calabi–Yau threefolds based on large N dualities. Since the large N duality/topological vertex approach computes Gromov–Witten invariants in terms of Chern–Simons knot and link invariants, Sect. 2 is devoted to a review of these. Section 3 reviews topological strings and Gromov–Witten invariants, and gives some information about the open string case. Section 4 introduces the class of geometries we will deal with, namely toric (noncompact) Calabi–Yau manifolds, and we present a useful graphical way to represent these manifolds which constitutes the geometric core of the theory of the topological vertex. Finally, in Sect. 5, we define the vertex and present some explicit formulae for it and some simple applications. A brief Appendix contains useful information about symmetric polynomials. It has not been possible to present all the relevant background and physical derivations in this set of lectures. However, these...
On topological RNA interaction structures.
Qin, Jing; Reidys, Christian M
2013-07-01
Recently a folding algorithm of topological RNA pseudoknot structures was presented in Reidys et al. (2011). This algorithm folds single-stranded γ-structures, that is, RNA structures composed by distinct motifs of bounded topological genus. In this article, we set the theoretical foundations for the folding of the two backbone analogues of γ structures: the RNA γ-interaction structures. These are RNA-RNA interaction structures that are constructed by a finite number of building blocks over two backbones having genus at most γ. Combinatorial properties of γ-interaction structures are of practical interest since they have direct implications for the folding of topological interaction structures. We compute the generating function of γ-interaction structures and show that it is algebraic, which implies that the numbers of interaction structures can be computed recursively. We obtain simple asymptotic formulas for 0- and 1-interaction structures. The simplest class of interaction structures are the 0-interaction structures, which represent the two backbone analogues of secondary structures.
Algebraic topology a first course
Fulton, William
1995-01-01
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: ...
Spintronics Based on Topological Insulators
Fan, Yabin; Wang, Kang L.
2016-10-01
Spintronics using topological insulators (TIs) as strong spin-orbit coupling (SOC) materials have emerged and shown rapid progress in the past few years. Different from traditional heavy metals, TIs exhibit very strong SOC and nontrivial topological surface states that originate in the bulk band topology order, which can provide very efficient means to manipulate adjacent magnetic materials when passing a charge current through them. In this paper, we review the recent progress in the TI-based magnetic spintronics research field. In particular, we focus on the spin-orbit torque (SOT)-induced magnetization switching in the magnetic TI structures, spin-torque ferromagnetic resonance (ST-FMR) measurements in the TI/ferromagnet structures, spin pumping and spin injection effects in the TI/magnet structures, as well as the electrical detection of the surface spin-polarized current in TIs. Finally, we discuss the challenges and opportunities in the TI-based spintronics field and its potential applications in ultralow power dissipation spintronic memory and logic devices.
Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Liu, Xiaojun; Christensen, Johan
2017-12-01
Topologically protected wave engineering in artificially structured media resides at the frontier of ongoing metamaterials research, which is inspired by quantum mechanics. Acoustic analogs of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation by means of robust edge mode excitations through analogies drawn to exotic quantum states. A variety of artificial acoustic systems hosting topological edge states have been proposed analogous to the quantum Hall effect, topological insulators, and Floquet topological insulators in electronic systems. However, those systems were characterized by a fixed geometry and a very narrow frequency response, which severely hinders the exploration and design of useful applications. Here we establish acoustic multipolar pseudospin states as an engineering degree of freedom in time-reversal invariant flow-free phononic crystals and develop reconfigurable topological insulators through rotation of their meta-atoms and reshaping of the metamolecules. Specifically, we show how rotation forms man-made snowflakelike molecules, whose topological phase mimics pseudospin-down (pseudospin-up) dipolar and quadrupolar states, which are responsible for a plethora of robust edge confined properties and topological controlled refraction disobeying Snell's law.
Topological phases of interacting fermions in one-dimensional superconductor - normal metal geometry
Energy Technology Data Exchange (ETDEWEB)
Meidan, Dganit [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universitaet Berlin, 14195 Berlin (Germany); Romito, Alessandro; Brouwer, Piet W. [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)
2015-07-01
One-dimensional superconductors can be in non-trivial topological phases harboring Majorana end-states, which possess non-abelian statistics. It has been recently established that in the presence of interactions the classification of topological superconducting phases can be significantly altered. Specifically, for one-dimensional superconductors possessing a time reversal symmetry (BDI class), interactions reduce the infinitely many non-interacting phases (Z topological index) to eight distinct ones (Z{sub 8} topological index). In this talk I will consider multi-mode superconducting wires in such BDI class when probed by an external contact, and discuss their low temperature and voltage bias transport properties. I will first show that the Andreev reflection component of the scattering matrix of the probing lead provides a topological index, r=-4,.., 4, which distinguish the eight topological phases. The two topologically equivalent phases with r= 4,-4 support emergent many-body end states, which are identified to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops.
Topological Structures on DMC Spaces †
Directory of Open Access Journals (Sweden)
Rajai Nasser
2018-05-01
Full Text Available Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. A topology on the space of equivalent channels with fixed input alphabet X and arbitrary but finite output alphabet is said to be natural if and only if it induces the quotient topology on the subspaces of equivalent channels sharing the same output alphabet. We show that every natural topology is σ -compact, separable and path-connected. The finest natural topology, which we call the strong topology, is shown to be compactly generated, sequential and T 4 . On the other hand, the strong topology is not first-countable anywhere, hence it is not metrizable. We introduce a metric distance on the space of equivalent channels which compares the noise levels between channels. The induced metric topology, which we call the noisiness topology, is shown to be natural. We also study topologies that are inherited from the space of meta-probability measures by identifying channels with their Blackwell measures.
Braid foliations in low-dimensional topology
LaFountain, Douglas J
2017-01-01
This book is a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more specifically in contact 3-manifolds. With style and content accessible to beginning students interested in geometric topology, each chapter centers around a key theorem or theorems. The particular braid foliation techniques needed to prove these theorems are introduced in parallel, so that the reader has an immediate "take-home" for the techniques involved. The reader will learn that braid foliations provide a flexible toolbox capable of proving classical results such as Markov's theorem for closed braids and the transverse Markov theorem for transverse links, as well as recent results such as the generalized Jones conjecture for closed braids and the Legendrian grid number conjecture for Legendrian links. Connections are also made between the Dehornoy ordering of the braid groups and braid foliations on surfaces. All of this is accomplished w...
Topology control with IPD network creation games
International Nuclear Information System (INIS)
Scholz, Jan C; Greiner, Martin O W
2007-01-01
Network creation games couple a two-players game with the evolution of network structure. A vertex player may increase its own payoff with a change of strategy or with a modification of its edge-defined neighbourhood. By referring to the iterated prisoners dilemma (IPD) game we show that this evolutionary dynamics converges to network-Nash equilibria, where no vertex is able to improve its payoff. The resulting network structure exhibits a strong dependence on the parameter of the payoff matrix. Degree distributions and cluster coefficients are also strongly affected by the specific interactions chosen for the neighbourhood exploration. This allows network creation games to be seen as a promising artificial-social-systems approach for a distributive topology control of complex networked systems
Topology optimization of Channel flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical......This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002......]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...
Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus
Directory of Open Access Journals (Sweden)
Zhong Wang
2014-01-01
Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.
Multi-planed unified switching topologies
Chen, Dong; Heidelberger, Philip; Sugawara, Yutaka
2017-07-04
An apparatus and method for extending the scalability and improving the partitionability of networks that contain all-to-all links for transporting packet traffic from a source endpoint to a destination endpoint with low per-endpoint (per-server) cost and a small number of hops. An all-to-all wiring in the baseline topology is decomposed into smaller all-to-all components in which each smaller all-to-all connection is replaced with star topology by using global switches. Stacking multiple copies of the star topology baseline network creates a multi-planed switching topology for transporting packet traffic. Point-to-point unified stacking method using global switch wiring methods connects multiple planes of a baseline topology by using the global switches to create a large network size with a low number of hops, i.e., low network latency. Grouped unified stacking method increases the scalability (network size) of a stacked topology.
Topological Aspects of Solitons in Ferromagnets
International Nuclear Information System (INIS)
Ren Jirong; Wang Jibiao; Li Ran; Xu Donghui; Duan Yishi
2008-01-01
Two kinds of topological soliton (skyrmion and magnetic vortex ring) in ferromagnets are studied. They have the common topological origin, a tensor H αβ = n-vector · (∂ α n-vector x ∂ β n-vector ), which describes the non-trivial distribution of local orientation of magnetization n-vector at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings
Topological theory of dynamical systems recent advances
Aoki, N
1994-01-01
This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.
An improved genetic algorithm with dynamic topology
International Nuclear Information System (INIS)
Cai Kai-Quan; Tang Yan-Wu; Zhang Xue-Jun; Guan Xiang-Min
2016-01-01
The genetic algorithm (GA) is a nature-inspired evolutionary algorithm to find optima in search space via the interaction of individuals. Recently, researchers demonstrated that the interaction topology plays an important role in information exchange among individuals of evolutionary algorithm. In this paper, we investigate the effect of different network topologies adopted to represent the interaction structures. It is found that GA with a high-density topology ends up more likely with an unsatisfactory solution, contrarily, a low-density topology can impede convergence. Consequently, we propose an improved GA with dynamic topology, named DT-GA, in which the topology structure varies dynamically along with the fitness evolution. Several experiments executed with 15 well-known test functions have illustrated that DT-GA outperforms other test GAs for making a balance of convergence speed and optimum quality. Our work may have implications in the combination of complex networks and computational intelligence. (paper)
Basic algebraic topology and its applications
Adhikari, Mahima Ranjan
2016-01-01
This book provides an accessible introduction to algebraic topology, a ﬁeld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book oﬀers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...
Topological supersymmetric structure of hadron cross sections
International Nuclear Information System (INIS)
Gauron, P.; Nicolescu, B.; Ouvry, S.
1980-12-01
Recently a way of fully implementing unitarity in the framework of a Dual Topological Unitarization theory, including not only mesons but also baryons, was found. This theory consists in the topological description of hadron interactions involving confined quarks in terms of two 2-dimensional surfaces (a closed 'quantum' surface and a bounded 'classical' surface). We show that this description directly leads, at the zeroth order of the topological expansion, to certain relations between hadron cross-sections, in nice agreement with experimental data. A new topological suppression mechanism is shown to play an important dynamical role. We also point out a new topological supersymmetry property, which leads to realistic experimental consequences. A possible topological origin of the rho and ω universality relations emerges as a by-product of our study
Signature of Topological Phases in Zitterbewegung
Ghosh, Sumit; Manchon, Aurelien
2016-01-01
We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.
Charges and Electromagnetic Radiation as Topological Excitations
Directory of Open Access Journals (Sweden)
Manfried Faber
2017-01-01
Full Text Available We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Algebra and topology for applications to physics
Rozhkov, S. S.
1987-01-01
The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.
Signature of Topological Phases in Zitterbewegung
Ghosh, Sumit
2016-09-02
We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.
Vector supersymmetry in topological field theories
International Nuclear Information System (INIS)
Gieres, F.; Grimstrup, J.; Pisar, T.; Schweda, M.
2000-01-01
We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges. (author)
The nucleon as a topological chiral soliton
International Nuclear Information System (INIS)
Rho, M.
1983-10-01
Through topology, baryon charge ''leaks'' from a confinement region into a meson-cloud region. This suggests that there is a sort of topological equivalence principle which renders physically equivalent the Skyrmion description with a zero bag radius and the chiral bag description with a non-zero bag radius. The issue as to whether future nuclear physics experiments will reveal a ''smoking gun'' evidence for a quark presence in nuclei is discussed in the light of the recently discovered topological structure
A topological extension of GR: Black holes induce dark energy
International Nuclear Information System (INIS)
Spaans, M
2013-01-01
A topological extension of general relativity is presented. The superposition principle of quantum mechanics, as formulated by the Feynman path integral, is taken as a starting point. It is argued that the trajectories that enter this path integral are distinct and thus that space-time topology is multiply connected. Specifically, space-time at the Planck scale consists of a lattice of three-tori that facilitates many distinct paths for particles to travel along. To add gravity, mini black holes are attached to this lattice. These mini black holes represent Wheeler's quantum foam and result from the fact that GR is not conformally invariant. The number of such mini black holes in any time-slice through four-space is found to be equal to the number of macroscopic (so long-lived) black holes in the entire universe. This connection, by which macroscopic black holes induce mini black holes, is a topological expression of Mach's principle. The proposed topological extension of GR can be tested because, if correct, the dark energy density of the universe should be proportional the total number of macroscopic black holes in the universe at any time. This prediction, although strange, agrees with current astrophysical observations.
Impact of network topology on synchrony of oscillatory power grids
Energy Technology Data Exchange (ETDEWEB)
Rohden, Martin; Sorge, Andreas; Witthaut, Dirk [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Faculty of Physics, Georg August Universität Göttingen, Göttingen (Germany)
2014-03-15
Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. In particular, power generation in the resulting grid will be far more decentralized, with a distinctly different topology. Here, we analyze the impact of grid topologies on spontaneous synchronization, considering regular, random, and small-world topologies and focusing on the influence of decentralization. We model the consumers and sources of the power grid as second order oscillators. First, we analyze the global dynamics of the simplest non-trivial (two-node) network that exhibit a synchronous (normal operation) state, a limit cycle (power outage), and coexistence of both. Second, we estimate stability thresholds for the collective dynamics of small network motifs, in particular, star-like networks and regular grid motifs. For larger networks, we numerically investigate decentralization scenarios finding that decentralization itself may support power grids in exhibiting a stable state for lower transmission line capacities. Decentralization may thus be beneficial for power grids, regardless of the details of their resulting topology. Regular grids show a specific sharper transition not found for random or small-world grids.
Supersymmetric Quantum Mechanics and Topology
International Nuclear Information System (INIS)
Wasay, Muhammad Abdul
2016-01-01
Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Neural Decoder for Topological Codes
Torlai, Giacomo; Melko, Roger G.
2017-07-01
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two-dimensional toric code with phase-flip errors.
Geometric Topology and Shape Theory
Segal, Jack
1987-01-01
The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Improving Topology Optimization using Games
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten; Christiansen, Asger Nyman; Bærentzen, J. Andreas
free of charge on iOS and Android devices1. The TopOptGame is inspired by puzzle-games (a genre of computer games), which constantly challenges the players and gives rewards when progress is made. This engagement loop will take the player on a journey starting with simple problems with few supports......, this will allow us to analyze the data to measure human performance of topology optimization and more importantly, in which cases people's intuition succeed or fail. The game is currently a working prototype and is scheduled for final release on both iOS and Android before WCSMO-10....
Topological entropy of autonomous flows
Energy Technology Data Exchange (ETDEWEB)
Badii, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-06-01
When studying fluid dynamics, especially in a turbulent regime, it is crucial to estimate the number of active degrees of freedom or of localized structures in the system. The topological entropy quantifies the exponential growth of the number of `distinct` orbits in a dynamical system as a function of their length, in the infinite spatial resolution limit. Here, I illustrate a novel method for its evaluation, which extends beyond maps and is applicable to any system, including autonomous flows: these are characterized by lack of a definite absolute time scale for the orbit lengths. (author) 8 refs.
Topological amplitudes in string theory
International Nuclear Information System (INIS)
Antoniadis, I.; Taylor, T.R.
1993-07-01
We show that certain type II string amplitudes at genus g are given by the topological partition F g discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form Σ g F g W 2g , where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of F g is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings. (author). 22 refs, 2 figs
Importance of being topologically excited
International Nuclear Information System (INIS)
Caldi, D.G.
1980-08-01
A class of Euclidean configurations that appear to be dominant in the functional integral of the CP/sup N-1/ models is identified. These configurations are point-like topological excitations, and they may be viewed as constituents of instantons, although they are defined independently of instantons through a continuum duality transformation. Not only do these configurations survive as N → infinity, but in the plasma phase they are responsible for the effects encountered within the 1/N expansion - confinement, theta dependence, and dynamical mass generation
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Topological Qubits from Valence Bond Solids
Wang, Dong-Sheng; Affleck, Ian; Raussendorf, Robert
2018-05-01
Topological qubits based on S U (N )-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with twofold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical Z rotation by an angle 2 π /N , for any integer N >2 , is provided by a global twist operation, which is of a topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.
On the topology of flux transfer events
Hesse, Michael; Birn, Joachim; Schindler, Karl
1990-01-01
A topological analysis is made of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose a global topological model of a closed magnetosphere is considered as the unperturbed state. The topological substructure of the model flux rope is discussed in detail.
Topology of polymer chains under nanoscale confinement.
Satarifard, Vahid; Heidari, Maziar; Mashaghi, Samaneh; Tans, Sander J; Ejtehadi, Mohammad Reza; Mashaghi, Alireza
2017-08-24
Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l p under a spherical confinement of radius R c . At low values of l p /R c , the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l p /R c , the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l p /R c , at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross
Proximity effects in topological insulator heterostructures
International Nuclear Information System (INIS)
Li Xiao-Guang; Wu Guang-Fen; Zhang Gu-Feng; Culcer Dimitrie; Zhang Zhen-Yu; Chen Hua
2013-01-01
Topological insulators (TIs) are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to Tl-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topological helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath. These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI-based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications. (topical review - low-dimensional nanostructures and devices)
Elastic energy for reflection-symmetric topologies
International Nuclear Information System (INIS)
Majumdar, A; Robbins, J M; Zyskin, M
2006-01-01
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with reflection-symmetric topologies, we derive a new lower bound for the one-constant elastic energy. For certain topologies, called conformal and anticonformal, the lower bound agrees with a previous result. For the remaining topologies, called nonconformal, the new bound is an improvement. For nonconformal topologies we derive an upper bound, which differs from the lower bound by a factor depending only on the aspect ratios of the prism
Form factors and excitations of topological solitons
International Nuclear Information System (INIS)
Weir, David J.; Rajantie, Arttu
2011-01-01
We show how the interaction properties of topological solitons in quantum field theory can be calculated with lattice Monte Carlo simulations. Topologically nontrivial field configurations are key to understanding the nature of the QCD vacuum through, for example, the dual superconductor picture. Techniques that we have developed to understand the excitations and form factors of topological solitons, such as kinks and 't Hooft-Polyakov monopoles, should be equally applicable to chromoelectric flux tubes. We review our results for simple topological solitons and their agreement with exact results, then discuss our progress towards studying objects of interest to high energy physics.
Topological fluid mechanics of Axisymmetric Flow
DEFF Research Database (Denmark)
Brøns, Morten
1998-01-01
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...
A novel approach to nano topology via neutrosophic sets
M. Lellis Thivagar; Saeid Jafari; V. Sutha Devi; V. Antonysamy
2018-01-01
The main objective of this study is to introduce a new hybrid intelligent structure called Neutrosophic nano topology. Fuzzy nano topology and intuitionistic nano topology can also be deduced from the neutrosophic nano topology. Based on the neutrosophic nano approximations we have classified neutrosophic nano topology. Some properties like neutrosophic nano interior and neutrosophic nano closure are derived.
Algebraic Modeling of Topological and Computational Structures and Applications
Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis
2017-01-01
This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w...
Cells behaviors and genotoxicity on topological surface
International Nuclear Information System (INIS)
Yang, N.; Yang, M.K.; Bi, S.X.; Chen, L.; Zhu, Z.Y.; Gao, Y.T.; Du, Z.
2013-01-01
To investigate different cells behaviors and genotoxicity, which were driven by specific microenvironments, three patterned surfaces (pillars, wide grooves and narrow grooves) and one smooth surface were prepared by template-based technique. Vinculin is a membrane-cytoskeletal protein in focal adhesion plaques and associates with cell–cell and cell–matrix junctions, which can promote cell adhesion and spreading. The immunofluorescence staining of vinculin revealed that the narrow grooves patterned substrate was favorable for L929 cell adhesion. For cell multiplication, the narrow grooves surface was fitted for the proliferation of L929, L02 and MSC cells, the pillars surface was only in favor of L929 cells to proliferate during 7 days of cell cultivation. Cell genetic toxicity was evaluated by cellular micronuclei test (MNT). The results indicated that topological surfaces were more suitable for L929 cells to proliferate and maintain the stability of genome. On the contrary, the narrow grooves surface induced higher micronuclei ratio of L02 and MSC cells than other surfaces. With the comprehensive results of cell multiplication and MNT, it was concluded that the wide grooves surface was best fitted for L02 cells to proliferate and have less DNA damages, and the smooth surface was optimum for the research of MSC cells in vitro. - Highlights: • Different cells behaviors on microstructure surfaces were discussed in this paper. • The expression of cell protein of Vinculin was studied in this research. • Cellular micronuclei test was applied to evaluate cells' genotoxicity. • Cell genotoxicity was first studied in the research field of topological surfaces
Symmetry, Symmetry Breaking and Topology
Directory of Open Access Journals (Sweden)
Siddhartha Sen
2010-07-01
Full Text Available The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.
An introduction to algebraic topology
Rotman, Joseph J
1988-01-01
There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead. Of course, this is false, as a glance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details. There are two types of obstacle for the student learning algebraic topology. The first is the formidable array of new techniques (e. g. , most students know very little homological algebra); the second obstacle is that the basic defini tions have been so abstracted that their geometric or analytic origins have been obscured. I have tried to overcome these barriers. In the first instance, new definitions are introduced only when needed (e. g. , homology with coeffi cients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat-singular, sim ...
Lattice topology dictates photon statistics.
Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A
2017-08-21
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.
Topological structure of dictionary graphs
International Nuclear Information System (INIS)
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Curvature-Controlled Topological Defects
Directory of Open Access Journals (Sweden)
Luka Mesarec
2017-05-01
Full Text Available Effectively, two-dimensional (2D closed films exhibiting in-plane orientational ordering (ordered shells might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.
Topology and condensed matter physics
Mj, Mahan; Bandyopadhyay, Abhijit
2017-01-01
This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a qui...
Topological dynamics in supramolecular rotors.
Palma, Carlos-Andres; Björk, Jonas; Rao, Francesco; Kühne, Dirk; Klappenberger, Florian; Barth, Johannes V
2014-08-13
Artificial molecular switches, rotors, and machines are set to establish design rules and applications beyond their biological counterparts. Herein we exemplify the role of noncovalent interactions and transient rearrangements in the complex behavior of supramolecular rotors caged in a 2D metal-organic coordination network. Combined scanning tunneling microscopy experiments and molecular dynamics modeling of a supramolecular rotor with respective rotation rates matching with 0.2 kcal mol(-1) (9 meV) precision, identify key steps in collective rotation events and reconfigurations. We notably reveal that stereoisomerization of the chiral trimeric units entails topological isomerization whereas rotation occurs in a topology conserving, two-step asynchronous process. In supramolecular constructs, distinct displacements of subunits occur inducing a markedly lower rotation barrier as compared to synchronous mechanisms of rigid rotors. Moreover, the chemical environment can be instructed to control the system dynamics. Our observations allow for a definition of mechanical cooperativity based on a significant reduction of free energy barriers in supramolecules compared to rigid molecules.
Stochastic quantization and topological theories
International Nuclear Information System (INIS)
Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.
1992-01-01
In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones
Dislocations and other topological oddities
Pieranski, Pawel
2016-03-01
We will show that the book Dislocations by Jacques Friedel, published half a century ago, can still be recommended, in agreement with the author's intention, as a textbook ;for research students at University and for students at engineering schools as well as for research engineers;. Indeed, today dislocations are known to occur not only in solid crystals but also in many other systems discovered more recently such as colloidal crystals or liquid crystals having periodic structures. Moreover, the concept of dislocations is an excellent starting point for lectures on topological defects occurring in systems equipped with order parameters resulting from broken symmetries: disclinations in nematic or hexatic liquid crystals, dispirations in chiral smectics or disorientations in lyotropic liquid crystals. The discussion of dislocations in Blue Phases will give us an opportunity to call on mind Sir Charles Frank, friend of Jacques Friedel since his Bristol years, who called these ephemeral mesophases ;topological oddities;. Being made of networks of disclinations, Blue Phases are similar to Twist Grain Boundary (TGB) smectic phases, which are made of networks of screw dislocations and whose existence was predicted by de Gennes in 1972 on the basis of the analogy between smectics and superconductors. We will stress that the book by Jacques Friedel contains seeds of this analogy.
ATLAS Level-1 Topological Trigger
Zheng, Daniel; The ATLAS collaboration
2018-01-01
The ATLAS experiment has introduced and recently commissioned a completely new hardware sub-system of its first-level trigger: the topological processor (L1Topo). L1Topo consist of two AdvancedTCA blades mounting state-of-the-art FPGA processors, providing high input bandwidth (up to 4 Gb/s) and low latency data processing (200 ns). L1Topo is able to select collision events by applying kinematic and topological requirements on candidate objects (energy clusters, jets, and muons) measured by calorimeters and muon sub-detectors. Results from data recorded using the L1Topo trigger will be presented. These results demonstrate a significantly improved background event rejection, thus allowing for a rate reduction without efficiency loss. This improvement has been shown for several physics processes leading to low-pT leptons, including H->tau tau and J/Psi->mu mu. In addition to describing the L1Topo trigger system, we will discuss the use of an accurate L1Topo simulation as a powerful tool to validate and optimize...
Topological dimension and dynamical systems
Coornaert, Michel
2015-01-01
Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active ar...
Gauge symmetries, topology, and quantisation
International Nuclear Information System (INIS)
Balachandran, A.P.
1994-01-01
The following two loosely connected sets of topics are reviewed in these lecture notes: (1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. (2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under (1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under (2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem
Robust network topologies for generating switch-like cellular responses.
Directory of Open Access Journals (Sweden)
Najaf A Shah
2011-06-01
Full Text Available Signaling networks that convert graded stimuli into binary, all-or-none cellular responses are critical in processes ranging from cell-cycle control to lineage commitment. To exhaustively enumerate topologies that exhibit this switch-like behavior, we simulated all possible two- and three-component networks on random parameter sets, and assessed the resulting response profiles for both steepness (ultrasensitivity and extent of memory (bistability. Simulations were used to study purely enzymatic networks, purely transcriptional networks, and hybrid enzymatic/transcriptional networks, and the topologies in each class were rank ordered by parametric robustness (i.e., the percentage of applied parameter sets exhibiting ultrasensitivity or bistability. Results reveal that the distribution of network robustness is highly skewed, with the most robust topologies clustering into a small number of motifs. Hybrid networks are the most robust in generating ultrasensitivity (up to 28% and bistability (up to 18%; strikingly, a purely transcriptional framework is the most fragile in generating either ultrasensitive (up to 3% or bistable (up to 1% responses. The disparity in robustness among the network classes is due in part to zero-order ultrasensitivity, an enzyme-specific phenomenon, which repeatedly emerges as a particularly robust mechanism for generating nonlinearity and can act as a building block for switch-like responses. We also highlight experimentally studied examples of topologies enabling switching behavior, in both native and synthetic systems, that rank highly in our simulations. This unbiased approach for identifying topologies capable of a given response may be useful in discovering new natural motifs and in designing robust synthetic gene networks.
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
Topology optimization of two-dimensional waveguides
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
Finite Topological Spaces as a Pedagogical Tool
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Network topology descriptions in hybrid networks
Grosso, P.; Brown, A.; Cedeyn, A.; Dijkstra, F.; van der Ham, J.; Patil, A.; Primet, P.; Swany, M.; Zurawski, J.
2010-01-01
The NML-WG goal is to define a schema for describing topologies of hybrid networks. This schema is in first instance intended for: • lightpath provisioning applications to exchange topology information intra and inter domain; • reporting performance metrics. This document constitutes Deliverable 1
Topological Indices of Textual Identity Networks.
Leazer, Gregory H.; Furner, Jonathan
1999-01-01
Reports on a continuing investigation of intertextual networks. Describes how intertextual networks can be modeled as directed graphs and extends this to matrix representations. Discusses topological index values of these networks and speculates how topological index values might be used in the estimation of retrieval values in information…
Quantum Hall Conductivity and Topological Invariants
Reyes, Andres
2001-04-01
A short survey of the theory of the Quantum Hall effect is given emphasizing topological aspects of the quantization of the conductivity and showing how topological invariants can be derived from the hamiltonian. We express these invariants in terms of Chern numbers and show in precise mathematical terms how this relates to the Kubo formula.
Improving topology optimization intuition through games
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten; Malmgren-Hansen, David; Bærentzen, J. Andreas
2016-01-01
This paper describes the educational game, TopOpt Game, which invites the player to solve various optimization challenges. The main purpose of gamifying topology optimization is to create a supplemental educational tool which can be used to introduce concepts of topology optimization to newcomers...
Search for Majorana fermions in topological superconductors.
Energy Technology Data Exchange (ETDEWEB)
Pan, Wei [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shi, Xiaoyan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hawkins, Samuel D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Klem, John Frederick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-10-01
The goal of this project is to search for Majorana fermions (a new quantum particle) in a topological superconductor (a new quantum matter achieved in a topological insulator proximitized by an s-wave superconductor). Majorana fermions (MFs) are electron-like particles that are their own anti-particles. MFs are shown to obey non-Abelian statistics and, thus, can be harnessed to make a fault-resistant topological quantum computer. With the arrival of topological insulators, novel schemes to create MFs have been proposed in hybrid systems by combining a topological insulator with a conventional superconductor. In this LDRD project, we will follow the theoretical proposals to search for MFs in one-dimensional (1D) topological superconductors. 1D topological superconductor will be created inside of a quantum point contact (with the metal pinch-off gates made of conventional s-wave superconductors such as niobium) in a two-dimensional topological insulator (such as inverted type-II InAs/GaSb heterostructure).
Problem of detecting inclusions by topological optimization
Directory of Open Access Journals (Sweden)
I. Faye
2014-01-01
Full Text Available In this paper we propose a new method to detect inclusions. The proposed method is based on shape and topological optimization tools. In fact after presenting the problem, we use topologication optimization tools to detect inclusions in the domain. Numerical results are presented.
Lectures on controlled topology: Mapping cylinder neighborhoods
Energy Technology Data Exchange (ETDEWEB)
Quinn, F [Department of Mathematics, Virginia Tech, Blacksburg, VA (United States)
2002-08-15
The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste, Italy 2001. (author)
Lectures on controlled topology: Mapping cylinder neighborhoods
International Nuclear Information System (INIS)
Quinn, F.
2002-01-01
The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste, Italy 2001. (author)
Algebraic K-theory and algebraic topology
Energy Technology Data Exchange (ETDEWEB)
Berrick, A J [Department of Mathematics, National University of Singapore (Singapore)
2003-09-15
This contribution treats the various topological constructions of Algebraic K-theory together with the underlying homotopy theory. Topics covered include the plus construction together with its various ramifications and applications, Topological Hochschild and Cyclic Homology as well as K-theory of the ring of integers.
Graphical Editor of the DDS Topology Configuration
Rusinov, Aleksandar
2015-01-01
An editor for the DDS topology configuration is created to allow the viewing of an existing topology, the editing of a topology, the creation of a new topology and the saving of a topology as a topology language XML file to be run directly on DDS or to be reloaded again for further editing. The development of the editor was started at GSI Darmstadt at the end of last year. The editor is designed as a web application that works on the client side. Recent and powerful JavaScript libraries were used – ReactJS and JointJS. It has two menus for editing – one for the declarative part and another for the executable part. A graph visualisation of the topology has also been developed and implemented fully to the editor. The output files have been tested and fully verified on the DDS. Future work will involve representation of the pipeline process and investigation on behavior when larger and more sophisticated topologies are used.
Quantum Geometry of Refined Topological Strings
Aganagic, M.; Cheng, M.C.N.; Dijkgraaf, R.; Kreft, D.; Vafa, C.
2012-01-01
We consider branes in refined topological strings. We argue that their wavefunctions satisfy a Schrödinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description. Furthermore, in the limit where one of the equivariant
Topological insulators and superconductors from string theory
International Nuclear Information System (INIS)
Ryu, Shinsei; Takayanagi, Tadashi
2010-01-01
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the θ term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).
International Nuclear Information System (INIS)
Posske, Thore Hagen
2016-01-01
Topological insulators are electronic phases that insulate in the bulk and accommodate a peculiar, metallic edge liquid with a spin-dependent dispersion. They are regarded to be of considerable future use in spintronics and for quantum computation. Besides determining the intrinsic properties of this rather novel electronic phase, considering its combination with well-known physical systems can generate genuinely new physics. In this thesis, we report on such combinations including topological insulators. Specifically, we analyze an attached Rashba impurity, a Kondo dot in the two channel setup, magnetic impurities on the surface of a strong three-dimensional topological insulator, the proximity coupling of the latter system to a superconductor, and hybrid systems consisting of a topological insulator and a semimetal. Let us summarize our primary results. Firstly, we determine an analytical formula for the Kondo cloud and describe its possible detection in current correlations far away from the Kondo region. We thereby rely on and extend the method of refermionizable points. Furthermore, we find a class of gapless topological superconductors and semimetals, which accommodate edge states that behave similarly to the ones of globally gapped topological phases. Unexpectedly, we also find edge states that change their chirality when affected by sufficiently strong disorder. We regard the presented research helpful in future classifications and applications of systems containing topological insulators, of which we propose some examples.
Energy Technology Data Exchange (ETDEWEB)
Posske, Thore Hagen
2016-02-26
Topological insulators are electronic phases that insulate in the bulk and accommodate a peculiar, metallic edge liquid with a spin-dependent dispersion. They are regarded to be of considerable future use in spintronics and for quantum computation. Besides determining the intrinsic properties of this rather novel electronic phase, considering its combination with well-known physical systems can generate genuinely new physics. In this thesis, we report on such combinations including topological insulators. Specifically, we analyze an attached Rashba impurity, a Kondo dot in the two channel setup, magnetic impurities on the surface of a strong three-dimensional topological insulator, the proximity coupling of the latter system to a superconductor, and hybrid systems consisting of a topological insulator and a semimetal. Let us summarize our primary results. Firstly, we determine an analytical formula for the Kondo cloud and describe its possible detection in current correlations far away from the Kondo region. We thereby rely on and extend the method of refermionizable points. Furthermore, we find a class of gapless topological superconductors and semimetals, which accommodate edge states that behave similarly to the ones of globally gapped topological phases. Unexpectedly, we also find edge states that change their chirality when affected by sufficiently strong disorder. We regard the presented research helpful in future classifications and applications of systems containing topological insulators, of which we propose some examples.
Anomalous Z2 antiferromagnetic topological phase in pressurized SmB6
Chang, Kai-Wei; Chen, Peng-Jen
2018-05-01
Antiferromagnetic materials, whose time-reversal symmetry is broken, can be classified into the Z2 topology if they respect some specific symmetry. Since the theoretical proposal, however, no materials have been found to host such Z2 antiferromagnetic topological (Z2-AFT ) phase to date. Here we demonstrate that the topological Kondo insulator SmB6 can be a Z2-AFT system when pressurized to undergo an antiferromagnetic phase transition. In addition to proposing the possible candidate for a Z2-AFT material, in this work we also illustrate the anomalous topological surface states of the Z2-AFT phase which have not been discussed before. Originating from the interplay between the topological properties and the antiferromagnetic surface magnetization, the topological surface states of the Z2-AFT phase behave differently as compared with those of a topological insulator. Besides, the Z2-AFT insulators are also found promising in the generation of tunable spin currents, which is an important application in spintronics.
Topological insulators Dirac equation in condensed matter
Shen, Shun-Qing
2017-01-01
This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already b...
Topological quantum field theory and four manifolds
Marino, Marcos
2005-01-01
The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...
Topology optimization of fluid mechanics problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...... processing tool. Prior to design manufacturing this allows the engineer to quantify the performance of the computed topology design using standard, credible analysis tools with a body-fitted mesh. [1] Borrvall and Petersson (2003) "Topology optimization of fluids in Stokes flow", Int. J. Num. Meth. Fluids...
The role of topology in materials
Saxena, Avadh
2018-01-01
This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foa...
Valley Topological Phases in Bilayer Sonic Crystals
Lu, Jiuyang; Qiu, Chunyin; Deng, Weiyin; Huang, Xueqin; Li, Feng; Zhang, Fan; Chen, Shuqi; Liu, Zhengyou
2018-03-01
Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.
Boundary Hamiltonian Theory for Gapped Topological Orders
Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
2017-06-01
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
Topology-Based Methods in Visualization 2015
Garth, Christoph; Weinkauf, Tino
2017-01-01
This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volum...
Topological anomalies for Seifert 3-manifolds
Energy Technology Data Exchange (ETDEWEB)
Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)
2015-07-14
We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.
Energy Management Dynamic Control Topology In MANET
Madhusudan, G.; Kumar, TNR
2017-08-01
Topology management via per-node transmission power adjustment has been shown effective in extending network lifetime. The existing algorithms constructs static topologies which fail to take the residual energy of network nodes, and cannot balance energy consumption efficiently. To address this problem, a Light Weighted Distributed Topology Control algorithm EMDCT(Energy Management Dynamic Control Topology ) is proposed in this paper. Based on the link metric of the network, both the energy consumption rate level and residual energy levels at the two end nodes are considered. EMDCT generates a Dynamic Topology that changes with the variation of node energy without the aid of location information, each node determines its transmission power according to local network information, which reduces the overhead complexity of EMDCT greatly. The experiment results show that EMDCT preserves network connectivity and manitains minimum-cost property of the network also it can extend network lifetime more remarkably.
Topological transitions in the theory of spacetime
International Nuclear Information System (INIS)
Konstantinov, M.Y.; Melnikov, V.N.
1986-01-01
Results of a realisation of the topological transitions hypothesis are presented. The basic difficulties in the construction of quantum topological transition theory are connected with a necessity to introduce a new non-local interaction defined on a space of topological states. So the general method of construction and study of topological transitions classical models is formulated as a necessary step towards a corresponding quantum description. Their local properties, including an asymptotic behaviour in the neighbourhood of the transition, are studied and applications to problems of gravitation and cosmology are given. The method used is shown to lead to a scalar-tensor theory of topological transitions. Different variants of this theory and its main features are discussed. (author)
Topological quantization of ensemble averages
International Nuclear Information System (INIS)
Prodan, Emil
2009-01-01
We define the current of a quantum observable and, under well-defined conditions, we connect its ensemble average to the index of a Fredholm operator. The present work builds on a formalism developed by Kellendonk and Schulz-Baldes (2004 J. Funct. Anal. 209 388) to study the quantization of edge currents for continuous magnetic Schroedinger operators. The generalization given here may be a useful tool to scientists looking for novel manifestations of the topological quantization. As a new application, we show that the differential conductance of atomic wires is given by the index of a certain operator. We also comment on how the formalism can be used to probe the existence of edge states
Edge instabilities of topological superconductors
Energy Technology Data Exchange (ETDEWEB)
Hofmann, Johannes S. [Institut fuer Theoretische Physik und Astrophysik, Universitaet Wuerzburg (Germany); Max-Planck-Institut fuer Festkoerperforschung, Stuttgart (Germany); Assaad, Fakher F. [Institut fuer Theoretische Physik und Astrophysik, Universitaet Wuerzburg (Germany); Schnyder, Andreas P. [Max-Planck-Institut fuer Festkoerperforschung, Stuttgart (Germany)
2016-07-01
Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground state degeneracy and a diverging density of states. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry broken phases, which lift the ground-state degeneracy. Here, we employ Monte Carlo simulations combined with mean-field considerations to examine the instabilities of the flat-band edge states of d{sub xy}-wave superconductors. We find that attractive interactions induce a complex s-wave pairing instability together with a density wave instability. Repulsive interactions, on the other hand, lead to ferromagnetism mixed with spin-triplet pairing at the edge. We discuss the implications of our findings for experiments on cuprate high-temperature superconductors.
Complete spacelike immersions with topology
International Nuclear Information System (INIS)
Harris, S.G.
1988-01-01
A fairly large class of Lorentz manifolds is defined, called WH normal manifolds, which are approximately those for which timelike infinity is a single point. It is shown that, in such a space, an immersed spacelike hypersurface which is complete must, if it is self-intersecting, not achronal or proper, satisfy strong topological conditions; in particular, if the immersion is injective in the fundamental group, then the hypersurface must be closed, embedded and achronal (i.e. a partial Cauchy surface). WH normal spaces include products of any Riemannian manifold with Minkowski 1-space; in such space, a complete immersed spacelike hypersurface must be immersed as a covering space for the Riemannian factor. (author)
Wavefunctions for topological quantum registers
International Nuclear Information System (INIS)
Ardonne, E.; Schoutens, K.
2007-01-01
We present explicit wavefunctions for quasi-hole excitations over a variety of non-abelian quantum Hall states: the Read-Rezayi states with k ≥ 3 clustering properties and a paired spin-singlet quantum Hall state. Quasi-holes over these states constitute a topological quantum register, which can be addressed by braiding quasi-holes. We obtain the braid properties by direct inspection of the quasi-hole wavefunctions. We establish that the braid properties for the paired spin-singlet state are those of 'Fibonacci anyons', and thus suitable for universal quantum computation. Our derivations in this paper rely on explicit computations in the parafermionic conformal field theories that underly these particular quantum Hall states
Spin-3 topologically massive gravity
Energy Technology Data Exchange (ETDEWEB)
Chen Bin, E-mail: bchen01@pku.edu.cn [Department of Physics, and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China); Center for High Energy Physics, Peking University, Beijing 100871 (China); Long Jiang, E-mail: longjiang0301@gmail.com [Department of Physics, and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China); Wu Junbao, E-mail: wujb@ihep.ac.cn [Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049 (China)
2011-11-24
In this Letter, we study the spin-3 topologically massive gravity (TMG), paying special attention to its properties at the chiral point. We propose an action describing the higher spin fields coupled to TMG. We discuss the traceless spin-3 fluctuations around the AdS{sub 3} vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with generalized Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical W{sub 3} algebra and central charge c{sub R}=3l/G.
Strings, conformal fields and topology
International Nuclear Information System (INIS)
Kaku, Michio
1991-01-01
String Theory has advanced at an astonishing pace in the last few years, and this book aims to acquaint the reader with the most active topics of research in the field. Building on the foundations laid in his Introduction to Superstrings, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, the non-polynominal closed string field theory, matrix models, and topological field theory. Several chapters review the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum. The book conveys the vitality of current research in string theory and places readers at its forefront. (orig.) With 40 figs. in 50 parts
Elementary symplectic topology and mechanics
Cardin, Franco
2015-01-01
This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in...
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
for mechanical problems, but has rapidly extended to many other disciplines, such as fluid dynamics and biomechanical problems. However, the novelty and improvements of optimization methods has been very limited. It is, indeed, necessary to develop of new optimization methods to improve the final designs......, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...
Experimental and Theoretical Methods in Algebra, Geometry and Topology
Veys, Willem; Bridging Algebra, Geometry, and Topology
2014-01-01
Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research f...
A design approach for integrating thermoelectric devices using topology optimization
International Nuclear Information System (INIS)
Soprani, S.; Haertel, J.H.K.; Lazarov, B.S.; Sigmund, O.; Engelbrecht, K.
2016-01-01
Highlights: • The integration of a thermoelectric (TE) cooler into a robotic tool is optimized. • Topology optimization is suggested as design tool for TE integrated systems. • A 3D optimization technique using temperature dependent TE properties is presented. • The sensitivity of the optimization process to the boundary conditions is studied. • A working prototype is constructed and compared to the model results. - Abstract: Efficient operation of thermoelectric devices strongly relies on the thermal integration into the energy conversion system in which they operate. Effective thermal integration reduces the temperature differences between the thermoelectric module and its thermal reservoirs, allowing the system to operate more efficiently. This work proposes and experimentally demonstrates a topology optimization approach as a design tool for efficient integration of thermoelectric modules into systems with specific design constraints. The approach allows thermal layout optimization of thermoelectric systems for different operating conditions and objective functions, such as temperature span, efficiency, and power recovery rate. As a specific application, the integration of a thermoelectric cooler into the electronics section of a downhole oil well intervention tool is investigated, with the objective of minimizing the temperature of the cooled electronics. Several challenges are addressed: ensuring effective heat transfer from the load, minimizing the thermal resistances within the integrated system, maximizing the thermal protection of the cooled zone, and enhancing the conduction of the rejected heat to the oil well. The design method incorporates temperature dependent properties of the thermoelectric device and other materials. The 3D topology optimization model developed in this work was used to design a thermoelectric system, complete with insulation and heat sink, that was produced and tested. Good agreement between experimental results and
Pavement cells and the topology puzzle.
Carter, Ross; Sánchez-Corrales, Yara E; Hartley, Matthew; Grieneisen, Verônica A; Marée, Athanasius F M
2017-12-01
D'Arcy Thompson emphasised the importance of surface tension as a potential driving force in establishing cell shape and topology within tissues. Leaf epidermal pavement cells grow into jigsaw-piece shapes, highly deviating from such classical forms. We investigate the topology of developing Arabidopsis leaves composed solely of pavement cells. Image analysis of around 50,000 cells reveals a clear and unique topological signature, deviating from previously studied epidermal tissues. This topological distribution is established early during leaf development, already before the typical pavement cell shapes emerge, with topological homeostasis maintained throughout growth and unaltered between division and maturation zones. Simulating graph models, we identify a heuristic cellular division rule that reproduces the observed topology. Our parsimonious model predicts how and when cells effectively place their division plane with respect to their neighbours. We verify the predicted dynamics through in vivo tracking of 800 mitotic events, and conclude that the distinct topology is not a direct consequence of the jigsaw piece-like shape of the cells, but rather owes itself to a strongly life history-driven process, with limited impact from cell-surface mechanics. © 2017. Published by The Company of Biologists Ltd.
Gapless topological order, gravity, and black holes
Rasmussen, Alex; Jermyn, Adam S.
2018-04-01
In this work we demonstrate that linearized gravity exhibits gapless topological order with an extensive ground state degeneracy. This phenomenon is closely related both to the topological order of the pyrochlore U (1 ) spin liquid and to recent work by Hawking and co-workers, who used the soft-photon and graviton theorems to demonstrate that the vacuum in linearized gravity is not unique. We first consider lattice models whose low-energy behavior is described by electromagnetism and linearized gravity, and then argue that the topological nature of these models carries over into the continuum. We demonstrate that these models can have many ground states without making assumptions about the topology of spacetime or about the high-energy nature of the theory, and show that the infinite family of symmetries described by Hawking and co-workers is simply the different topological sectors. We argue that in this context black holes appear as topological defects in the infrared theory, and that this suggests a potential approach to understanding both the firewall paradox and information encoding in gravitational theories. Finally, we use insights from the soft-boson theorems to make connections between deconfined gauge theories with continuous gauge groups and gapless topological order.
Two-dimensional topological photonic systems
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng
2017-09-01
The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.
Persistent topological features of dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Maletić, Slobodan, E-mail: slobodan@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia); Zhao, Yi, E-mail: zhao.yi@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Rajković, Milan, E-mail: milanr@vinca.rs [Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia)
2016-05-15
Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.
Topological orbifold models and quantum cohomology rings
International Nuclear Information System (INIS)
Zaslow, E.
1993-01-01
We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of CP 1 by the dihedral group D 4 , how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral CP 1 orbifolds. We then consider CP 2 /D 4 , and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds. (orig.)
Topological M Theory from Pure Spinor Formalism
Grassi, P A; Grassi, Pietro Antonio; Vanhove, Pierre
2005-01-01
We construct multiloop superparticle amplitudes in 11d using the pure spinor formalism. We explain how this construction reduces to the superparticle limit of the multiloop pure spinor superstring amplitudes prescription. We then argue that this construction points to some evidence for the existence of a topological M theory based on a relation between the ghost number of the full-fledged supersymmetric critical models and the dimension of the spacetime for topological models. In particular, we show that the extensions at higher orders of the previous results for the tree and one-loop level expansion for the superparticle in 11 dimensions is related to a topological model in 7 dimensions.
Introduction to set theory and topology
Kuratowski, Kazimierz; Stark, M
1972-01-01
Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its applica
On the topology of untrapped surfaces
Energy Technology Data Exchange (ETDEWEB)
Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)
2009-03-07
Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional (n >= 4) spacetimes was given by Racz I (2008 Class. Quantum Grav. 25 162001). By applying the associated new line of argument it is proven here that strictly stable untrapped surfaces possess exactly the same topological properties as strictly stable marginally outer trapped surfaces (MOTSs) are known to. In addition, a quasi-local notion of outwards and inwards pointing spacelike directions-applicable to untrapped and marginally trapped surfaces-is also introduced.
Topological vortices in gauge models of graphene
Zhang, Xin-Hui; Li, Xueqin; Hao, Jin-Bo
2018-06-01
Graphene-like structure possessing the topological vortices and knots, and the magnetic flux of the vortices configuration quantized, are proposed in this paper. The topological charges of the vortices are characterized by Hopf indices and Brower degrees. The Abelian background field action (BF action) is a topological invariant for the knot family, which is just the total sum of all the self-linking numbers and all the linking numbers. Flux quantization opens the possibility of having Aharonov-Bohm-type effects in graphene without external electromagnetic field.
Topology optimization for simplified structural fire safety
DEFF Research Database (Denmark)
Madsen, Søren; Lange, Nis P.; Giuliani, Luisa
2016-01-01
Topology optimization is applied in an idealized structural fire safety model, where the minimum compliance problem is constrained by temperature-controlled structural degradation. The constraint ensures a certain structural stiffness after a prescribed time. As this time period is extended......, resulting optimized topologies tend to become thicker or introduce redundant members that can take over when structural parts near the origin of the fire lose their load carrying capability. Hence, the structural degradation model acts as an erosion operator on the topology and indirectly enforces a minimum...
On two examples in linear topological spaces
International Nuclear Information System (INIS)
Iyahen, S.O.
1985-11-01
This note first gives examples of B-complete linear topological spaces, and shows that neither the closed graph theorem nor the open mapping theorem holds for linear mappings from such a space to itself. It then looks at Hausdorff linear topological spaces for which coarser Hausdorff linear topologies can be extended from hyperplanes. For B-complete spaces, those which are barrelled necessarily have countable dimension, and conversely. The paper had been motivated by two questions arising in earlier studies related to the closed graph and open mapping theorems; answers to these questions are contained therein. (author)
Nonperturbative summation over 3D discrete topologies
International Nuclear Information System (INIS)
Freidel, Laurent; Louapre, David
2003-01-01
The group field theories realizing the sum over all triangulations of all topologies of 3D discrete gravity amplitudes are known to be nonuniquely Borel summable. We modify these models to construct a new group field theory which is proved to be uniquely Borel summable, defining in an unambiguous way a nonperturbative sum over topologies in the context of 3D dynamical triangulations and spin foam models. Moreover, we give some arguments to support the fact that, despite our modification, this new model is similar to the original one, and therefore could be taken as a definition of the sum over topologies of 3D quantum gravity amplitudes
An extended topological Yang-Mills theory
International Nuclear Information System (INIS)
Deguchi, Shinichi
1992-01-01
Introducing infinite number of fields, we construct an extended version of the topological Yang-Mills theory. The properties of the extended topological Yang-Mills theory (ETYMT) are discussed from standpoint of the covariant canonical quantization. It is shown that the ETYMT becomes a cohomological topological field theory or a theory equivalent to a quantum Yang-Mills theory with anti-self-dual constraint according to subsidiary conditions imposed on state-vector space. On the basis of the ETYMT, we may understand a transition from an unbroken phase to a physical phase (broken phase). (author)
Uniform topology on EQ-algebras
Directory of Open Access Journals (Sweden)
Yang Jiang
2017-04-01
Full Text Available In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, , and then the part induce a uniform topology in E. We prove that the pair (E, is a topological EQ-algebra, and some properties of (E, are investigated. In particular, we show that (E, is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.
Topological stability through extremely tame retractions
DEFF Research Database (Denmark)
Feragen, Aasa
2012-01-01
not know whether f will be topologically stable if we can find a pair of continuous retractions r and s. The class of extremely tame (E-tame) retractions, introduced by du Plessis and Wall, are defined by their nice geometric properties, which are sufficient to ensure that f is topologically stable....... In this article, we present the E-tame retractions and their relation with topological stability, survey recent results by the author concerning their construction, and illustrate the use of our techniques by constructing E-tame retractions for certain germs belonging to the E- and Z-series of singularities....
Topological sigma B model in 4-dimensions
International Nuclear Information System (INIS)
Jun, Hyun-Keun; Park, Jae-Suk
2008-01-01
We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.
First Meeting in Topology and Functional Analysis
López-Pellicer, Manuel
2014-01-01
Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.
The simplest classical models of topological transitions
International Nuclear Information System (INIS)
Konstantinov, M.Yu.
1983-01-01
It is shown that simplest classical models of topologigal transitions possess scalar singularity of curvature with a point carrier being a source of space-time incompleteness. It is also shown that the condition of energy dominance is broken near the topological transition, asymptotic behaviour of the curvature tensor (growth of curvature at approximation to the topological transition) and energy-momentum tensor of (breaking the condition of energy dominance) being a common property of the considered models and being completely determined by the type of topological transition
Quantum computation with topological codes from qubit to topological fault-tolerance
Fujii, Keisuke
2015-01-01
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
Topological Schemas of Memory Spaces
Babichev, Andrey; Dabaghian, Yuri A.
2018-01-01
Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure. PMID:29740306
Topological geometrodynamics. III. Quantum theory
International Nuclear Information System (INIS)
Pitkanen, M.
1986-01-01
The description of 3-space as a spacelike 3-surface of the space H = M 4 x CP 2 (product of Minkowski space and two-dimensional complex projective space CP 2 ) and the idea that particles correspond to 3-surfaces of finite size in H are the basic ingredients of topological geometrodynamics, TGD, an attempt to a geometry-based unification of the fundamental interactions. The observations that the Schroedinger equation can be derived from a variational principle and that the existence of a unitary S matrix follows from the phase symmetry of this action lead to the idea that quantum TGD should be derivable from a quadratic phase symmetric variational principle in the space SH consisting of the spacelike 3-surfaces of H. In this paper a formal realization of this idea is proposed. First, the space SH is endowed with the necessary geometric structures (metric, vielbein, and spinor structures) induced from the corresponding structures of the space H. Second, the concepts of the scalar super field in SH (both fermions and bosons should be describable by the same probability amplitude) and of super d'Alambertian are defined. It is shown that the requirement of a maximal symmetry leads to a unique CP-breaking super d'Alambertian and thus to a unique theory ''predicting everything.'' Finally, a formal expression for the S matrix of the theory is derived
Topological defects from the multiverse
Zhang, Jun; Blanco-Pillado, Jose J.; Garriga, Jaume; Vilenkin, Alexander
2015-05-01
Many theories of the early universe predict the existence of a multiverse where bubbles continuously nucleate giving rise to observers in their interior. In this paper, we point out that topological defects of several dimensionalities will also be produced in de Sitter like regions of the multiverse. In particular, defects could be spontaneously nucleated in our parent vacuum. We study the evolution of these defects as they collide with and propagate inside of our bubble. We estimate the present distribution of defects in the observable part of the universe. The expected number of such nearby defects turns out to be quite small, even for the highest nucleation rate. We also study collisions of strings and domain walls with our bubble in our past light cone. We obtain simulated full-sky maps of the loci of such collisions, and find their angular size distribution. Similarly to what happens in the case of bubble collisions, the prospect of detecting any collisions of our bubble with ambient defects is greatly enhanced in the case where the cosmological constant of our parent vacuum is much higher than the vacuum energy density during inflation in our bubble.
Topological defects from the multiverse
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jun [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States); Blanco-Pillado, Jose J. [Department of Theoretical Physics, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, 48013, Bilbao (Spain); Garriga, Jaume [Departament de Fisica Fonamental i Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques, 1, 08028, Barcelona (Spain); Vilenkin, Alexander [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2015-05-28
Many theories of the early universe predict the existence of a multiverse where bubbles continuously nucleate giving rise to observers in their interior. In this paper, we point out that topological defects of several dimensionalities will also be produced in de Sitter like regions of the multiverse. In particular, defects could be spontaneously nucleated in our parent vacuum. We study the evolution of these defects as they collide with and propagate inside of our bubble. We estimate the present distribution of defects in the observable part of the universe. The expected number of such nearby defects turns out to be quite small, even for the highest nucleation rate. We also study collisions of strings and domain walls with our bubble in our past light cone. We obtain simulated full-sky maps of the loci of such collisions, and find their angular size distribution. Similarly to what happens in the case of bubble collisions, the prospect of detecting any collisions of our bubble with ambient defects is greatly enhanced in the case where the cosmological constant of our parent vacuum is much higher than the vacuum energy density during inflation in our bubble.
Topological defects from the multiverse
International Nuclear Information System (INIS)
Zhang, Jun; Vilenkin, Alexander; Blanco-Pillado, Jose J.; Garriga, Jaume
2015-01-01
Many theories of the early universe predict the existence of a multiverse where bubbles continuously nucleate giving rise to observers in their interior. In this paper, we point out that topological defects of several dimensionalities will also be produced in de Sitter like regions of the multiverse. In particular, defects could be spontaneously nucleated in our parent vacuum. We study the evolution of these defects as they collide with and propagate inside of our bubble. We estimate the present distribution of defects in the observable part of the universe. The expected number of such nearby defects turns out to be quite small, even for the highest nucleation rate. We also study collisions of strings and domain walls with our bubble in our past light cone. We obtain simulated full-sky maps of the loci of such collisions, and find their angular size distribution. Similarly to what happens in the case of bubble collisions, the prospect of detecting any collisions of our bubble with ambient defects is greatly enhanced in the case where the cosmological constant of our parent vacuum is much higher than the vacuum energy density during inflation in our bubble
Topological Schemas of Memory Spaces
Directory of Open Access Journals (Sweden)
Andrey Babichev
2018-04-01
Full Text Available Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.
Quintic quasi-topological gravity
Energy Technology Data Exchange (ETDEWEB)
Cisterna, Adolfo [Vicerrectoría académica, Universidad Central de Chile,Toesca 1783 Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile,Casilla 567, Valdivia (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Física, Universidad de Talca,Casilla 747, Talca (Chile); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla, 160-C, Concepción (Chile)
2017-04-11
We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R{sup 5} terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff’s Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler’s polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in https://arxiv.org/abs/1003.4773, the general geometric structure of these Lagrangians remains an open problem.
On filter boundary conditions in topology optimization
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik
2017-01-01
Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...
Topology Explains Why Automobile Sunshades Fold Oddly
Feist, Curtis; Naimi, Ramin
2009-01-01
Automobile sunshades always fold into an "odd" number of loops. The explanation why involves elementary topology (braid theory and linking number, both explained in detail here with definitions and examples), and an elementary fact from algebra about symmetric group.
Topology optimisation of natural convection problems
DEFF Research Database (Denmark)
Alexandersen, Joe; Aage, Niels; Andreasen, Casper Schousboe
2014-01-01
This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations...... coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences...... in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach...
Topology Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport...... in a surrounding uid, governed by a convection-diffusion equation, where the convective velocity field is found from solving the isothermal incompressible steady-state Navier-Stokes equations. Topology optimisation is also applied to steady-state natural convection problems. The modelling is done using stabilised...... finite elements, the formulation and implementation of which was done partly during a special course as prepatory work for this thesis. The formulation is extended with a Brinkman friction term in order to facilitate the topology optimisation of fluid flow and convective cooling problems. The derived...
Topological properties of a curved spacetime
Agrawal, Gunjan; Shrivastava, Sampada; Godani, Nisha; Sinha, Soami Pyari
2017-12-01
The present paper aims at the study of a topology on Lorentzian manifolds, defined by Göbel [4] using the ideas of Zeeman [16]. Observing that on the Minkowski space it is the same as Zeeman's time topology, it has been found that a Lorentzian manifold with this topology is path connected, nonfirst countable and nonsimply connected while the Minkowski space with time topology is, in addition nonregular and separable. Furthermore, using the notion of Zeno sequences it is obtained that a compact set does not contain a nonempty open set and that a set is compact if and only if each of its infinite subsets has a limit point if and only if each of its sequences has a convergent subsequence.
Exotic Lifshitz transitions in topological materials
Volovik, G. E.
2018-01-01
Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stability-supporting topological invariant ( N_1, N_2, N_3, {\\tilde N}_3, etc.). The topology of the shape of Fermi surfaces and Dirac lines and the interconnection of objects of different dimensionalities produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transition-related singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe, and a black hole horizon serves as the surface of the Lifshitz transition between vacua with type-I and type-II Weyl points.
ABCD of Beta Ensembles and Topological Strings
Krefl, Daniel
2012-01-01
We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.
Synchronization in complex networks with switching topology
International Nuclear Information System (INIS)
Wang, Lei; Wang, Qing-guo
2011-01-01
This Letter investigates synchronization issues of complex dynamical networks with switching topology. By constructing a common Lyapunov function, we show that local and global synchronization for a linearly coupled network with switching topology can be evaluated by the time average of second smallest eigenvalues corresponding to the Laplacians of switching topology. This result is quite powerful and can be further used to explore various switching cases for complex dynamical networks. Numerical simulations illustrate the effectiveness of the obtained results in the end. -- Highlights: → Synchronization of complex networks with switching topology is investigated. → A common Lyapunov function is established for synchronization of switching network. → The common Lyapunov function is not necessary to monotonically decrease with time. → Synchronization is determined by the second smallest eigenvalue of its Laplacian. → Synchronization criterion can be used to investigate various switching cases.
Universalities of thermodynamic signatures in topological phases
Kempkes, S. N.; Quelle, A.; de Morais Smith, C.
2016-01-01
Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive
Topological protection of multiparticle dissipative transport
Loehr, Johannes; Loenne, Michael; Ernst, Adrian; de Las Heras, Daniel; Fischer, Thomas M.
2016-06-01
Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.
Topology and prediction of RNA pseudoknots
DEFF Research Database (Denmark)
Reidys, Christian; Huang, Fenix; Andersen, Jørgen Ellegaard
2011-01-01
Motivation: Several dynamic programming algorithms for predicting RNA structures with pseudoknots have been proposed that differ dramatically from one another in the classes of structures considered. Results: Here, we use the natural topological classification of RNA structures in terms...
Multiple topological phases in phononic crystals
Chen, Zeguo; Wu, Ying
2017-01-01
We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases: quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C-6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases: quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.
Machine Learning Topological Invariants with Neural Networks
Zhang, Pengfei; Shen, Huitao; Zhai, Hui
2018-02-01
In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.
Topological entropy for induced hyperspace maps
International Nuclear Information System (INIS)
Canovas Pena, Jose S.; Lopez, Gabriel Soler
2006-01-01
Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive
Topological Phases in the Real World
Hsu, Yi-Ting
The experimental discovery and subsequent theoretical understanding of the integer quantum Hall effect, the first known topological phase, has started a revolutionary breakthrough in understanding states of matter since its discovery four decades ago. Topological phases are predicted to have many generic signatures resulting from their underlying topological nature, such as quantized Hall transport, robust boundary states, and possible fractional excitations. The intriguing nature of these signatures and their potential applications in quantum computation has intensely fueled the efforts of the physics community to materialize topological phases. Among various topological phases initially predicted on theoretical grounds, chiral topological superconductors and time-reversal symmetric topological insulators (TI) in three dimension (3D) are two promising candidates for experimental realization and application. The family of materials, Bi2X3 (X = Se, Te), has been predicted and shown experimentally to be time-reversal symmetric 3D TIs through the observation of robust Dirac surface states with Rashba-type spin-winding. Due to their robust surface states with spin-windings, these 3D TIs are expected to be promising materials for producing large spin-transfer torques which are advantageous for spintronics application. As for topological superconductors, despite the exotic excitations that have been extensively proposed as qubits for topological quantum computing, materials hosting topological superconductivity are rare to date and the leading candidate in two dimensions (2D), Sr 2RuO4, has a low transition temperature (Tc ). The goal of my phd study is to push forward the current status of realization of topological phases by materializing higher Tc topological superconductors and investigating the stability of Dirac surface states in 3D TIs. In the first part of this thesis, I will discuss our double-pronged objective for topological superconductors: to propose how to
On topological properties of sierpinski networks
International Nuclear Information System (INIS)
Imran, Muhammad; Sabeel-e-Hafi; Gao, Wei; Reza Farahani, Mohammad
2017-01-01
Sierpinski graphs constitute an extensively studied class of graphs of fractal nature applicable in topology, mathematics of Tower of Hanoi, computer science, and elsewhere. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, biological activity, etc. are determined by the chemical applications of graph theory. These properties can be characterized by certain graph invariants referred to as topological indices. In QRAR/QSPR study these graph invariants has played a vital role. In this paper, we study the molecular topological properties of Sierpinski networks and derive the analytical closed formulas for the atom-bond connectivity (ABC) index, geometric-arithmetic (GA) index, and fourth and fifth version of these topological indices for Sierpinski networks denoted by S(n, k).
Exploring topological phases with quantum walks
International Nuclear Information System (INIS)
Kitagawa, Takuya; Rudner, Mark S.; Berg, Erez; Demler, Eugene
2010-01-01
The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete-time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigations. In particular, we demonstrate that recent experimental realizations of quantum walks with cold atoms, photons, and ions simulate a nontrivial one-dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases, which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the nontrivial topological character of the system.
Topology of classical vacuum space-time
International Nuclear Information System (INIS)
Cho, Y.M.
2007-04-01
We present a topological classification of classical vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology π 3 (S 3 ) = π 3 (S 2 ). Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity. (author)
Topological entropy for induced hyperspace maps
Energy Technology Data Exchange (ETDEWEB)
Canovas Pena, Jose S. [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Jose.canovas@upct.es; Lopez, Gabriel Soler [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Gabriel.soler@upct.es
2006-05-15
Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive.
Topological photonic crystals with zero Berry curvature
Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori
2018-02-01
Topological photonic crystals are designed based on the concept of Zak's phase rather than the topological invariants such as the Chern number and spin Chern number, which rely on the existence of a nonvanishing Berry curvature. Our photonic crystals (PCs) are made of pure dielectrics and sit on a square lattice obeying the C4 v point-group symmetry. Two varieties of PCs are considered: one closely resembles the electronic two-dimensional Su-Schrieffer-Heeger model, and the other continues as an extension of this analogy. In both cases, the topological transitions are induced by adjusting the lattice constants. Topological edge modes (TEMs) are shown to exist within the nontrivial photonic band gaps on the termination of those PCs. The high efficiency of these TEMs transferring electromagnetic energy against several types of disorders has been demonstrated using the finite-element method.
Topological Modeling and Stochastic Analysis of Images
National Research Council Canada - National Science Library
Krim, Hamid
2004-01-01
.... Concepts in classification and recognition problems. 1. We have explored the potential of combining geometrical as well as topological information in capturing the essence of an object for classification and recognition purposes...
Geared Topological Metamaterials with Tunable Mechanical Stability
Directory of Open Access Journals (Sweden)
Anne S. Meeussen
2016-11-01
Full Text Available The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that are stable and yet capable of harboring protected edge and bulk modes, analogous to those in electronic topological insulators and Weyl semimetals. To do so, we exploit gear assemblies that, unlike point masses connected by springs, incorporate both translational and rotational degrees of freedom. Global structural stability is achieved by eliminating geometrical frustration of collective gear rotations extending through the assembly. The topological robustness of the mechanical modes makes them appealing across scales from engineered macrostructures to networks of toothed microrotors of potential use in micromachines.
Topological photonic orbital-angular-momentum switch
Luo, Xi-Wang; Zhang, Chuanwei; Guo, Guang-Can; Zhou, Zheng-Wei
2018-04-01
The large number of available orbital-angular-momentum (OAM) states of photons provides a unique resource for many important applications in quantum information and optical communications. However, conventional OAM switching devices usually rely on precise parameter control and are limited by slow switching rate and low efficiency. Here we propose a robust, fast, and efficient photonic OAM switch device based on a topological process, where photons are adiabatically pumped to a target OAM state on demand. Such topological OAM pumping can be realized through manipulating photons in a few degenerate main cavities and involves only a limited number of optical elements. A large change of OAM at ˜10q can be realized with only q degenerate main cavities and at most 5 q pumping cycles. The topological photonic OAM switch may become a powerful device for broad applications in many different fields and motivate a topological design of conventional optical devices.
Multiple topological phases in phononic crystals
Chen, Zeguo
2017-11-20
We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases: quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C-6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases: quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.
Topological Material-Based Spin Devices
Zhang, Minhao; Wang, Xuefeng
Three-dimensional topological insulators have insulating bulk and gapless helical surface states. One of the most fascinating properties of the metallic surface states is the spin-momentum helical locking. The giant current-driven torques on the magnetic layer have been discovered in TI/ferromagnet bilayers originating from the spin-momentum helical locking, enabling the efficient magnetization switching with a low current density. We demonstrated the current-direction dependent on-off state in TIs-based spin valve devices for memory and logic applications. Further, we demonstrated the Bi2Se3 system will go from a topologically nontrivial state to a topologically trivial state when Bi atoms are replaced by lighter In atoms. Here, topologically trivial metal (BixIny)2 Se3 with high mobility also facilitates the realization of its application in multifunctional spintronic devices.
A dynamical topology for the space of states
International Nuclear Information System (INIS)
Dittrich, J.
1979-01-01
A new topology is introduced for the space of states of a physical system. This topology is given by dynamics, every state has a neighbourhood consisting of states connected by the time evolution only. With respect to the new topology, all conservation laws can be treated as topological laws. (author)
Proceeding of the workshop on quantum gravity and topology
International Nuclear Information System (INIS)
Oda, Ichiro
1991-10-01
The workshop on Quantum Gravity and Topology was held at INS on February 21-23, 1991. Several introductory lectures and more than 15 talks were delivered for about 100 participants. The main subjects discussed were i) Topological quantum field theories and topological gravity ii) Low dimensional and four dimensional gravity iii) Topology change iv) Superstring theories etc. (J.P.N.)
Adiabatic photo-steering theory in topological insulators
International Nuclear Information System (INIS)
Inoue, Jun-ichi
2014-01-01
Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane–Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed. (focus issue review)
Topology design and performance analysis of an integrated communication network
Li, V. O. K.; Lam, Y. F.; Hou, T. C.; Yuen, J. H.
1985-01-01
A research study on the topology design and performance analysis for the Space Station Information System (SSIS) network is conducted. It is begun with a survey of existing research efforts in network topology design. Then a new approach for topology design is presented. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. The algorithm for generating subsets is described in detail, and various aspects of the overall design procedure are discussed. Two more efficient versions of this algorithm (applicable in specific situations) are also given. Next, two important aspects of network performance analysis: network reliability and message delays are discussed. A new model is introduced to study the reliability of a network with dependent failures. For message delays, a collection of formulas from existing research results is given to compute or estimate the delays of messages in a communication network without making the independence assumption. The design algorithm coded in PASCAL is included as an appendix.
A-Soft Separation Axioms in Soft Topological Space
Directory of Open Access Journals (Sweden)
Luay Abd –Al-Hani Al-Sweedi
2018-01-01
Full Text Available The important science tools in a different kinds and specialties , that considered the basic mainstay of ( the set theory and because of huge development in all life fields. This causes great problems , that need solution and parallel tools for those developments , so the scientis become responsible to work on the development of number theory and open new horizons , that a new science had appeared which is ( soft figures theory which is considered the important tool to solve most difficult problems or overcome them ,in these sciences and their specific life specialization, economy, medicine , geometry and others. Also the theory of soft numbers had entered in general topology in power full and active way. The last years a new science has appeared is (soft topological space. The main idea of this research is to define the separation axioms in (soft topological space and practically in certain point , and to study the most important properties and results of it .
Topological Toughening of graphene and other 2D materials
Gao, Huajian
It has been claimed that graphene, with the elastic modulus of 1TPa and theoretical strength as high as 130 GPa, is the strongest material. However, from an engineering point of view, it is the fracture toughness that determines the actual strength of materials, as crack-like flaws (i.e., cracks, holes, notches, corners, etc.) are inevitable in the design, fabrication, and operation of practical devices and systems. Recently, it has been demonstrated that graphene has very low fracture toughness, in fact close to that of ideally brittle solids. These findings have raised sharp questions and are calling for efforts to explore effective methods to toughen graphene. Recently, we have been exploring the potential use of topological effects to enhance the fracture toughness of graphene. For example, it has been shown that a sinusoidal graphene containing periodically distributed disclination quadrupoles can achieve a mode I fracture toughness nearly twice that of pristine graphene. Here we report working progresses on further studies of topological toughening of graphene and other 2D materials. A phase field crystal method is adopted to generate the atomic coordinates of material with specific topological patterns. We then perform molecular dynamics simulations of fracture in the designed samples, and observe a variety of toughening mechanisms, including crack tip blunting, crack trapping, ligament bridging, crack deflection and daughter crack initiation and coalescence.
Entanglement from topology in Chern-Simons theory
Salton, Grant; Swingle, Brian; Walter, Michael
2017-05-01
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.