Mukherjee, Amiya
2015-01-01
This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem, and the generalised Poincaré conjecture. The material is the outcome of lectures and seminars on various aspects of differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities throughout India. The book will appeal to graduate students and researchers interested in these topics. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis, and algebraic topology is recommended.
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
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
Differential topology an introduction
Gauld, David B
2006-01-01
Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curv
Differential topology of semimetals
Mathai, Varghese
2016-01-01
The subtle interplay between local and global charges for topological semimetals exactly parallels that for singular vector fields. Part of this story is the relationship between cohomological semimetal invariants, Euler structures, and ambiguities in the torsion of manifolds. Dually, semimetal invariants can be represented by Euler chains from which the surface Fermi arc connectivity can be deduced. These dual pictures, and the link to insulators, are organised using geometric exact sequences. We go beyond Dirac-type Hamiltonians and introduce new classes of semimetals whose local charges are subtle Atiyah-Dupont-Thomas invariants globally constrained by the Kervaire semicharacteristic, leading to the prediction of torsion Fermi arcs.
Applications of Differential Topology to Grid Generation.
1985-11-25
Differential Topology, Annals of Mathematics Studies Number 54, Princeton University Press, Princeton, New Jersey, 1966. * 4. Rudin, W., Principles of...Springer-Verlag, 1976. 8. Munkres, J. R., Elementary Differential Topology, Annals of Mathematics Studies Number 54, Princeton University Press
Topologies for neutral functional differential equations.
Melvin, W. R.
1973-01-01
Bounded topologies are considered for functional differential equations of the neutral type in which present dynamics of the system are influenced by its past behavior. A special bounded topology is generated on a collection of absolutely continuous functions with essentially bounded derivatives, and an application to a class of nonlinear neutral functional differential equations due to Driver (1965) is presented.
Categorical properties of topological and differentiable stacks
Carchedi, D.J.
2011-01-01
The focus of this PhD research is on the theory of topological and differentiable stacks. There are two main themes of this research. The first, is the creation of the theory of compactly generated stacks, which solve many categorical shortcomings of the theory of classical topological stacks. In pa
Topology Optimization of Structure Using Differential Evolution
Chun-Yin Wu
2008-02-01
Full Text Available The population-based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems. A promising new evolutionary algorithm, differential evolution, has garnered significant attention in the engineering optimization research. Differential evolution has the advantage of incorporating a relatively simple and efficient form of mutation and crossover. This paper aims at introducing differential evolution as an alternative approach for topology optimization of truss and continuous structure with stress and displacement constraints. In comparison the results with other studies, it shows that differential evolution algorithms are very effective and efficient in solving topology optimization problem of structure.
Advances in differential geometry and topology
Institute for Scientific Interchange. Turin
1990-01-01
The aim of this volume is to offer a set of high quality contributions on recent advances in Differential Geometry and Topology, with some emphasis on their application in physics.A broad range of themes is covered, including convex sets, Kaehler manifolds and moment map, combinatorial Morse theory and 3-manifolds, knot theory and statistical mechanics.
Chiral differential operators and topology
Cheung, Pokman
2010-01-01
The first part of this paper provides a new formulation of chiral differential operators (CDOs) in terms of global geometric quantities. The main result is a recipe to define essentially all sheaves of smooth CDOs on a cs-manifold; its ingredients consist of an affine connection and an even 3-form that trivializes the first Pontrjagin form. With the connection fixed, two suitable 3-forms define isomorphic sheaves of CDOs if and only if their difference is exact. Moreover, conformal structures are in one-to-one correspondence with even 1-forms that trivialize the first Chern form. The second part of this paper concerns the construction of what may be called "chiral Dolbeault complexes". The classical Dolbeault complex of a complex manifold M may be viewed as the functions on an associated cs-manifold with the action of an odd vector field Q that satisfies Q^2=0. Motivated by this, we study the condition under which a conformal sheaf of CDOs on that cs-manifold admits an odd derivation Q' that extends Q and sat...
Topological and differential geometrical gauge field theory
Saaty, Joseph
between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
Topology in Dynamics, Differential Equations, and Data
Day, Sarah; Vandervorst, Robertus C. A. M.; Wanner, Thomas
2016-11-01
This special issue is devoted to showcasing recent uses of topological methods in the study of dynamical behavior and the analysis of both numerical and experimental data. The twelve original research papers span a wide spectrum of results from abstract index theories, over homology- and persistence-based data analysis techniques, to computer-assisted proof techniques based on topological fixed point arguments.
Differential topology interacts with isoparametric foliations
Ge, Jianquan; Qian, Chao
2015-01-01
Comment: 11 pages, to appear in Geometry and Topology of Manifolds/ The 10th Geomtery Conference for the Friendship of China and Japan 2014, edited by Akito Futaki, Reiko Miyaoka, Zizhou Tang, Weiping Zhang, Springer Proceedings in Mathematics & Statistics
Relative Topological Integrals and Relative Cheeger-Simons Differential Characters
Zucchini, R
2000-01-01
Topological integrals appear frequently in Lagrangian field theories. On manifolds without boundary, they can be treated in the framework of ordinary (co)homology using the formalism of Cheeger-Simons differential characters. String and D-brane theory involve field theoretic models on worldvolumes with border. On manifolds with boundary, the proper treatment of topological integrals requires a generalization of the usual differential topological set up and leads naturally to relative (co)homology and relative Cheeger-Simons differential characters. In this paper, we present a construction of relative Cheeger-Simons differential characters which is computable in principle and which contains the ordinary Cheeger-Simons differential characters as a particular case.
3D surface topology guides stem cell adhesion and differentiation.
Viswanathan, Priyalakshmi; Ondeck, Matthew G; Chirasatitsin, Somyot; Ngamkham, Kamolchanok; Reilly, Gwendolen C; Engler, Adam J; Battaglia, Giuseppe
2015-06-01
Polymerized high internal phase emulsion (polyHIPE) foams are extremely versatile materials for investigating cell-substrate interactions in vitro. Foam morphologies can be controlled by polymerization conditions to result in either open or closed pore structures with different levels of connectivity, consequently enabling the comparison between 2D and 3D matrices using the same substrate with identical surface chemistry conditions. Additionally, here we achieve the control of pore surface topology (i.e. how different ligands are clustered together) using amphiphilic block copolymers as emulsion stabilizers. We demonstrate that adhesion of human mesenchymal progenitor (hES-MP) cells cultured on polyHIPE foams is dependent on foam surface topology and chemistry but is independent of porosity and interconnectivity. We also demonstrate that the interconnectivity, architecture and surface topology of the foams has an effect on the osteogenic differentiation potential of hES-MP cells. Together these data demonstrate that the adhesive heterogeneity of a 3D scaffold could regulate not only mesenchymal stem cell attachment but also cell behavior in the absence of soluble growth factors.
Fast Micro-Differential Evolution for Topological Active Net Optimization.
Li, Yuan-Long; Zhan, Zhi-Hui; Gong, Yue-Jiao; Zhang, Jun; Li, Yun; Li, Qing
2016-06-01
This paper studies the optimization problem of topological active net (TAN), which is often seen in image segmentation and shape modeling. A TAN is a topological structure containing many nodes, whose positions must be optimized while a predefined topology needs to be maintained. TAN optimization is often time-consuming and even constructing a single solution is hard to do. Such a problem is usually approached by a "best improvement local search" (BILS) algorithm based on deterministic search (DS), which is inefficient because it spends too much efforts in nonpromising probing. In this paper, we propose the use of micro-differential evolution (DE) to replace DS in BILS for improved directional guidance. The resultant algorithm is termed deBILS. Its micro-population efficiently utilizes historical information for potentially promising search directions and hence improves efficiency in probing. Results show that deBILS can probe promising neighborhoods for each node of a TAN. Experimental tests verify that deBILS offers substantially higher search speed and solution quality not only than ordinary BILS, but also the genetic algorithm and scatter search algorithm.
A shape representation for computer vision based on differential topology.
Blicher, A P
1995-01-01
We describe a shape representation for use in computer vision, after a brief review of shape representation and object recognition in general. Our shape representation is based on graph structures derived from level sets whose characteristics are understood from differential topology, particularly singularity theory. This leads to a representation which is both stable and whose changes under deformation are simple. The latter allows smoothing in the representation domain ('symbolic smoothing'), which in turn can be used for coarse-to-fine strategies, or as a discrete analog of scale space. Essentially the same representation applies to an object embedded in 3-dimensional space as to one in the plane, and likewise for a 3D object and its silhouette. We suggest how this can be used for recognition.
Gorbuzov, V N
2011-01-01
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and projective matrix Riccati equations.
CHENG LIXIN; TENG YANMEI
2005-01-01
This paper presents a type of variational principles for real valued w* lower semicon tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.
Lefschetz, Solomon
1930-01-01
Lefschetz's Topology was written in the period in between the beginning of topology, by PoincarÃ©, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of
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
Kuratowski, Kazimierz
1966-01-01
Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations
Kuratowski, Kazimierz
1968-01-01
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connecte
Global topological classification of Lotka-Volterra quadratic differential systems
Dana Schlomiuk
2012-04-01
Full Text Available The Lotka-Volterra planar quadratic differential systems have numerous applications but the global study of this class proved to be a challenge difficult to handle. Indeed, the four attempts to classify them (Reyn (1987, W"orz-Buserkros (1993, Georgescu (2007 and Cao and Jiang (2008 produced results which are not in agreement. The lack of adequate global classification tools for the large number of phase portraits encountered, explains this situation. All Lotka-Volterra systems possess invariant straight lines, each with its own multiplicity. In this article we use as a global classification tool for Lotka-Volterra systems the concept of configuration of invariant lines (including the line at infinity. The class splits according to the types of configurations in smaller subclasses which makes it easier to have a good control over the phase portraits in each subclass. At the same time the classification becomes more transparent and easier to grasp. We obtain a total of 112 topologically distinct phase portraits: 60 of them with exactly three invariant lines, all simple; 27 portraits with invariant lines with total multiplicity at least four; 5 with the line at infinity filled up with singularities; 20 phase portraits of degenerate systems. We also make a thorough analysis of the results in the paper of Cao and Jiang [13]. In contrast to the results on the classification in [13], done in terms of inequalities on the coefficients of normal forms, we construct invariant criteria for distinguishing these portraits in the whole parameter space $mathbb{R}^{12}$ of coefficients.
Differential and symplectic topology of knots and curves
Tabachnikov, S
1999-01-01
This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory (""quantum"" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is
Differential topological characteristics of the DSR on injection space of electrical power system
余贻鑫; 曾沅; 冯飞
2002-01-01
This paper analyzes the differential topological characteristics of the dynamic security region (DSR) on injection space of electrical power system by differential topology theories. It is shown that the boundary of the DSR on injection space has no suspension and is compact, and there are no holes inside the DSR defined based on controlling unstable equilibrium point (UEP) method. The 10-generator, 39-bus New England Test System, is taken as an example to show these characteristics of the DSR on injection space.
Integrable differential systems of topological type and reconstruction by the topological recursion
Belliard, Raphaël; Marchal, Olivier
2016-01-01
Starting from a $d\\times d$ rational Lax pair system of the form $\\hbar \\partial_x \\Psi= L\\Psi$ and $\\hbar \\partial_t \\Psi=R\\Psi$ we prove that, under certain assumptions (genus $0$ spectral curve and additional conditions on $R$ and $L$), the system satisfies the "topological type property". A consequence is that the formal $\\hbar$-WKB expansion of its determinantal correlators, satisfy the topological recursion. This applies in particular to all $(p,q)$ minimal models reductions of the KP hierarchy, or to the six Painlev\\'e systems.
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.
Differential geometry and topology with a view to dynamical systems
Burns, Keith
2005-01-01
MANIFOLDSIntroductionReview of topological conceptsSmooth manifoldsSmooth mapsTangent vectors and the tangent bundleTangent vectors as derivationsThe derivative of a smooth mapOrientationImmersions, embeddings and submersionsRegular and critical points and valuesManifolds with boundarySard's theoremTransversalityStabilityExercisesVECTOR FIELDS AND DYNAMICAL SYSTEMSIntroductionVector fieldsSmooth dynamical systemsLie derivative, Lie bracketDiscrete dynamical systemsHyperbolic fixed points and periodic orbitsExercisesRIEMANNIAN METRICSIntroductionRiemannian metricsStandard geometries on surfacesExercisesRIEMANNIAN CONNECTIONS AND GEODESICSIntroductionAffine connectionsRiemannian connectionsGeodesicsThe exponential mapMinimizing properties of geodesicsThe Riemannian distanceExercisesCURVATUREIntroductionThe curvature tensorThe second fundamental formSectional and Ricci curvaturesJacobi fieldsManifolds of constant curvatureConjugate pointsHorizontal and vertical sub-bundlesThe geodesic flowExercisesTENSORS AND DI...
Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation
Lazarov, Boyan Stefanov; Sigmund, Ole
2009-01-01
The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology...... information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential...... equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimisation problems in linear elasticity, solved on sequential and parallel computers....
2011-01-01
In differential conductometric systems, for example in biosensor systems, often use co-planar thinly-pellicle structure double-sensors with pectinate topology. Simple and useful devices could be realized with help of them. But sensitivity and producibility of results those devices depends on parameters of sensors which we probe. On base of metrological research frequency descriptions, parameters conductometric differential sensors was analyzed effectiveness of using this sensors with differen...
Filters in topology optimization based on Helmholtz‐type differential equations
Lazarov, Boyan Stefanov; Sigmund, Ole
2011-01-01
The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology optimizat......The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology...... optimization require information about the neighbor cells, which is difficult to obtain for fine meshes or complex domains and geometries. The complexity of the problem increases further in parallel computing, when the design domain is decomposed into multiple non‐overlapping partitions. Obtaining information...... from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation...
Topological and non-topological soliton solutions to some time-fractional differential equations
M Mirzazadeh
2015-07-01
This paper investigates, for the first time, the applicability and effectiveness of He’s semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He’s semi-inverse variational principle method and the ansatz method are used to construct exact solutions of nonlinear fractional Klein–Gordon equation and generalized Hirota–Satsuma coupled KdV system. These equations have been widely applied in many branches of nonlinear sciences such as nonlinear optics, plasma physics, superconductivity and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theoretical and numerical studies.
Solving Partial Differential Equations Numerically on Manifolds with Arbitrary Spatial Topologies
Lindblom, Lee
2012-01-01
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as a set of non-overlapping cubic regions, plus a set of maps to identify the faces of adjoining regions. The differential structure on these manifolds is fixed by specifying a smooth reference metric tensor. Matching conditions that ensure the appropriate levels of continuity and differentiability across region boundaries are developed for arbitrary tensor fields. Standard numerical methods are then used to solve the equations with the appropriate boundary conditions, which are determined from these inter-region matching conditions. Numerical examples are presented which use pseudo-spectral methods to solve simple elliptic equations on multi-cube representations of manifolds with the topologies T^3, S^2 x S^1 and S^3. Examples are also presented of numerical solutions of sim...
Differential topology and general equilibrium with complete and incomplete markets
Villanacci, Antonio; Benevieri, Pierluigi; Battinelli, Andrea
2002-01-01
General equilibrium In this book we try to cope with the challenging task of reviewing the so called general equilibrium model and of discussing one specific aspect of the approach underlying it, namely, market completeness. With the denomination "general equilibrium" (from now on in short GE) we shall mainly refer to two different things. On one hand, in particular when using the expression "GE approach", we shall refer to a long established methodolog ical tradition in building and developing economic models, which includes, as of today, an enormous amount of contributions, ranging in number by several 1 thousands • On the other hand, in particular when using the expression "stan dard differentiable GE model", we refer to a very specific version of economic model of exchange and production, to be presented in Chapters 8 and 9, and to be modified in Chapters 10 to 15. Such a version is certainly formulated within the GE approach, but it is generated by making several quite restrictive 2 assumptions •...
Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation
Lazarov, Boyan Stefanov; Sigmund, Ole
2009-01-01
The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology...... information about the neighbour cells, which is difficult to obtain when the mesh program is separated from the computational code, especially for irregular meshes. The problem becomes even tougher in parallel environments, where the domain is decomposed into multiple non-overlapping partitions. Obtaining...... information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential...
Singular and non-topological soliton solutions for nonlinear fractional differential equations
Ozkan Guner
2015-01-01
In this article, the fractional derivatives are described in the modified Riemann–Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space–time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.
Lee, Ching Hua; Zhang, Xiao; Guan, Bochen
2015-12-01
Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. GaAs employed in the Gunn diode. In this work, we show that negative differential resistance also generically arise in Dirac ring systems, an example of which has been experimentally observed in the surface states of Topological Insulators. This novel realization of negative differential resistance is based on a completely different physical mechanism from that of the Gunn effect, relying on the characteristic non-monotonicity of the response curve that remains robust in the presence of nonzero temperature, chemical potential, mass gap and impurity scattering. As such, it opens up new possibilities for engineering applications, such as frequency upconversion devices which are highly sought for terahertz signal generation. Our results may be tested with thin films of Bi2Se3 Topological Insulators, and are expected to hold qualitatively even in the absence of a strictly linear Dirac dispersion, as will be the case in more generic samples of Bi2Se3 and other materials with topologically nontrivial Fermi sea regions.
D. A. Makarov
2011-06-01
Full Text Available In differential conductometric systems, for example in biosensor systems, often use co-planar thinly-pellicle structure double-sensors with pectinate topology. Simple and useful devices could be realized with help of them. But sensitivity and producibility of results those devices depends on parameters of sensors which we probe. On base of metrological research frequency descriptions, parameters conductometric differential sensors was analyzed effectiveness of using this sensors with different geometrical parameters and materials for better descriptions of biosensor system with them.
Yoon, G. H.; Kim, Y. Y.; Bendsøe, Martin P.;
2004-01-01
In topology optimization applications for the design of compliant mechanisms, the formation of hinges is typically encountered. Often such hinges are unphysical artifacts that appear due to the choice of discretization spaces for design and analysis. The objective of this work is to present a new...... in the multiscale design space. To imbed the shrinkage method implicitly in the optimization formulation and thus facilitate sensitivity analysis, the shrinkage method is made differentiable by means of differentiable versions of logical operators. The validity of the present method is confirmed by solving typical...... two-dimensional compliant mechanism design problems....
Differential models for B-type open-closed topological Landau-Ginzburg theories
Babalic, Mirela; Lazaroiu, Calin Iuliu; Tavakol, Mehdi
2016-01-01
We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is any non-compact Calabi-Yau manifold and $W$ is any holomorphic complex-valued function defined on $X$ whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector valued forms and a twisted Dolbeault category of holomorphic factorizations of $W$. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed topological field theory are satisfied on cohomology and conjecture that the remaining axioms are also satisfied.
Notchenko A.V.
2011-01-01
Full Text Available An automated system for morpho-topological determination of cell division phases and structur al differentiation of tissues during morphogenesis was implemented on the basis of topological properties of cell cultures, considered within the framework of set and manifold theories. A simple robotic hardware and software system based on Zeiss microscope with a modified stage and a Velleman manipulator KSR-1 allow to control the laser module position, carrying out the angular irradiation of samples either in transmission or in darkfield or luminescent modes and the subsequent math ematical data processing. This low-budget system can be easily assembled and programmed in any cytomorphological or histomorphologi-cal laboratory. The code for data processing in MATLAB is given at the end of the paper.
Resting-State Network Topology Differentiates Task Signals across the Adult Life Span.
Chan, Micaela Y; Alhazmi, Fahd H; Park, Denise C; Savalia, Neil K; Wig, Gagan S
2017-03-08
Brain network connectivity differs across individuals. For example, older adults exhibit less segregated resting-state subnetworks relative to younger adults (Chan et al., 2014). It has been hypothesized that individual differences in network connectivity impact the recruitment of brain areas during task execution. While recent studies have described the spatial overlap between resting-state functional correlation (RSFC) subnetworks and task-evoked activity, it is unclear whether individual variations in the connectivity pattern of a brain area (topology) relates to its activity during task execution. We report data from 238 cognitively normal participants (humans), sampled across the adult life span (20-89 years), to reveal that RSFC-based network organization systematically relates to the recruitment of brain areas across two functionally distinct tasks (visual and semantic). The functional activity of brain areas (network nodes) were characterized according to their patterns of RSFC: nodes with relatively greater connections to nodes in their own functional system ("non-connector" nodes) exhibited greater activity than nodes with relatively greater connections to nodes in other systems ("connector" nodes). This "activation selectivity" was specific to those brain systems that were central to each of the tasks. Increasing age was accompanied by less differentiated network topology and a corresponding reduction in activation selectivity (or differentiation) across relevant network nodes. The results provide evidence that connectional topology of brain areas quantified at rest relates to the functional activity of those areas during task. Based on these findings, we propose a novel network-based theory for previous reports of the "dedifferentiation" in brain activity observed in aging.SIGNIFICANCE STATEMENT Similar to other real-world networks, the organization of brain networks impacts their function. As brain network connectivity patterns differ across
Cohn, Steven F.
1986-01-01
Discusses effects of funding variations upon the rate of knowledge growth in algebraic and differential topology. Results based on a marginal productivity model indicated that funding variations had little or no effect upon the rate of knowledge growth. Lists 150 of the field's most highly rated papers. (ML)
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
Statistics and topology of the COBE differential microwave radiometer first-year sky maps
Smoot, G. F.; Tenorio, L.; Banday, A. J.; Kogut, A.; Wright, E. L.; Hinshaw, G.; Bennett, C. L.
1994-01-01
We use statistical and topological quantities to test the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) first-year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases. Recent papers discuss specific quantities as discriminators between Gaussian and non-Gaussian behavior, but the treatment of instrumental noise on the data is largely ignored. The presence of noise in the data biases many statistical quantities in a manner dependent on both the noise properties and the unknown cosmic microwave background temperature field. Appropriate weighting schemes can minimize this effect, but it cannot be completely eliminated. Analytic expressions are presented for these biases, and Monte Carlo simulations are used to assess the best strategy for determining cosmologically interesting information from noisy data. The genus is a robust discriminator that can be used to estimate the power-law quadrupole-normalized amplitude, Q(sub rms-PS), independently of the two-point correlation function. The genus of the DMR data is consistent with Gaussian initial fluctuations with Q(sub rms-PS) = (15.7 +/- 2.2) - (6.6 +/- 0.3)(n - 1) micro-K, where n is the power-law index. Fitting the rms temperature variations at various smoothing angles gives Q(sub rms-PS) = 13.2 +/- 2.5 micro-K and n = 1.7(sup (+0.3) sub (-0.6)). While consistent with Gaussian fluctuations, the first year data are only sufficient to rule out strongly non-Gaussian distributions of fluctuations.
Ilias Chlis
2014-01-01
Full Text Available This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity.
Chlis, Ilias; Pepe, Domenico; Zito, Domenico
2014-01-01
This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity.
Differential geometry and mathematical physics part II fibre bundles, topology and gauge fields
Rudolph, Gerd
2017-01-01
The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional r...
Botnan, Magnus Bakke
2011-01-01
We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.
Ó, João; Tomei, Carlos
2014-01-01
This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical ...
Shine, James M; Koyejo, Oluwasanmi; Poldrack, Russell A
2016-08-30
Little is currently known about the coordination of neural activity over longitudinal timescales and how these changes relate to behavior. To investigate this issue, we used resting-state fMRI data from a single individual to identify the presence of two distinct temporal states that fluctuated over the course of 18 mo. These temporal states were associated with distinct patterns of time-resolved blood oxygen level dependent (BOLD) connectivity within individual scanning sessions and also related to significant alterations in global efficiency of brain connectivity as well as differences in self-reported attention. These patterns were replicated in a separate longitudinal dataset, providing additional supportive evidence for the presence of fluctuations in functional network topology over time. Together, our results underscore the importance of longitudinal phenotyping in cognitive neuroscience.
Bishop, S. A.; Ayoola, E. O.
2016-03-01
In this paper, we establish results on continuous mappings of the space of the matrix elements of an arbitrary nonempty set of pseudo solutions of non Lipschitz quantum Stochastic differential inclusion (QSDI) into the space of the matrix elements of its solutions. we show that under the non Lipschitz condition, the space of the matrix elements of solutions is still an absolute retract, contractible, locally and integrally connected in an arbitrary dimension. The results here generalize existing results in the literature.
1988-01-01
The main subjects of the Siegen Topology Symposium are reflected in this collection of 16 research and expository papers. They center around differential topology and, more specifically, around linking phenomena in 3, 4 and higher dimensions, tangent fields, immersions and other vector bundle morphisms. Manifold categories, K-theory and group actions are also discussed.
Solving equations by topological methods
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.
Rosinger, Elemer E
2010-01-01
Arguments on the need, and usefulness, of going beyond the usual Hausdorff-Kuratowski-Bourbaki, or in short, HKB concept of topology are presented. The motivation comes, among others, from well known {\\it topological type processes}, or in short TTP-s, in the theories of Measure, Integration and Ordered Spaces. These TTP-s, as shown by the classical characterization given by the {\\it four Moore-Smith conditions}, can {\\it no longer} be incorporated within the usual HKB topologies. One of the most successful recent ways to go beyond HKB topologies is that developed in Beattie & Butzmann. It is shown in this work how that extended concept of topology is a {\\it particular} case of the earlier one suggested and used by the first author in the study of generalized solutions of large classes of nonlinear partial differential equations.
Balanced Topological Field Theories
Dijkgraaf, R.; Moore, G.
We describe a class of topological field theories called ``balanced topological field theories''. These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.
Balanced Topological Field Theories
Dijkgraaf, R
1997-01-01
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.
2013-01-01
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology, including persistent homology.
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.
Kuo, Yung-Chih; Chung, Chiu-Yen
2012-12-01
The neuronal differentiation of induced pluripotent stem (iPS) cells in scaffolding biomaterials is an emerging issue in nervous regeneration and repair. This study presents the production of neuron-lineage cells from iPS cells in inverted colloidal crystal (ICC) scaffolds comprising alginate, poly(γ-glutamic acid) (γ-PGA), and TATVHL peptide. The ability of iPS cells to differentiate toward neurons in the constructs was demonstrated by flow-cytometeric sorting and immunochemical staining. The results revealed that hexagonally arrayed microspheres molded alginate/γ-PGA hydrogel into ICC topology with adequate interconnected pores. An increase in the quantity of surface TATVHL peptide enhanced the atomic ratio of nitrogen and the adhesion efficiency of iPS cells in constructs. However, the effect of TATVHL peptide on the viability of iPS cells was insignificant. The adhesion and viability of iPS cells in ICC constructs was higher than those in freeform ones. TATVHL peptide raised the percentage of β III tubulin-identified cells differentiating from iPS cells, indicating that TATVHL peptide stimulated the neuronal development in alginate/γ-PGA ICC constructs. TATVHL peptide-grafted alginate/γ-PGA ICC scaffolds can be promising for establishing nerve tissue from iPS cells.
Topology and geometry for physicists
Nash, Charles
2011-01-01
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
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
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.
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...
Tomás, D; Brazão, J; Viegas, W; Silva, M
2013-01-01
The plant stress response has been extensively characterized at the biochemical and physiological levels. However, knowledge concerning repetitive sequence genome fraction modulation during extreme temperature conditions is scarce. We studied high-temperature effects on subtelomeric repetitive sequences (pSc200) and 45S rDNA in rye seedlings submitted to 40°C during 4 h. Chromatin organization patterns were evaluated through fluorescent in situ hybridization and transcription levels were assessed using quantitative real-time PCR. Additionally, the nucleolar dynamics were evaluated through fibrillarin immunodetection in interphase nuclei. The results obtained clearly demonstrated that the pSc200 sequence organization is not affected by high-temperature stress (HTS) and proved for the first time that this noncoding subtelomeric sequence is stably transcribed. Conversely, it was demonstrated that HTS treatment induces marked rDNA chromatin decondensation along with nucleolar enlargement and a significant increase in ribosomal gene transcription. The role of noncoding and coding repetitive rye sequences in the plant stress response that are suggested by their clearly distinct behaviors is discussed. While the heterochromatic conformation of pSc200 sequences seems to be involved in the stabilization of the interphase chromatin architecture under stress conditions, the dynamic modulation of nucleolar and rDNA topology and transcription suggest their role in plant stress response pathways.
Theiss, P; Karpas, A; Wise, K S
1996-05-01
Antibodies to P29, a major lipid-modified surface protein of Mycoplasma fermentans, reveal phase variation of surface epitopes occurring with high frequency in clonal lineages of the organism. This occurs despite continuous expression of the entire epitope-bearing P29 product (detected by Western immunoblotting) and contrasts with phase variation of other surface antigens mediated by differential expression of proteins. To understand the structure and antigenic topology of P29, the single-copy p29 gene from strain PG18 was cloned and sequenced. The gene encodes a prolipoprotein containing a signal sequence predicted to be modified with lipid and cleaved at the N-terminal Cys-1 residue of the mature P29 lipoprotein. The remaining 218-residue hydrophilic sequence of P29 is predicted to be located external to the single plasma membrane. Additional Cys residues at positions 91 and 128 in the mature protein were shown to form a 36-residue disulfide loop by selectively labeling sulfhydryl groups that were liberated only after chemical reduction of monomeric P29. Two nearly identical charged amino acid sequences occurred in P29, within the disulfide loop and upstream of this structure. Two distinct epitopes binding different monoclonal antibodies were associated with opposite ends of the P29 protein, by mapping products expressed in Escherichia coli from PCR-generated 3' deletion mutations of the p29 gene. Each monoclonal antibody detected high-frequency and noncoordinate changes in accessibility of the corresponding epitopes in colony immunoblots of clonal variants, yet sequencing of the p29 gene from these variants and analysis of disulfide bonds revealed no associated changes in the primary sequence or disulfide loop structure of P29. These results suggest that P29 surface epitope variation may involve masking of selected regions of P29, possibly by other surface components undergoing phase variation by differential expression. Differential masking may be an important
Dijkgraaf, Robbert; Verlinde, Herman; Verlinde, Erik
1991-03-01
We calculate correlation functions in minimal topological field theories. These twisted versions of N = 2 minimal models have recently been proposed to describe d < 1 matrix models, once coupled to topological gravity. In our calculation we make use of the Landau-Ginzburg formulation of the N = 2 models, and we find a direct relation between the Landau-Ginzburg superpotential and the KdV differential operator. Using this correspondence we show that the minimal topological models are in perfect agreement with the matrix models as solved in terms of the KdV hierarchy. This proves the equivalence at tree-level of topological and ordinary string thoery in d < 1.
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
Pąk Karol
2015-02-01
Full Text Available Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary, i.e. where each point has a neighborhood that is homeomorphic to a closed ball of En for some n.
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
Warner, S
1989-01-01
Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.
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...
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...
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.
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
Milewski, Emil G
2013-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, co
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
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...
Frank-Kamenetskii, Maxim D.
2013-01-01
A new variety on non-coding RNA has been discovered by several groups: circular RNA (circRNA). This discovery raises intriguing questions about the possibility of the existence of knotted RNA molecules and the existence of a new class of enzymes changing RNA topology, RNA topoisomerases.
金亚东; 施俊
2013-01-01
In this paper, we studied degree of functions in differential topology() to be equal to degree of functions in algebraic topology (). It showed that the proposition about one of two degrees is true if the proposition about another is true. Under this result, we get some applications.% 研究了球面到球面的连续映射 f 在微分拓扑的映射度等于在代数拓扑的映射度 degAf。这就表明凡是与两种度中其中一种度有关的命题成立，那么与另一种度有关的命题也成立。在此结论下，给出了一些它的应用。
王非
2013-01-01
在叶彦谦的齐二次系统、李学敏的齐三次系统、杨小京的齐四次系统、高洁的齐五次系统等的基础上，本文将平面齐次系统推广到齐六次系统，所得结论包含了齐二次系统、齐四次系统的拓扑结构。而且给出了一、二、三对例外方向下的58种全局结构图。%Predecessors are extended in this paper by raising degree of planar homogenous polynomial differential system. The obvious difference is that its global topological classification included the second and fourth orders, while there are new topological structures. In the paper,58 global structures have been given.
Topological Charge of Lattice Abelian Gauge Theory
Fujiwara, T; Wu, K
2001-01-01
Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle.
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 ...
Dijkgraaf, R.; Verlinde, H. (Princeton Univ., NJ (USA). Joseph Henry Labs.); Verlinde, E. (California Univ., Santa Barbara (USA). Inst. for Theoretical Physics)
1991-03-18
We calculate correlation functions in minimal topological field theories. These twisted versions of N = 2 minimal models have recently been proposed to describe d < 1 matrix models, once coupled to topological gravity. In our calculation we make use of the Landau-Ginzburg formulation of the N = 2 models, and we find a direct relation between the Landau-Ginzburg superpotential and the KdV differential operator. Using this correspondence we show that the minimal topological models are in perfect agreement with the matrix models as solved in terms of the KdV hierarchy. This proves the equivalence at tree-level of topological and ordinary string theory in d < 1. (orig.).
Proton spin: A topological invariant
Tiwari, S. C.
2016-11-01
Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein-Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to ℏ 2, i.e. proton spin decomposition has no meaning in this approach.
Discretising geometry and preserving topology I
de Beauce, V; Beauce, Vivien de; Sen, Siddhartha
2004-01-01
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated while preserving topological features present. Issues of convergence and a numerical implementation are discussed. The follow-up article covers the resulting discretisation of Riemannian geometry and some applications.
Kosinski, Antoni A
2007-01-01
The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho
Marsden, S C; Vélez, J C Ramírez; Alecian, E; Brown, C J; Carter, B D; Donati, J F; Dunstone, N; Hart, R; Semel, M; Waite, I A
2011-01-01
Spectroscopic and spectropolarimetric observations of the pre-main sequence early-G star HD 141943 were obtained at four observing epochs (in 2006, 2007, 2009 and 2010). The observations were undertaken at the 3.9-m Anglo-Australian Telescope using the UCLES echelle spectrograph and the SEMPOL spectropolarimeter visitor instrument. Brightness and surface magnetic field topologies were reconstructed for the star using the technique of least-squares deconvolution to increase the signal-to-noise of the data. The reconstructed brightness maps show that HD 141943 had a weak polar spot and a significant amount of low latitude features, with little change in the latitude distribution of the spots over the 4 years of observations. The surface magnetic field was reconstructed at three of the epochs from a high order (l <= 30) spherical harmonic expansion of the spectropolarimetric observations. The reconstructed magnetic topologies show that in 2007 and 2010 the surface magnetic field was reasonably balanced betwee...
Steckbeck, Jonathan D; Sun, Chengqun; Sturgeon, Timothy J; Montelaro, Ronald C
2010-01-01
The C-terminal tail (CTT) of the HIV-1 gp41 envelope (Env) protein is increasingly recognized as an important determinant of Env structure and functional properties, including fusogenicity and antigenicity. While the CTT has been commonly referred to as the "intracytoplasmic domain" based on the assumption of an exclusive localization inside the membrane lipid bilayer, early antigenicity studies and recent biochemical analyses have produced a credible case for surface exposure of specific CTT sequences, including the classical "Kennedy epitope" (KE) of gp41, leading to an alternative model of gp41 topology with multiple membrane-spanning domains. The current study was designed to test these conflicting models of CTT topology by characterizing the exposure of native CTT sequences and substituted VSV-G epitope tags in cell- and virion-associated Env to reference monoclonal antibodies (MAbs). Surface staining and FACS analysis of intact, Env-expressing cells demonstrated that the KE is accessible to binding by MAbs directed to both an inserted VSV-G epitope tag and the native KE sequence. Importantly, the VSV-G tag was only reactive when inserted into the KE; no reactivity was observed in cells expressing Env with the VSV-G tag inserted into the LLP2 domain. In contrast to cell-surface expressed Env, no binding of KE-directed MAbs was observed to Env on the surface of intact virions using either immune precipitation or surface plasmon resonance spectroscopy. These data indicate apparently distinct CTT topologies for virion- and cell-associated Env species and add to the case for a reconsideration of CTT topology that is more complex than currently envisioned.
Jonathan D Steckbeck
Full Text Available The C-terminal tail (CTT of the HIV-1 gp41 envelope (Env protein is increasingly recognized as an important determinant of Env structure and functional properties, including fusogenicity and antigenicity. While the CTT has been commonly referred to as the "intracytoplasmic domain" based on the assumption of an exclusive localization inside the membrane lipid bilayer, early antigenicity studies and recent biochemical analyses have produced a credible case for surface exposure of specific CTT sequences, including the classical "Kennedy epitope" (KE of gp41, leading to an alternative model of gp41 topology with multiple membrane-spanning domains. The current study was designed to test these conflicting models of CTT topology by characterizing the exposure of native CTT sequences and substituted VSV-G epitope tags in cell- and virion-associated Env to reference monoclonal antibodies (MAbs. Surface staining and FACS analysis of intact, Env-expressing cells demonstrated that the KE is accessible to binding by MAbs directed to both an inserted VSV-G epitope tag and the native KE sequence. Importantly, the VSV-G tag was only reactive when inserted into the KE; no reactivity was observed in cells expressing Env with the VSV-G tag inserted into the LLP2 domain. In contrast to cell-surface expressed Env, no binding of KE-directed MAbs was observed to Env on the surface of intact virions using either immune precipitation or surface plasmon resonance spectroscopy. These data indicate apparently distinct CTT topologies for virion- and cell-associated Env species and add to the case for a reconsideration of CTT topology that is more complex than currently envisioned.
Asorey, Manuel
2016-01-01
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
The topology of geology 2: Topological uncertainty
Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Wellmann, J. Florian; Pakyuz-Charrier, Evren
2016-10-01
Uncertainty is ubiquitous in geology, and efforts to characterise and communicate it are becoming increasingly important. Recent studies have quantified differences between perturbed geological models to gain insight into uncertainty. We build on this approach by quantifying differences in topology, a property that describes geological relationships in a model, introducing the concept of topological uncertainty. Data defining implicit geological models were perturbed to simulate data uncertainties, and the amount of topological variation in the resulting model suite measured to provide probabilistic assessments of specific topological hypotheses, sources of topological uncertainty and the classification of possible model realisations based on their topology. Overall, topology was found to be highly sensitive to small variations in model construction parameters in realistic models, with almost all of the several thousand realisations defining distinct topologies. In particular, uncertainty related to faults and unconformities was found to have profound topological implications. Finally, possible uses of topology as a geodiversity metric and validation filter are discussed, and methods of incorporating topological uncertainty into physical models are suggested.
The topology of geology 1: Topological analysis
Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Ogarko, Vitaliy; Wellmann, J. Florian; Pakyuz-Charrier, Evren
2016-10-01
Topology has been used to characterise and quantify the properties of complex systems in a diverse range of scientific domains. This study explores the concept and applications of topological analysis in geology. We have developed an automatic system for extracting first order 2D topological information from geological maps, and 3D topological information from models built with the Noddy kinematic modelling system, and equivalent analyses should be possible for other implicit modelling systems. A method is presented for describing the spatial and temporal topology of geological models using a set of adjacency relationships that can be expressed as a topology network, thematic adjacency matrix or hive diagram. We define three types of spatial topology (cellular, structural and lithological) that allow us to analyse different aspects of the geology, and then apply them to investigate the geology of the Hamersley Basin, Western Australia.
Optical image encryption topology.
Yong-Liang, Xiao; Xin, Zhou; Qiong-Hua, Wang; Sheng, Yuan; Yao-Yao, Chen
2009-10-15
Optical image encryption topology is proposed based on the principle of random-phase encoding. Various encryption topological units, involving peer-to-peer, ring, star, and tree topologies, can be realized by an optical 6f system. These topological units can be interconnected to constitute an optical image encryption network. The encryption and decryption can be performed in both digital and optical methods.
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....
Narici, Lawrence
2011-01-01
BackgroundTopology Valuation Theory Algebra Linear Functionals Hyperplanes Measure Theory Normed SpacesCommutative Topological GroupsElementary ConsiderationsSeparation and Compactness Bases at 0 for Group Topologies Subgroups and Products Quotients S-Topologies Metrizability CompletenessCompleteness Function Groups Total BoundednessCompactness and Total Boundedness Uniform Continuity Extension of Uniformly Continuous Maps CompletionTopological Vector SpacesAbsorbent and Balanced Sets Convexity-AlgebraicBasic PropertiesConvexity-Topological Generating Vector Topologies A Non-Locally Convex Spa
Topological superconductors: a review.
Sato, Masatoshi; Ando, Yoichi
2017-04-03
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.
Strongly Correlated Topological Insulators
2016-02-03
Research Triangle Park , NC 27709-2211 Condensed Matter, Topological Phases of Matter REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S...Strongly Correlated Topological Insulators In the past year, the grant was used for work in the field of topological phases, with emphasis on finding...surface of topological insulators. In the past 3 years, we have started a new direction, that of fractional topological insulators. These are materials
Relative Smooth Topological Spaces
B. Ghazanfari
2009-01-01
Full Text Available In 1992, Ramadan introduced the concept of a smooth topological space and relativeness between smooth topological space and fuzzy topological space in Chang's (1968 view points. In this paper we give a new definition of smooth topological space. This definition can be considered as a generalization of the smooth topological space which was given by Ramadan. Some general properties such as relative smooth continuity and relative smooth compactness are studied.
龚石林; 曾臻; 冯彦钊; 张兆云; 陈卫; 王晨
2015-01-01
This paper introduces some fault location principle at home and broad and puts forward a current differential protection principle with station domain based on network topology. We also simulate the principle with PSCAD/EMTDC to make sure that the principle will simplify the existing protection configuration and improve the reliability of the protection of substation.%介绍了国内外站域保护的故障定位原理，同时提出一种基于网络拓扑的电流差动站域保护原理，并通过仿真来验证此原理在简化现有保护配置的同时还能提高变电站保护的可靠性。
Probing (topological) Floquet states through DC transport
Fruchart, M.; Delplace, P.; Weston, J.; Waintal, X.; Carpentier, D.
2016-01-01
We consider the differential conductance of a periodically driven system connected to infinite electrodes. We focus on the situation where the dissipation occurs predominantly in these electrodes. Using analytical arguments and a detailed numerical study we relate the differential conductances of such a system in two and three terminal geometries to the spectrum of quasi-energies of the Floquet operator. Moreover these differential conductances are found to provide an accurate probe of the existence of gaps in this quasi-energy spectrum, being quantized when topological edge states occur within these gaps. Our analysis opens the perspective to describe the intermediate time dynamics of driven mesoscopic conductors as topological Floquet filters.
A complete topological invariant for braided magnetic fields
Yeates, A R
2013-01-01
A topological flux function is introduced to quantify the topology of magnetic braids: non-zero line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, whose integral over the cross-section yields the relative magnetic helicity. Recognising that the topological flux function is an action in the Hamiltonian formulation of the field line equations, a simple formula for its differential is obtained. We use this to prove that the topological flux function uniquely characterises the field line mapping and hence the magnetic topology. A simple example is presented.
Topological inverse semigroups
ZHU Yongwen
2004-01-01
That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup,the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Horn (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory,all these results generalize the corresponding ones related to topological semigroups or topological groups.
Topological insulators: Engineered heterostructures
Hesjedal, Thorsten; Chen, Yulin
2017-01-01
The combination of topological properties and magnetic order can lead to new quantum states and exotic physical phenomena. In particular, the coupling between topological insulators and antiferromagnets enables magnetic and electronic structural engineering.
Book Review: Computational Topology
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...
Classical topology and quantum states
A P Balachandran
2001-02-01
Any two inﬁnite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further reﬁnements of the axiom, its - and ∞ - structures) can be reconstructed using Gel’fand–Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed.
Colloquium: Topological band theory
Bansil, A.; Lin, Hsin; Das, Tanmoy
2016-04-01
The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. This review begins by discussing underpinnings of the topological band theory, which involve a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder and interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary, and quaternary compounds, transition metal and f -electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites, and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultrathin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. This Colloquium concludes by giving a perspective on research directions where further work will broadly benefit the topological materials field.
On generalized topological spaces
Piȩkosz, Artur
2009-01-01
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved. Generalized topological spaces help to reconstruct the important elements of the theory of locally definable and weakly definable spaces in the wide context of weakly topological structures.
Free Boolean Topological Groups
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.
Giuseppe Di Maio
2008-04-01
Full Text Available The subject of hyperspace topologies on closed or closed and compact subsets of a topological space X began in the early part of the last century with the discoveries of Hausdorff metric and Vietoris hit-and-miss topology. In course of time, several hyperspace topologies were discovered either for solving some problems in Applied or Pure Mathematics or as natural generalizations of the existing ones. Each hyperspace topology can be split into a lower and an upper part. In the upper part the original set inclusion of Vietoris was generalized to proximal set inclusion. Then the topologization of the Wijsman topology led to the upper Bombay topology which involves two proximities. In all these developments the lower topology, involving intersection of finitely many open sets, was generalized to locally finite families but intersection was left unchanged. Recently the authors studied symmetric proximal topology in which proximity was used for the first time in the lower part replacing intersection with its generalization: nearness. In this paper we use two proximities also in the lower part and we obtain the lower Bombay hypertopology. Consequently, a new hypertopology arises in a natural way: the symmetric Bombay topology which is the join of a lower and an upper Bombay topology.
A Brief Introduction to Fibrewise Topological Spaces Theory
Baolin GUO; Yingzhao HAN
2012-01-01
Fibrewise topological spaces theory,presented in the recent 20 years,is a new branch of mathematics developed on the basis of General Topology,Algebra topology and Fibrewise spaces theory.It is associated with differential geometry,Lie groups and dynamical systems theory. From the perspective of Category theory,it is in the higher category of general topological space,so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance.This paper introduces the process of the origin and development of Fibrewise topological spaces theory.Then,we study the main contents and important results in this branch.Finally,we review the research status of Fibrewise topological spaces theory and some important topics.
Triple Point Topological Metals
Ziming Zhu
2016-07-01
Full Text Available Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.
Real Topological Cyclic Homology
Høgenhaven, Amalie
The main topics of this thesis are real topological Hochschild homology and real topological cyclic homology. If a ring or a ring spectrum is equipped with an anti-involution, then it induces additional structure on the topological Hochschild homology spectrum. The group O(2) acts on the spectrum......, where O(2) is the semi-direct product of T, the multiplicative group of complex number of modulus 1, by the group G=Gal(C/R). We refer to this O(2)-spectrum as the real topological Hochschild homology. This generalization leads to a G-equivariant version of topological cyclic homology, which we call...... real topological cyclic homology. The first part of the thesis computes the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings at a prime p with anti-involution induced by taking inverses in the group. The second part of the thesis investigates the derived G...
A scheme for a topological insulator field effect transistor
Vali, Mehran; Dideban, Daryoosh; Moezi, Negin
2015-05-01
We propose a scheme for a topological insulator field effect transistor. The idea is based on the gate voltage control of the Dirac fermions in a ferromagnetic topological insulator channel with perpendicular magnetization connecting to two metallic topological insulator leads. Our theoretical analysis shows that the proposed device displays a switching effect with high on/off current ratio and a negative differential conductance with a good peak to valley ratio.
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
Fundamentals of algebraic topology
Weintraub, Steven H
2014-01-01
This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.
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.
Photonic Floquet Topological Insulators
Rechtsman, Mikael C; Plotnik, Yonatan; Lumer, Yaakov; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2012-01-01
The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating and technologically important aspect of this material: it provides robustness that is otherwise known only for superconductors. However, unlike superconductivity and the quantum Hall effect, which necessitate low temperatures or magnetic fields, the immunity to disorder of topological insulators occurs at room temperature and without any external magnetic field. For this reason, topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards bringing the concept into the domain of photonics: achieving topological protection of light at optical frequencies. ...
S. Nazmul
2014-03-01
Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.
F. G. Arenas
1999-01-01
pairwise-disjoint interiors. Tilings of ℝ2 have received considerable attention (see [2] for a wealth of interesting examples and results as well as an extensive bibliography. On the other hand, the study of tilings of general topological spaces is just beginning (see [1, 3, 4, 6]. We give some generalizations for topological spaces of some results known for certain classes of tilings of topological vector spaces.
Discretization of topological spaces
Amini, Massoud; Golestani, Nasser
2014-01-01
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compact...
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
Sober Topological Molecular Lattices
张德学; 李永明
2003-01-01
A topological molecular lattice (TML) is a pair (L, T), where L is a completely distributive lattice and r is a subframe of L. There is an obvious forgetful functor from the category TML of TML's to the category Loc of locales. In this note,it is showed that this forgetful functor has a right adjoint. Then, by this adjunction,a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.
Brower, Richard C; Negele, John W; Wiese, U J
2003-01-01
Since present Monte Carlo algorithms for lattice QCD may become trapped in a fixed topological charge sector, it is important to understand the effect of calculating at fixed topology. In this work, we show that although the restriction to a fixed topological sector becomes irrelevant in the infinite volume limit, it gives rise to characteristic finite size effects due to contributions from all $\\theta$-vacua. We calculate these effects and show how to extract physical results from numerical data obtained at fixed topology.
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
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.
Computational topology an introduction
Edelsbrunner, Herbert
2010-01-01
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through alg
Zomorodian, Afra J
2005-01-01
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a comp
Continuity in weak topology: higher order linear systems of ODE
ZHANG MeiRong
2008-01-01
We will introduce a type of Fredholm operators which are shown to have a certain continuity in weak topologies. From this, we will prove that the fundamental matrix solutions of k-th,k≥ 2, order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies. Consequently, Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies. Moreover, for the scalar Hill's equations, Sturm-Liouville eigenvalues,periodic and anti-periodic eigenvalues, and rotation numbers are all continuous in potentials with weak topologies. These results will lead to many interesting variational problems.
Topological invariants in nonlinear boundary value problems
Vinagre, Sandra [Departamento de Matematica, Universidade de Evora, Rua Roma-tilde o Ramalho 59, 7000-671 Evora (Portugal)]. E-mail: smv@uevora.pt; Severino, Ricardo [Departamento de Matematica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)]. E-mail: ricardo@math.uminho.pt; Ramos, J. Sousa [Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: sramos@math.ist.utl.pt
2005-07-01
We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions.
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.
A topological derivative method for topology optimization
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....
Tanda, Satoshi; Matsuyama, Toyoki; Oda, Migaku; Asano, Yasuhiro; Yakubo, Kousuke
2006-08-01
I. Topology as universal concept. Optical vorticulture / M. V. Berry. On universality of mathematical structure in nature: topology / T. Matsuyama. Topology in physics / R. Jackiw. Isoholonomic problem and holonomic quantum computation / S. Tanimura -- II. Topological crystals. Topological crystals of NbSe[symbol] / S. Tanda ... [et al.]. Superconducting states on a Möbius strip / M. Hayashi ... [et al.]. Structure analyses of topological crystals using synchrotron radiation / Y. Nogami ... [et al.]. Transport measurement for topological charge density waves / T. Matsuura ... [et al.]. Theoretical study on Little-Parks oscillation in nanoscale superconducting ring / T. Suzuki, M. Hayashi and H. Ebisawa. Frustrated CDW states in topological crystals / K. Kuboki ... [et al.]. Law of growth in topological crystal / M. Tsubota ... [et al.]. Synthesis and electric properties of NbS[symbol]: possibility of room temperature charge density wave devices / H. Nobukane ... [et al.]. How does a single crystal become a Möbius strip? / T. Matsuura ... [et al.]. Development of X-ray analysis method for topological crystals / K. Yamamoto ... [et al.] -- III. Topological materials. Femtosecond-timescale structure dynamics in complex materials: the case of (NbSe[symbol])[symbol]I / D. Dvorsek and D. Mihailovic. Ultrafast dynamics of charge-density-wave in topological crystals / K. Shimatake ... [et al.]. Topology in morphologies of a folded single-chain polymer / Y. Takenaka, D. Baigl and K. Yoshikawa. One to two-dimensional conversion in topological crystals / T. Toshima, K. Inagaki and S. Tanda. Topological change of Fermi surface in Bismuth under high pressure / M. Kasami ... [et al.]. Topological change of 4, 4'-bis[9-dicarbazolyl]-2, 2'-biphenyl (CBP) by international rearrangement / K. S. Son ... [et al.]. Spin dynamics in Heisenberg triangular system VI5 cluster studied by [symbol]H-NMR / Y. Furukawa ... [et al.]. STM/STS on NbSe[symbol] nanotubes / K. Ichimura ...[et al
Topological gravitation on graph manifolds
Mitskievich, N V; Magdaleno, A M Hernández
2008-01-01
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the topological structure of our universe.
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.
Topological Design of Protocols
Jaffe, Arthur; Wozniakowski, Alex
2016-01-01
We give a topological simulation for tensor networks that we call the two-string model. In this approach we give a new way to design protocols, and we discover a new multipartite quantum communication protocol. We introduce the notion of topologically compressed transformations. Our new protocol can implement multiple, non-local compressed transformations among multi-parties using one multipartite resource state.
Bietenholz, W; Pepe, M; Wiese, U -J
2010-01-01
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge $Q$. Irrespective of this, in the 2-d O(3) model the topological susceptibility $\\chi_t = \\l/V$ is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some cla...
Bradlyn, Barry; Elcoro, L.; Cano, Jennifer; Vergniory, M. G.; Wang, Zhijun; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei
2017-07-01
Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more.
Topology optimization approaches
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...
Syed M. Fakhruddin
1985-01-01
Full Text Available In this note, we show that if a topology F¯ over a ring A satisfies a certain finiteness condition, then the Gabriel topology G¯ generated by F¯ can be explicitly constructed and it also satisfies the same finiteness condition.
Conceptions of Topological Transitivity
Akin, Ethan
2011-01-01
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various equivalences are proved in different places, but the full story is difficult to find. This note provides a complete description of the relationships among the different properties.
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, exist
Interactive Topology Optimization
Nobel-Jørgensen, Morten
software where the users are assumed to be well-educated both in the finite element method and topology optimization. This dissertation describes how various topology optimization methods have been used for creating cross-platform applications with high performance. The user interface design is based......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...... in an interactive and intuitive way. By creating such applications with an intuitive and simple user interface we allow non-engineers like designers and architects to easily experiment with boundary conditions, design domains and other optimization settings. This is in contrast to commercial topology optimization...
Reconstruction of topology and geometry from digitisations
2016-01-01
. The first problem, the reconstruction of topology in dimension three, is approached using combinatorics of voxel reconstructions in combination with differential topology results. An improved digital re-construction based on binary images of objects with sufficiently smooth boundary is proposed. It is shown...... that this reconstruction is ambient isotopic to the underlying object provided the resolution of the digitisation be sufficiently high and under certain assumptions on the classical voxel reconstruction. The exact lower bound on the resolution, related to the curvature of the boundary of the object, is given...
Barreira N
2005-01-01
Full Text Available The topological active volumes (TAVs model is a general model for 3D image segmentation. It is based on deformable models and integrates features of region-based and boundary-based segmentation techniques. Besides segmentation, it can also be used for surface reconstruction and topological analysis of the inside of detected objects. The TAV structure is flexible and allows topological changes in order to improve the adjustment to object's local characteristics, find several objects in the scene, and identify and delimit holes in detected structures. This paper describes the main features of the TAV model and shows its ability to segment volumes in an automated manner.
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
Barr, Stephen
1989-01-01
""A mathematician named KleinThought the Moebius band was divine.Said he: 'If you glueThe edges of two,You'll get a weird bottle like mine.' "" - Stephen BarrIn this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics:New Surfaces (Orientability, Dimension, The Klein Bottle, etc.)The Shortest Moebius StripThe
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.
Plasmonics in Topological Insulators
Yi-Ping Lai
2014-04-01
Full Text Available With strong spin-orbit coupling, topological insulators have an insulating bulk state, characterized by a band gap, and a conducting surface state, characterized by a Dirac cone. Plasmons in topological insulators show high frequency-tunability in the mid-infrared and terahertz spectral regions with transverse spin oscillations, also called “spin-plasmons”. This paper presents a discussion and review of the developments in this field from the fundamental theory of plasmons in bulk, thin-film, and surface-magnetized topological insulators to the techniques of plasmon excitation and future applications.
Topology-driven magnetic quantum phase transition in topological insulators.
Zhang, Jinsong; Chang, Cui-Zu; Tang, Peizhe; Zhang, Zuocheng; Feng, Xiao; Li, Kang; Wang, Li-Li; Chen, Xi; Liu, Chaoxing; Duan, Wenhui; He, Ke; Xue, Qi-Kun; Ma, Xucun; Wang, Yayu
2013-03-29
The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.
Topological fixed point theory of multivalued mappings
Górniewicz, Lech
1999-01-01
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...
A topological introduction to nonlinear analysis
Brown, Robert F
2014-01-01
This third edition of A Topological Introduction to Nonlinear Analysis is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. For this third edition, several new chapters present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply...
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Pseudo-topological Riesz spaces
Muller, M. A.(Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil)
1997-01-01
Pseudo-topological spaces (i.e. limit spaces) were defined by Fischer in 1959. Properties of topological Riesz spaces are well-known. In this paper it is shown that if the topology on a Riesz space is replaced by a pseudo-topology more general results are obtained.
Concepts of polymer statistical topology
Nechaev, S K
2016-01-01
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called statistical (or probabilistic) topology.
Real topological string amplitudes
Narain, K. S.; Piazzalunga, N.; Tanzini, A.
2017-03-01
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_{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' = -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_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.
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.
Topological nodal line semimetals
Fang, Chen; Weng, Hongming; Dai, Xi; Fang, Zhong
2016-11-01
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials; (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals, and other topological phases; and (v) we discuss the possible physical effects accessible to experimental probes in these materials. Project partially supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0302400 and 2016YFA0300604), partially by the National Natural Science Foundation of China (Grant Nos. 11274359 and 11422428), the National Basic Research Program of China (Grant No. 2013CB921700), and the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB07020100).
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.
Wilce, Alexander
2004-01-01
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among ...
Topology optimized microbioreactors
Schäpper, Daniel; Lencastre Fernandes, Rita; Eliasson Lantz, Anna
2011-01-01
. Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement...... in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced....
Topological equivalence for discontinuous random dynamical systems and applications
Qiao, Huijie; Duan, Jinqiao
2012-01-01
After defining non-Gaussian L\\'evy processes for two-sided time, stochastic differential equations with such L\\'evy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an It\\^o stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman-Grobman theorem is proved for the linearization of the It\\^o ...
Tunable Topological Phononic Crystals
Chen, Ze-Guo
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.
Superconducting doped topological materials
Sasaki, Satoshi, E-mail: sasaki@sanken.osaka-u.ac.jp [Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047 (Japan); Mizushima, Takeshi, E-mail: mizushima@mp.es.osaka-u.ac.jp [Department of Materials Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Department of Physics, Okayama University, Okayama 700-8530 (Japan)
2015-07-15
Highlights: • Studies on both normal- and SC-state properties of doped topological materials. • Odd-parity pairing systems with the time-reversal-invariance. • Robust superconductivity in the presence of nonmagnetic impurity scattering. • We propose experiments to identify the existence of Majorana fermions in these SCs. - Abstract: Recently, the search for Majorana fermions (MFs) has become one of the most important and exciting issues in condensed matter physics since such an exotic quasiparticle is expected to potentially give rise to unprecedented quantum phenomena whose functional properties will be used to develop future quantum technology. Theoretically, the MFs may reside in various types of topological superconductor materials that is characterized by the topologically protected gapless surface state which are essentially an Andreev bound state. Superconducting doped topological insulators and topological crystalline insulators are promising candidates to harbor the MFs. In this review, we discuss recent progress and understanding on the research of MFs based on time-reversal-invariant superconducting topological materials to deepen our understanding and have a better outlook on both the search for and realization of MFs in these systems. We also discuss some advantages of these bulk systems to realize MFs including remarkable superconducting robustness against nonmagnetic impurities.
Essentials of topology with applications
Krantz, Steven G
2009-01-01
Fundamentals What Is Topology? First Definitions Mappings The Separation Axioms Compactness Homeomorphisms Connectedness Path-Connectedness Continua Totally Disconnected Spaces The Cantor Set Metric Spaces Metrizability Baire's Theorem Lebesgue's Lemma and Lebesgue NumbersAdvanced Properties of Topological Spaces Basis and Sub-Basis Product Spaces Relative Topology First Countable, Second Countable, and So ForthCompactifications Quotient Topologies Uniformities Morse Theory Proper Mappings Paracompactness An Application to Digital ImagingBasic Algebraic Topology Homotopy Theory Homology Theory
He, Cheng; Lin, Liang; Sun, Xiao-Chen; Liu, Xiao-Ping; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
As exotic phenomena in optics, topological states in photonic crystals have drawn much attention due to their fundamental significance and great potential applications. Because of the broken time-reversal symmetry under the influence of an external magnetic field, the photonic crystals composed of magneto-optical materials will lead to the degeneracy lifting and show particular topological characters of energy bands. The upper and lower bulk bands have nonzero integer topological numbers. The gapless edge states can be realized to connect two bulk states. This topological photonic states originated from the topological property can be analogous to the integer quantum Hall effect in an electronic system. The gapless edge state only possesses a single sign of gradient in the whole Brillouin zone, and thus the group velocity is only in one direction leading to the one-way energy flow, which is robust to disorder and impurity due to the nontrivial topological nature of the corresponding electromagnetic states. Furthermore, this one-way edge state would cross the Brillouin center with nonzero group velocity, where the negative-zero-positive phase velocity can be used to realize some interesting phenomena such as tunneling and backward phase propagation. On the other hand, under the protection of time-reversal symmetry, a pair of gapless edge states can also be constructed by using magnetic-electric coupling meta-materials, exhibiting Fermion-like spin helix topological edge states, which can be regarded as an optical counterpart of topological insulator originating from the spin-orbit coupling. The aim of this article is to have a comprehensive review of recent research literatures published in this emerging field of photonic topological phenomena. Photonic topological states and their related phenomena are presented and analyzed, including the chiral edge states, polarization dependent transportation, unidirectional waveguide and nonreciprocal optical transmission, all
A review of module inverter topologies suitable for photovoltaic system
Variath, Reshmi C; Andersen, Michael A. E.; Nielsen, Ole Neis
2010-01-01
This paper evaluates eight module inverter topologies and provides an overview of the merits and demerits of each on the basis of circuit level Pspice simulation. The complete system is modeled in Pspice and the model is made as realistic as possible by including the parasitic elements. Only...... the output stage is varied for different topologies keeping the system model unaltered with the same control system and degree of demodulation so as to differentiate the variation of efficiency of these topologies. The purpose of the analysis is to determine which of this topology would be a best fit...... for the system and what are the compromises to be made (if any) to select one of these topologies as the output stage in the PV system....
Topology optimization problems with design-dependent sets of constraints
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...... using both discrete and continuous design variables. Using discrete design variables is the natural modeling frame. However, we cannot solve real-size problems with the technological limits of today. Using continuous design variables makes it possible to also study topology optimization problems...
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.
Solar storms, cycles and topology
Lundstedt H.
2010-12-01
Full Text Available Solar storms are produced due to plasma processes inside and between coronal loops. These loops are topologically examined using knot and braid theory. Solar cycles are topologically explored with a complex generalization of the three ordinary differential equations studied by Lorenz. By studying the Poincaré map we give numerical evidence that the flow has an attractor with fractal structure. The period is defined as the time needed for a point on a hyperplane to return to the hyperplane again. The periods are distributed in an interval. For large values of the Dynamo number there is a long tail toward long periods and other interesting comet-like features. We also found a relationship between the intensity of a cycle and the length for the previous cycle. Maunder like minima are also appearing. These general relations found for periods can further be physically interpreted with improved helioseismic estimates of the parameters used by the dynamical systems. Solar Dynamic Observatory is expected to offer such improved measurements.
Reprint of : Probing (topological) Floquet states through DC transport
Fruchart, M.; Delplace, P.; Weston, J.; Waintal, X.; Carpentier, D.
2016-08-01
We consider the differential conductance of a periodically driven system connected to infinite electrodes. We focus on the situation where the dissipation occurs predominantly in these electrodes. Using analytical arguments and a detailed numerical study we relate the differential conductances of such a system in two and three terminal geometries to the spectrum of quasi-energies of the Floquet operator. Moreover these differential conductances are found to provide an accurate probe of the existence of gaps in this quasi-energy spectrum, being quantized when topological edge states occur within these gaps. Our analysis opens the perspective to describe the intermediate time dynamics of driven mesoscopic conductors as topological Floquet filters.
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
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.
Topological vector spaces and their applications
Bogachev, V I
2017-01-01
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
p-topological Cauchy completions
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.
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...
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
ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACES AND APPLICATION
SHIHMAU-HSIAN; TAMPING-KWAN; TANKOK-KEONG
1999-01-01
Shlnultaneous contractificttions, simultaneous proper contractification8 and scxnlgroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are given for single bounded llner operator being a topo-logical proper contraction. By using complexification of a real Banach space and by applying afixed point theorem of Edelstein, it is shown that every compact topological strict contractionon a Banach space is a topological proper contraction. Finally, results on simultaneous propercontractification are applied to study the stability of a common fixed point of maps which areFr6chet differentiable at that point.
Noncommutative topology and the world's simplest index theorem.
van Erp, Erik
2010-05-11
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry.
Topology theory on rough sets.
Wu, QingE; Wang, Tuo; Huang, YongXuan; Li, JiSheng
2008-02-01
For further studying the theories and applications of rough sets (RS), this paper proposes a new theory on RS, which mainly includes topological space, topological properties, homeomorphism, and its properties on RS by some new definitions and theorems given. The relationship between partition and countable open covering is discussed, and some applications based on the topological rough space and its topological properties are introduced. Moreover, some perspectives for future research are given. Throughout this paper, the advancements of the new theory on RS and topological algebra not only represent an important theoretical value but also exhibit significant applications of RS and topology.
Oda, Ichiro
2016-01-01
We propose a topological model of induced gravity (pregeometry) where both Newton's coupling constant and the cosmological constant appear as integration constants in solving field equations. The matter sector of a scalar field is also considered, and by solving field equations it is shown that various types of cosmological solutions in the FRW universe can be obtained. A detailed analysis is given of the meaning of the BRST transformations, which make the induced gravity be a topological field theory, by means of the canonical quantization analysis, and the physical reason why such BRST transformations are needed in the present formalism is clarified. Finally, we propose a dynamical mechanism for fixing the Lagrange multiplier fields by following the Higgs mechanism. The present study clearly indicates that the induced gravity can be constructed at the classical level without recourse to quantum fluctuations of matter and suggests an interesting relationship between the induced gravity and the topological qu...
Zou, L P; 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 as vacuum excitations. 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.
Topology optimized microbioreactors.
Schäpper, Daniel; Lencastre Fernandes, Rita; Lantz, Anna Eliasson; Okkels, Fridolin; Bruus, Henrik; Gernaey, Krist V
2011-04-01
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. Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced.
Algebraic topology and concurrency
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......, giving information about important properties of the program, such as deadlocks, unreachables, serializability, essential schedules, etc. In fact, it is not quite ordinary homotopy that has to be used, but rather a “directed homotopy” that does not reverse the flow of time. We show some of the essential...... 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...
Anna Maria D'Aristotile
2006-08-01
Full Text Available We consider sets of inequalities in Real Analysis and construct a topology such that inequalities usually called "limit cases" of certain sequences of inequalities are in fact limits - in the precise topological sense - of such sequences. To show the generality of the results, several examples are given for the notions introduced, and three main examples are considered: Sequences of inequalities relating real numbers, sequences of classical Hardy's inequalities, and sequences of embedding inequalities for fractional Sobolev spaces. All examples are considered along with their limit cases, and it is shown how they can be considered as sequences of one "big" space of inequalities. As a byproduct, we show how an abstract process to derive inequalities among homogeneous operators can be a tool for proving inequalities. Finally, we give some tools to compute limits of sequences of inequalities in the topology introduced, and we exhibit new applications.
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.
Manufacturing tolerant topology optimization
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...
Hormonal induction of transfected genes depends on DNA topology.
Piña, B; Haché, R J; Arnemann, J; Chalepakis, G; Slater, E P; Beato, M
1990-02-01
Plasmids containing the hormone regulatory element of mouse mammary tumor virus linked to the thymidine kinase promoter of herpes simplex virus and the reporter gene chloramphenicol acetyltransferase of Escherichia coli respond to glucocorticoids and progestins when transfected into appropriate cells. In the human mammary tumor cell line T47D, the response to progestins, but not to glucocorticoids, is highly dependent on the topology of the transfected DNA. Although negatively supercoiled plasmids respond optimally to the synthetic progestin R5020, their linearized counterparts exhibit markedly reduced progestin inducibility. This is not due to changes in the efficiency of DNA transfection, since the amount of DNA incorporated into the cell nucleus is not significantly dependent on the initial topology of the plasmids. In contrast, cotransfection experiments with glucocorticoid receptor cDNA in the same cell line show no significant influence of DNA topology on induction by dexamethasone. A similar result was obtained with fibroblasts that contain endogenous glucocorticoid receptors. When the distance between receptor-binding sites or between the binding sites and the promoter was increased, the dependence of progestin induction on DNA topology was more pronounced. In contrast to the original plasmid, these constructs also revealed a similar topological dependence for induction by glucocorticoids. The differential influence of DNA topology is not due to differences in the affinity of the two hormone receptors for DNA of various topologies, but probably reflects an influence of DNA topology on the interaction between different DNA-bound receptor molecules and between receptors and other transcription factors.
Locally minimal topological groups
Außenhofer, Lydia; Chasco, María Jesús; Dikranjan, Dikran; Domínguez, Xabier
2009-01-01
A Hausdorff topological group $(G,\\tau)$ is called locally minimal if there exists a neighborhood $U$ of 0 in $\\tau$ such that $U$ fails to be a neighborhood of zero in any Hausdorff group topology on $G$ which is strictly coarser than $\\tau.$ Examples of locally minimal groups are all subgroups of Banach-Lie groups, all locally compact groups and all minimal groups. Motivated by the fact that locally compact NSS groups are Lie groups, we study the connection between local minimality and the ...
Entanglement and topological interfaces
Brehm, Enrico M; Jaud, Daniel; Schmidt-Colinet, Cornelius
2015-01-01
In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples.
Fowler, Austin G; McInnes, Angus L; Rabbani, Alimohammad
2012-01-01
Tailoring a fault-tolerant quantum error correction scheme to a specific physical architecture can be a laborious task. We describe a tool Autotune capable of analyzing and optimizing the classical processing for an arbitrary 2-D qubit architecture making use of arbitrary circuits implementing either the surface code or progressively generated slices of a 3-D topological cluster state with arbitrary stochastic error models for each quantum gate. Autotune is designed to facilitate precise study of the performance of real hardware running topological quantum error correction.
Filters in topology optimization
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...
Filters in topology optimization
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...
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 ...
Syropoulos, Apostolos
2011-01-01
Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri nets to deal with fuzzy topological systems. One basic idea is to use as the dualizing object in the Dialectica categories construction, the unit real interval [0,1], which has all the properties of a {\\em lineale}. The second basic idea is to generalize Vickers's notion of a topological system.
Topological De-Noising: Strengthening the Topological Signal
2009-01-01
Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow for the recovery of topological information. We present an easy to implement, computationally efficient pre-processing algorithm to prepare noisy point cloud data sets for topological data analysis. The topological de-noising algorithm allows for the recover...
Topological hierarchy matters — topological matters with superlattices of defects
He, Jing; Kou, Su-Peng
2016-11-01
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. Project supported by the National Basic Research Program of China (Grant Nos. 2011CB921803 and 2012CB921704), the National Natural Science Foundation of China (Grant Nos. 11174035, 11474025, 11404090, and 11674026), the Natural Science Foundation of Hebei Province, China (Grant No. A2015205189), the Hebei Education Department Natural Science Foundation, China (Grant No. QN2014022), and the Specialized Research Fund for the Doctoral Program of Higher Education, China.
Order Topology and Bi-Scott Topology on a Poset
Bin ZHAO; Kai Yun WANG
2011-01-01
In this paper,some properties of order topology and bi-Scott topology on a poset are obtained.Order-convergence in posets is further studied.Especially,a sufficient and necessary condition for order-convergence to be topological is given for some kind of posets.
Topology Optimization with Stress Constraints
Verbart, A.
2015-01-01
This thesis contains contributions to the development of topology optimization techniques capable of handling stress constraints. The research that led to these contributions was motivated by the need for topology optimization techniques more suitable for industrial applications. Currently, topolo
Topology optimization of viscoelastic rectifiers
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...
Degree 3 Networks Topological Routing
Gutierrez Lopez, Jose Manuel; Riaz, M. Tahir; Pedersen, Jens Myrup;
2009-01-01
Topological routing is a table free alternative to traditional routing methods. It is specially well suited for organized network interconnection schemes. Topological routing algorithms correspond to the type O(1), constant complexity, being very attractive for large scale networks. It has been...... proposed for many topologies and this work compares the algorithms for three degree three topologies using a more analytical approach than previous studies....
Locally minimal topological groups
enhofer, Lydia Au\\ss; Dikranjan, Dikran; Domínguez, Xabier
2009-01-01
A Hausdorff topological group $(G,\\tau)$ is called locally minimal if there exists a neighborhood $U$ of 0 in $\\tau$ such that $U$ fails to be a neighborhood of zero in any Hausdorff group topology on $G$ which is strictly coarser than $\\tau.$ Examples of locally minimal groups are all subgroups of Banach-Lie groups, all locally compact groups and all minimal groups. Motivated by the fact that locally compact NSS groups are Lie groups, we study the connection between local minimality and the NSS property, establishing that under certain conditions, locally minimal NSS groups are metrizable. A symmetric subset of an abelian group containing zero is said to be a GTG set if it generates a group topology in an analogous way as convex and symmetric subsets are unit balls for pseudonorms on a vector space. We consider topological groups which have a neighborhood basis at zero consisting of GTG sets. Examples of these locally GTG groups are: locally pseudo--convex spaces, groups uniformly free from small subgroups (...
Topological Quantum Entanglement
2014-02-19
Landau level more generally. “Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases”, Jennifer Cano, Meng Cheng, Michael Mulligan ...2012). arXiv:1103.2770 34. Effective Field Theory of Fractional Quantized Hall Nematics (M. Mulligan , C. Nayak, and S. Kachru), Phys. Rev. B 84
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
Topology evolutions of silhouettes
无
2007-01-01
We give the topology changing of the silhouette in 3D space while others study the projections in an image. Silhouettes play a crucial role in visualization, graphics and vision. This work focuses on the global behaviors of silhouettes, especially their topological evolutions, such as splitting, merging, appearing and disappearing. The dynamics of silhouettes are governed by the topology, the curvature of the surface, and the view point. In this paper, we work on a more theoretical level to give enumerative properties of the silhouette including: the integration of signed geodesic curvature along a silhouette is equal to the view cone angle; in elliptic regions, no silhouette can be contained in another one; in hyperbolic regions, ifa silhouette is homotopic to a point, then it has at least 4 cusps; finally, critical events can only happen when the view point is on the aspect surfaces (ruled surface of the asymptotic lines of parabolic points with surface itself). We also introduce a method to visualize the evolution of silhouettes, especially all the critical events where the topologies of the silhouettes change. The results have broad applications in computer vision for recognition, graphics for rendering and visualization.
Manufacturing tolerant topology optimization
Ole Sigmund
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 that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization.
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...
LHCb Topological Trigger Reoptimization
Likhomanenko, Tatiana; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; 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. ...
2016-01-01
Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some of these methods.
Rendering the Topological Spines
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.
杨悦; 袁超; 李国庆
2011-01-01
Reactive power optimization is the basis of stability and economy of power system.The neighborhood topology cultural differential evolution algorithm is proposed.The premature convergence and easy to fall into local optimal solution of the Cultural differential evolution algorithm are improved.The algorithm is the first time applied to reactive power optimization,and the model of reactive power optimization based on the algorithm is established.The neighborhood topology cultural differential evolution algorithm is a directly and randomly searching method.The study shows that the algorithm can quickly obtain the global optimal solution,have a good property of global convergence,and meet the requirements for reactive power optimization goals.The algorithm of reactive power optimization is on a check with IEEE 30 buses system,and is analyzed with common cultural differential evolution algorithm.The results of simulation shows that the neighborhood topology cultural differential evolution algorithm has the better ability for optimization.%提出了求解无功优化问题的一种新算法——基于邻域拓扑文化差分进化算法。将邻域拓扑结构纳入了文化差分进化算法,改进了文化差分进化算法过早收敛,易于陷入局部最优解的问题。并首次将该算法应用到无功优化问题中,使其能迅速获得全局优化解,具有很好的全局收敛性能和更好的优化能力。最后,将该算法在IEEE 30节点系统上进行了无功优化问题的求解,并与应用普通文化差分进化算法的结果进行了比较分析。仿真结果验证了基于邻域拓扑文化差分进化算法在无功优化应用中的有效性。
Fuzzy Soft Compact Topological Spaces
Seema Mishra
2016-01-01
Full Text Available In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.
Topological susceptibility from overlap fermion
应和平; 张剑波
2003-01-01
We numerically calculate the topological charge of the gauge configurations on a finite lattice by the fermionic method with overlap fermions. By using the lattice index theorem, we identify the index of the massless overlap fermion operator to the topological charge of the background gauge configuration. The resulting topological susceptibility X is in good agreement with the anticipation made by Witten and Veneziano.
Lecture Notes on Differential Forms
2016-01-01
This is a series of lecture notes, with embedded problems, aimed at students studying differential topology. Many revered texts, such as Spivak's "Calculus on Manifolds" and Guillemin and Pollack's "Differential Topology" introduce forms by first working through properties of alternating tensors. Unfortunately, many students get bogged down with the whole notion of tensors and never get to the punch lines: Stokes' Theorem, de Rham cohomology, Poincare duality, and the realization of various t...
Computing the topological susceptibility from fixed topology QCD simulations
Dromard, Arthur; Cichy, Krzysztof; Wagner, Marc
2016-01-01
The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update steps --- in particular the HMC algorithm --- tend to get stuck in a single topological sector. In such cases, the computation of the topological susceptibility is not straightforward. Here, we explore two methods to extract the topological susceptibility from lattice QCD simulations restricted to a single topological sector. The first method is based on the correlation function of the topological charge density, while the second method relies on measuring the topological charge within spacetime subvolumes. Numerical results for two-flavor QCD obtained by using both methods are presented.
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
The Topological Effects of Smoothing.
Shafii, S; Dillard, S E; Hlawitschka, M; Hamann, B
2012-01-01
Scientific data sets generated by numerical simulations or experimental measurements often contain a substantial amount of noise. Smoothing the data removes noise but can have potentially drastic effects on the qualitative nature of the data, thereby influencing its characterization and visualization via topological analysis, for example. We propose a method to track topological changes throughout the smoothing process. As a preprocessing step, we oversmooth the data and collect a list of topological events, specifically the creation and destruction of extremal points. During rendering, it is possible to select the number of topological events by interactively manipulating a merging parameter. The result that a specific amount of smoothing has on the topology of the data is illustrated using a topology-derived transfer function that relates region connectivity of the smoothed data to the original regions of the unsmoothed data. This approach enables visual as well as quantitative analysis of the topological effects of smoothing.
Laws of granular solids: geometry and topology.
DeGiuli, Eric; McElwaine, Jim
2011-10-01
In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton's laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton's laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables that describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy's expression for a divergence-free, symmetric stress tensor in two and three dimensions.
TWO-DIMENSIONAL TOPOLOGY OF COSMOLOGICAL REIONIZATION
Wang, Yougang; Xu, Yidong; Chen, Xuelei [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 China (China); Park, Changbom [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Kim, Juhan, E-mail: wangyg@bao.ac.cn, E-mail: cbp@kias.re.kr [Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)
2015-11-20
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two-dimensional genus curve for the early, middle, and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometre Array.
Two dimensional topology of cosmological reionization
Wang, Yougang; Xu, Yidong; Chen, Xuelei; Kim, Juhan
2015-01-01
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two dimensional genus curve for the early, middle and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometer Array.
Computational algebraic topology-based video restoration
Rochel, Alban; Ziou, Djemel; Auclair-Fortier, Marie-Flavie
2005-03-01
This paper presents a scheme for video denoising by diffusion of gray levels, based on the Computational Algebraic Topology (CAT) image model. The diffusion approach is similar to the one used to denoise static images. Rather than using the heat transfer partial differential equation, discretizing it and solving it by a purely mathematical process, the CAT approach considers the global expression of the heat transfer and decomposes it into elementary physical laws. Some of these laws describe conservative relations, leading to error-free expressions, whereas others depend on metric quantities and require approximation. This scheme allows for a physical interpretation for each step of the resolution process. We propose a nonlinear and an anisotropic diffusion algorithms based on the extension to video of an existing 2D algorithm thanks to the flexibility of the topological support. Finally it is validated with experimental results.
Ekman, Ulrik
2015-01-01
This article discusses the issue of approaching the design of the ubiquitous city as a matter of topology. The general context here is the design of contemporary global urbanity in the form of u-cities, smart cities, or intelligent cities emerging with the second phase of network societies...... 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...
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
Entanglement and topological interfaces
Brehm, E.; Brunner, I.; Jaud, D.; Schmidt-Colinet, C. [Arnold Sommerfeld Center, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, 80333, Muenchen (Germany)
2016-06-15
In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
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.
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.
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.
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...
Quist, Daniel A.; Gavrilov, Eugene M.; Fisk, Michael E.
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.
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.
Topological confinement and superconductivity
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.
Gods as Topological Invariants
Schoch, Daniel
2012-01-01
We show that the number of gods in a universe must equal the Euler characteristics of its underlying manifold. By incorporating the classical cosmological argument for creation, this result builds a bridge between theology and physics and makes theism a testable hypothesis. Theological implications are profound since the theorem gives us new insights in the topological structure of heavens and hells. Recent astronomical observations can not reject theism, but data are slightly in favor of atheism.
Controlled algebra and topology
Pedersen, Erik K.
1997-01-01
Surgery and Geometric Topology : Proceedings of the conference held at Josai University 17-20 September, 1996 / edited by Andrew Ranicki and Masayuki Yamasaki. 本文データは許諾を得てeditorのHPサイトhttp://surgery.matrix.jp/math/josai96/proceedings.html から複製再利用したものである。
Smooth Neutrosophic Topological Spaces
M. K. EL Gayyar
2016-08-01
Full Text Available As a new branch of philosophy, the neutrosophy was presented by Smarandache in 1980. It was presented as the study of origin, nature, and scope of neutralities; as well as their interactions with different ideational spectra. The aim in this paper is to introduce the concepts of smooth neutrosophic topological space, smooth neutrosophic cotopological space, smooth neutrosophic closure, and smooth neutrosophic interior. Furthermore, some properties of these concepts will be investigated.
Smooth Neutrosophic Topological Spaces
M. K. EL GAYYAR
2016-01-01
As a new branch of philosophy, the neutrosophy was presented by Smarandache in 1980. It was presented as the study of origin, nature, and scope of neutralities; as well as their interactions with different ideational spectra. The aim in this paper is to introduce the concepts of smooth neutrosophic topological space, smooth neutrosophic cotopological space, smooth neutrosophic closure, and smooth neutrosophic interior. Furthermore, some properties of these concepts will be investigated.
Computably regular topological spaces
Weihrauch, Klaus
2013-01-01
This article continues the study of computable elementary topology started by the author and T. Grubba in 2009 and extends the author's 2010 study of axioms of computable separation. Several computable T3- and Tychonoff separation axioms are introduced and their logical relation is investigated. A number of implications between these axioms are proved and several implications are excluded by counter examples, however, many questions have not yet been answered. Known results on computable metr...
Topology optimization problems with design-dependent sets of constraints
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... properties and designing through changing these coefficients. For example, consider a continuous structure. Then the basic concept is to represent this structure by small pieces of material that are coinciding with the elements of a finite element model of the structure. This thesis treats stress constrained...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...
Topological Substituent Descriptors
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.
Topology and Fermionic Condensate
Kulikov, I.; Pronin, P.
The purpose of this paper is to investigate an influence of a space-time topology on the formation of fermionic condensate in the model with four-fermion interaction ()2. The value for the space-time with topology of R1 × R1 × S1 is found. Moreover a relation of the value of fermionic condensate to a periodic length is studied. In this connection the possibility of a relation of the topologic deposits to structure of hadrons is discussed.Translated AbstractTopologie und FermikondensatEs wird der Einfluß einer Raum-Zeittopologie auf die Bildung des Fermikondensats in einem Modell mit Vierfermionenwechselwirkung ()2 untersucht. Für eine Raum-Zeit mit der Topologie R1 × R2 × S1 werden die Parameter gegeben. Weiterhin wird die Relation der Größe des Fermikondensats zu einer periodischen Länge untersucht. In diesem Zusammenhang wird die Verbindung des topologischen Depots zur Struktur der Hadronen diskutiert.
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
Topological De-Noising: Strengthening the Topological Signal
Kloke, Jennifer
2009-01-01
Topological methods such as persistent homology are powerful tools for data analysis of high-dimensional data sets but these methods almost exclusively rely on thresholding techniques. However, in noisy data sets thesholding does not always allow for the recovery of topological information. We present a computationally-efficient algorithm to allow for topological data analysis on noisy high-dimensional point cloud data sets. In many cases, the algorithm returns data that has so few outliers that there is no need to threshold the data before performing topological analysis. We apply the algorithm to synthetically-generated noisy data sets and show the recovery of topological information which is impossible to obtain via thresholding. We also apply the algorithm to natural image data in $\\mathbb{R}^8$ and show a very clean recovery of topological information previously only available with significant amounts of thresholding. Finally, we discuss future directions for improving this algorithm using zig-zag persis...
Probing the moduli dependence of refined topological amplitudes
I. Antoniadis
2015-12-01
Full Text Available With the aim of providing a worldsheet description of the refined topological string, we continue the study of a particular class of higher derivative couplings Fg,n in the type II string effective action compactified on a Calabi–Yau threefold. We analyse first order differential equations in the anti-holomorphic moduli of the theory, which relate the Fg,n to other component couplings. From the point of view of the topological theory, these equations describe the contribution of non-physical states to twisted correlation functions and encode an obstruction for interpreting the Fg,n as the free energy of the refined topological string theory. We investigate possibilities of lifting this obstruction by formulating conditions on the moduli dependence under which the differential equations simplify and take the form of generalised holomorphic anomaly equations. We further test this approach against explicit calculations in the dual heterotic theory.
QCD as topologically ordered system
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 analysis of the so-called ``deformed QCD" which is a weakly coupled gauge theory, but nevertheless preserves all crucial elements of strongly interacting QCD, including confinement, nontrivial $\\theta$ 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 can not be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated $U(1)_A$ problem when would be $\\eta'$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We identify the non-propagating auxiliary topo...
Topological structures in computer science
Efim Khalimsky
1987-01-01
Full Text Available Topologies of finite spaces and spaces with countably many points are investigated. It is proven, using the theory of ordered topological spaces, that any topology in connected ordered spaces, with finitely many points or in spaces similar to the set of all integers, is an interval-alternating topology. Integer and digital lines, arcs, and curves are considered. Topology of N-dimensional digital spaces is described. A digital analog of the intermediate value theorem is proven. The equivalence of connectedness and pathconnectedness in digital and integer spaces is also proven. It is shown here how methods of continuous mathematics, for example, topological methods, can be applied to objects, that used to be investigated only by methods of discrete mathematics. The significance of methods and ideas in digital image and picture processing, robotic vision, computer tomography and system's sciences presented here is well known.
Infrared Topological Plasmons in Graphene
Jin, Dafei; Christensen, Thomas; Soljačić, Marin; Fang, Nicholas X.; Lu, Ling; Zhang, Xiang
2017-06-01
We propose a two-dimensional plasmonic platform—periodically patterned monolayer graphene—which hosts topological one-way edge states operable up to infrared frequencies. We classify the band topology of this plasmonic system under time-reversal-symmetry breaking induced by a static magnetic field. At finite doping, the system supports topologically nontrivial band gaps with mid-gap frequencies up to tens of terahertz. By the bulk-edge correspondence, these band gaps host topologically protected one-way edge plasmons, which are immune to backscattering from structural defects and subject only to intrinsic material and radiation loss. Our findings reveal a promising approach to engineer topologically robust chiral plasmonic devices and demonstrate a realistic example of high-frequency topological edge states.
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…
Intuitionistic supra fuzzy topological spaces
Abbas, S.E. E-mail: sabbas73@yahoo.com
2004-09-01
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.
Transport Experiments on Topological Insulators
2016-08-16
UU UU UU 16-08-2016 15-Sep-2011 14-Oct-2014 Final Report: Transport Experiments on Topological Insulators The views, opinions and/or findings contained...Triangle Park, NC 27709-2211 Topological Insulators, Dirac Semimetals, Transport in magnetic field, High mobility REPORT DOCUMENTATION PAGE 11. SPONSOR...ABSTRACT Final Report: Transport Experiments on Topological Insulators Report Title The ARO-supported research focused on uncovering novel materials and
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.
Nutrition Modeling Through Nano Topology
M. Lellis Thivagar,
2014-01-01
Full Text Available Nutrition is the provision, to cells and organisms, of the materials necessary in the form of food to support life. Many common health problems can be prevented or alleviated with a healthy, balanced diet. The purpose of this paper is to apply topological reduction of attributes in set-valued ordered information systems in finding the key foods suitable for two age groups in order to be healthy. We have already introduced a new topology called nano topology. The tactic applied here is in terms of basis of nano topology.
Fermions as Topological Objects
Yershov V. N.
2006-01-01
Full Text Available A preon-based composite model of the fundamental fermions is discussed, in which the fermions are bound states of smaller entities — primitive charges (preons. The preon is regarded as a dislocation in a dual 3-dimensional manifold — a topological object with no properties, save its unit mass and unit charge. It is shown that the dualism of this manifold gives rise to a hierarchy of complex structures resembling by their properties three families of the fundamental fermions. Although just a scheme for building a model of elementary particles, this description yields a quantitative explanation of many observable particle properties, including their masses.
Fermions as topological objects
Yershov, V N
2002-01-01
A conceptual preon-based model of fermions is discussed. The preon is regarded as a topological object with three degrees of freedom in a dual three-dimensional manifold. It is shown that properties of this manifold give rise to a set of preon structures, which resemble three families of fermions. The number of preons in each structure is easily associated with the mass of a fermion. Being just a kind of zero-approximation to a theory of particles and interactions below the quark scale, our model however predicts masses of fermions with an accuracy of about 0.0002% without using any experimental input parameters.
Topological forms of information
Baudot, Pierre [Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig (Germany); Bennequin, Daniel [Universite Paris Diderot-Paris 7, UFR de Mathematiques, Equipe Geometrie et Dynamique, Batiment Sophie Germain, 5 rue Thomas Mann, 75205 Paris Cedex 13 (France)
2015-01-13
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: 1) classical probabilities and random variables; 2) quantum probabilities and observable operators; 3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes. We discuss briefly its application to complex data, in particular to the structures of information flows in biological systems. This short note summarizes results obtained during the last years by the authors. The proofs are not included, but the definitions and theorems are stated with precision.
Algebraic Topology, Rational Homotopy
1988-01-01
This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, Moore conjectures on the exponents of the homotopy groups of a finite CW-c-complex and homology of loop spaces. Of particular interest for specialists are papers on construction of the minimal model in tame theory and computation of the Lusternik-Schnirelmann category by means articles on Moore conjectures, on tame homotopy and on the properties of Poincaré series of loop spaces.
Counting and Topological Order
陈阳军
1997-01-01
The counting method is a simple and efficient method for processing linear recursive datalog queries.Its time complexity is bounded by O(n,e)where n and e denote the numbers the numbers of nodes and edges,respectively,in the graph representing the input.relations.In this paper,the concepts of heritage appearance function and heritage selection function are introduced,and an evaluation algorithm based on the computation of such functions in topological order is developed .This new algorithm requires only linear time in the case of non-cyclic data.
Knitter, Sebastian; Xiong, Wen; Guy, Mikhael I; Solomon, Glenn S; Cao, Hui
2014-01-01
We demonstrate topological defect lasers in a GaAs membrane with embedded InAs quantum dots. By introducing a disclination to a square-lattice of elliptical air holes, we obtain spatially confined optical resonances with high quality factor. Such resonances support powerflow vortices, and lase upon optical excitation of quantum dots, embedded in the structure. The spatially inhomogeneous variation of the unit cell orientation adds another dimension to the control of a lasing mode, enabling the manipulation of its field pattern and energy flow landscape.
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
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
Continuity in weak topology:higher order linear systems of ODE
2008-01-01
We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.
Topological Transformation during Normal Grain Growth
Chaogang LOU; Michael A.Player
2004-01-01
This paper investigates topological transformation during normal grain growth by carrying out a computer vertex simulation.Results show that topological correlation agrees with the models proposed by Blanc et al. and Weaire. Topological transformation occurs more often on grains with some topological classes instead of equal probability on each boundary. This can be qualitatively explained by topological correlation.
PARTIAL DIFFERENTIAL EQUATIONS , THEORY), (*COMPLEX VARIABLES, PARTIAL DIFFERENTIAL EQUATIONS ), FUNCTIONS(MATHEMATICS), BOUNDARY VALUE PROBLEMS, INEQUALITIES, TRANSFORMATIONS (MATHEMATICS), TOPOLOGY, SET THEORY
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...
Dennis, E; Landahl, A; Preskill, J; Dennis, Eric; Kitaev, Alexei; Landahl, Andrew; Preskill, John
2002-01-01
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require m...
Bonneau, Philippe
Following a preceding paper showing how the introduction of a t.v.s. topology on quantum groups led to a remarkable unification and rigidification of the different definitions, we adapt here, in the same way, the definition of quantum double. This topological double is dualizable and reflexive (even for infinite dimensional algebras). In a simple case we show, considering the double as the "zero class" of an extension theory, the uniqueness of the double structure as a quasi-Hopf algebra. A la suite d'un précédent article montrant comment l'introduction d'une topologie d'e.v.t. sur les groupes quantiques permet une unification et une rigidification remarquables des différentes définitions, on adapte ici de la même manière la définition du double quantique. Ce double topologique est alors dualisable et reflexif (même pour des algèbres de dimension infinie). Dans un cas simple on montre, en considérant le double comme la "classe zéro" d'une théorie d'extensions, l'unicité de cette structure comme algèbre quasi-Hopf.
A natural topological insulator.
Gehring, P; Benia, H M; Weng, Y; Dinnebier, R; Ast, C R; Burghard, M; Kern, K
2013-03-13
The earth's crust and outer space are rich sources of technologically relevant materials which have found application in a wide range of fields. Well-established examples are diamond, one of the hardest known materials, or graphite as a suitable precursor of graphene. The ongoing drive to discover novel materials useful for (opto)electronic applications has recently drawn strong attention to topological insulators. Here, we report that Kawazulite, a mineral with the approximate composition Bi2(Te,Se)2(Se,S), represents a naturally occurring topological insulator whose electronic properties compete well with those of its synthetic counterparts. Kawazulite flakes with a thickness of a few tens of nanometers were prepared by mechanical exfoliation. They exhibit a low intrinsic bulk doping level and correspondingly a sizable mobility of surface state carriers of more than 1000 cm(2)/(V s) at low temperature. Based on these findings, further minerals which due to their minimized defect densities display even better electronic characteristics may be identified in the future.
Topological Transitions in Metamaterials
Krishnamoorthy, Harish N S; Narimanov, Evgenii; Kretzschmar, Ilona; Menon, Vinod M
2011-01-01
The ideas of mathematical topology play an important role in many aspects of modern physics - from phase transitions to field theory to nonlinear dynamics (1, 2). An important example of this is the Lifshitz transition (3), where the transformation of the Fermi surface of a metal from a closed to an open geometry (due to e.g. external pressure) leads to a dramatic effect on the electron magneto-transport (4). Here, we present the optical equivalent of the Lifshitz transition in strongly anisotropic metamaterials. When one of the components of the dielectric permittivity tensor of such a composite changes sign, the corresponding iso-frequency surface transforms from an ellipsoid to a hyperboloid. Since the photonic density of states can be related to the volume enclosed by the iso-frequency surface (5), such a topological transition in a metamaterial leads to a dramatic change in the photonic density of states, with a resulting effect on every single physical parameter related to the metamaterial - from thermo...
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...
Algebraic topology of finite topological spaces and applications
Barmak, Jonathan A
2011-01-01
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen’s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Baulieu, L.; Toppan, Francesco
2016-11-01
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
L. Baulieu
2016-11-01
Full Text Available We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al. and condensed matter properties (Kane et al., where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Baulieu, L., E-mail: baulieu@lpthe.jussieu.fr [LPTHE – Sorbonne Universités, UPMC, 4 Place Jussieu, 75 005 Paris (France); Toppan, Francesco [CBPF, Rio de Janeiro, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180 (RJ) (Brazil)
2016-11-15
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Baulieu, Laurent
2016-01-01
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories of effective models are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Topological phases and transport properties of screened interacting quantum wires
Xu, Hengyi; Xiong, Ye; Wang, Jun
2016-10-01
We study theoretically the effects of long-range and on-site Coulomb interactions on the topological phases and transport properties of spin-orbit-coupled quasi-one-dimensional quantum wires imposed on a s-wave superconductor. The distributions of the electrostatic potential and charge density are calculated self-consistently within the Hartree approximation. Due to the finite width of the wires and charge repulsion, the potential and density distribute inhomogeneously in the transverse direction and tend to accumulate along the lateral edges where the hard-wall confinement is assumed. This result has profound effects on the topological phases and the differential conductance of the interacting quantum wires and their hybrid junctions with superconductors. Coulomb interactions renormalize the gate voltage and alter the topological phases strongly by enhancing the topological regimes and producing jagged boundaries. Moreover, the multicritical points connecting different topological phases are modified remarkably in striking contrast to the predictions of the two-band model. We further suggest the possible non-magnetic topological phase transitions manipulated externally with the aid of long-range interactions. Finally, the transport properties of normal-superconductor junctions are further examined, in particular, the impacts of Coulomb interactions on the zero-bias peaks related to the Majorana fermions and near zero-energy peaks.
Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).
The birth of topological insulators.
Moore, Joel E
2010-03-11
Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.
Topological arguments for Kolmogorov complexity
Alexander Shen
2012-08-01
Full Text Available We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.
Observational modeling of topological spaces
Molaei, M.R. [Department of Mathematics, Shahid Bahonar University of Kerman, Kerman 76169-14111 (Iran, Islamic Republic of)], E-mail: mrmolaei@mail.uk.ac.ir
2009-10-15
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 Vortices in Superfluid Films
WANGJun-Ping; DUANYi-Shi
2005-01-01
We study the topological structure of the vortex system in a superfluid film. Explicit expressions for the vortex density and velocity field as functions of the superfluid order parameter are derived. The evolution of vortices is also studied from the topological properties of the superfluid order parameter field.
Acoustic design by topology optimization
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...
Concept Model on Topological Learning
Ae, Tadashi; Kioi, Kazumasa
2010-11-01
We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.
Topological susceptibility from the overlap
Del Debbio, L; Debbio, Luigi Del; 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 ...
Combined Shape and Topology Optimization
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...
Topological susceptibility from the overlap
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...... 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...
Topological defects in two-dimensional crystals
Chen, Yong; Qi, Wei-Kai
2008-01-01
By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal, one for dislocations and the other for disclinations. The topological quantization and evolution of topological defects in two-dimensional crystals are discussed. Finally, We compare our theory with Brownian-dynamics simulations in 2D Yukawa systems.
Gregoire, T; 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.
The Orbifold Topological Vertex
Bryan, Jim; Young, Ben
2010-01-01
We define Donaldson-Thomas invariants of Calabi-Yau orbifolds and we develop a topological vertex formalism for computing them. The basic combinatorial object is the orbifold vertex, a generating function for the number of 3D partitions asymptotic to three given 2D partitions and colored by representations of a finite Abelian group G acting on C^3. In the case where G=Z_n acting on C^3 with transverse A_{n-1} quotient singularities, we give an explicit formula for the vertex in terms of Schur functions. We discuss applications of our formalism to the Donaldson-Thomas Crepant Resolution Conjecture and to the orbifold Donaldson-Thomas/Gromov-Witten correspondence. We also explicitly compute the Donaldson-Thomas partition function for some simple orbifold geometries: the local football and the local BZ_2 gerbe.
Topological convolution algebras
Alpay, Daniel
2012-01-01
In this paper we introduce a new family of topological convolution algebras of the form $\\bigcup_{p\\in\\mathbb N} L_2(S,\\mu_p)$, where $S$ is a Borel semi-group in a locally compact group $G$, which carries an inequality of the type $\\|f*g\\|_p\\le A_{p,q}\\|f\\|_q\\|g\\|_p$ for $p > q+d$ where $d$ pre-assigned, and $A_{p,q}$ is a constant. We give a sufficient condition on the measures $\\mu_p$ for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.
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...... multiplicities of environmental, technical, and human interactants tend towards gathering and dispersing in a single mixed reality street transport scenario. The need for ‘intelligent’ ad hoc connection, routing, and disconnection of multitudes of humans, technical systems, and environmental entities makes....... It is demonstrated that design as topology offers significant resources with respect to traits of the u-city such as continuous material and energetic flows, its environmental landscaping of mixed realities, its ongoing virtual and physical infrastructural developments, the folding and unfolding of its architecture...
On sequential countably compact topological semigroups
Gutik, Oleg V; RepovÅ¡, DuÅ¡an
2008-01-01
We study topological and algebraic properties of sequential countably compact topological semigroups similar to compact topological semigroups. We prove that a sequential countably compact topological semigroup does not contain the bicyclic semigroup. Also we show that the closure of a subgroup in a sequential countably compact topological semigroup is a topological group, that the inversion in a Clifford sequential countably compact topological semigroup is continuous and we prove the analogue of the Rees-Suschkewitsch Theorem for simple regular sequential countably compact topological semigroups.
The Construction of Finer Compact Topologies
2005-01-01
It is well known that each locally compact strongly sober topology is contained in a compact Hausdorff topology; just take the supremum of its topology with its dual topology. On the other hand, examples of compact topologies are known that do not have a finer compact Hausdorff topology. This led to the question (first explicitly formulated by D.E. Cameron) whether each compact topology is contained in a compact topology with respect to which all compact sets are closed. (For the obvious r...
Dense topological spaces and dense continuity
Aldwoah, Khaled A.
2013-09-01
There are several attempts to generalize (or "widen") the concept of topological space. This paper uses equivalence relations to generalize the concept of topological space via the concept of equivalence relations. By the generalization, we can introduce from particular topology on a nonempty set X many new topologies, we call anyone of these new topologies a dense topology. In addition, we formulate some simple properties of dense topologies and study suitable generalizations of the concepts of limit points, closeness and continuity, as well as Jackson, Nörlund and Hahn dense topologies.
Methods from Differential Geometry in Polytope Theory
Adiprasito, Karim Alexander
2014-01-01
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-dimensional topology.
Cultural Topology of Creativity
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.
Cultural Topology of Creativity
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.
Streamline topologies near a fixed wall using normal forms
Hartnack, Johan
1998-01-01
Streamline patterns and their bifurcations in two-dimensional incompressible flow in the vicinity of a fixed wall has been investigated from a topological point of view by Bakker [Bifurcations in Flow Patterns. Kluwer Academic Publishers, 1991]. Bakkers work is revisited in a more general setting...... allowing curvature of the fixed wall and a time dependence of the streamlines. The velocity field is expanded at a point on the wall, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate changes results in a much simplified system of differential...... of the Navier-Stokes equations on the local topology is considered....
Homogenization and structural topology optimization theory, practice and software
Hassani, Behrooz
1999-01-01
Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.
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.
Some New Sets and Topologies in Ideal Topological Spaces
R. Manoharan
2013-01-01
Full Text Available An ideal topological space is a triplet (X, τ, ℑ, where X is a nonempty set, τ is a topology on X, and ℑ is an ideal of subsets of X. In this paper, we introduce L∗-perfect, R∗-perfect, and C∗-perfect sets in ideal spaces and study their properties. We obtained a characterization for compatible ideals via R∗-perfect sets. Also, we obtain a generalized topology via ideals which is finer than τ using R∗-perfect sets on a finite set.
Synthesizing topological structures containing RNA
Liu, Di; Shao, Yaming; Chen, Gang; Tse-Dinh, Yuk-Ching; Piccirilli, Joseph A.; Weizmann, Yossi
2017-03-01
Though knotting and entanglement have been observed in DNA and proteins, their existence in RNA remains an enigma. Synthetic RNA topological structures are significant for understanding the physical and biological properties pertaining to RNA topology, and these properties in turn could facilitate identifying naturally occurring topologically nontrivial RNA molecules. Here we show that topological structures containing single-stranded RNA (ssRNA) free of strong base pairing interactions can be created either by configuring RNA-DNA hybrid four-way junctions or by template-directed synthesis with a single-stranded DNA (ssDNA) topological structure. By using a constructed ssRNA knot as a highly sensitive topological probe, we find that Escherichia coli DNA topoisomerase I has low RNA topoisomerase activity and that the R173A point mutation abolishes the unknotting activity for ssRNA, but not for ssDNA. Furthermore, we discover the topological inhibition of reverse transcription (RT) and obtain different RT-PCR patterns for an ssRNA knot and circle of the same sequence.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Topology Optimization using a Topology Description Function Approach
de Ruiter, M.J.
2005-01-01
During the last two decades, computational structural optimization methods have emerged, as computational power increased tremendously. Designers now have topological optimization routines at their disposal. These routines are able to generate the entire geometry of structures, provided only with in
Topology optimization for coated structures
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....
Topological Number of Edge States
Hashimoto, Koji
2016-01-01
We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analogue of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a non-commutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.
Topological Aspects of Triplet Superconductors
REN Ji-Rong; XU Dong-Hui; ZHANG Xin-Hui; LI Ran
2007-01-01
In this paper, using the φ-mapping theory, it is shown that two kinds of topological defects, i.e., the vortex lines and the monopoles exist in the helical configuration of magnetic field in triplet superconductors. And the inner topological structure of these defects is studied. Because the knot solitons in the triplet superconductors are characterized by the Hopf invariant, we also establish a relationship between the Hopf invariant and the linking number of knots family,and reveal the inner topological structure of the Hopf invariant.
Topology optimised wavelength dependent splitters
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...
Spherical Orbifolds for Cosmic Topology
Kramer, Peter
2012-01-01
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give basis functions for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. They provide new tools for detecting cosmic topology from the CMB radiation.
Topological Rankings in Communication Networks
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 Convection Problems
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...
Topological strength of magnetic skyrmions
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 optimised wavelength dependent splitters
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...
An introduction to differential manifolds
Lafontaine, Jacques
2015-01-01
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...
Dynamical topology and statistical properties of spatiotemporal chaos.
Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli
2012-12-01
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.
Emerging Trends in Topological Insulators and Topological Superconductors
A M Jayannavar; Arijit Saha
2017-08-01
Topological insulators are new class of materials which arecharacterized by a bulk band gap like ordinary band insulatorsbut have protected conducting states on their edgesor surfaces. These states emerge due to the combination ofspin-orbit coupling and time reversal symmetry. Also, thesestates are insensitive to scattering by non-magnetic impurities.A two-dimensional topological insulator has one dimensionaledge states in which the spin-momentum locking ofthe electrons give rise to quantum spin Hall effect. A threedimensionaltopological insulator supports novel spin-polarized2D Dirac fermions on its surface. These topological insulatormaterials have been theoretically predicted and experimentallyobserved in a variety of 2D and 3D systems, includingHgTe quantum wells, BiSb alloys, and Bi2Te3, Bi2Se3 crystals.Moreover, proximity induced superconductivity in these systemscan lead to a state that supports zero energy Majoranafermions, and the phase is known as topological superconductors.In this article, the basic idea of topological insulatorsand topological superconductors are presented alongwith their experimental development.
Theory of differential equations
Gel'fand, I M
1967-01-01
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations.This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cau
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.
Phantom stars and topology change
DeBenedictis, Andrew; Lobo, Francisco S N
2008-01-01
In this work, we consider time-dependent dark energy star models, with an evolving parameter $\\omega$ crossing the phantom divide, $\\omega=-1$. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark energy star into a wormhole. The criteria for this topology change are discussed, in particular, we consider the Morse Index analysis and a Casimir energy approach involving quasi-local energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being use...
Can topology reshape segregation patterns?
Gandica, Yerali; Carletti, Timoteo
2015-01-01
We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The role of the topology is to fix the places where the segregation patterns emerge. In addition we address the question of the time evolution of the segregation clusters, resulting from different dynamical regimes of a coarsening process, as a function of the tolerance parameter. We show that the underlying topology may alter the early stage of the coarsening process, once large values of the tolerance are used, while for lower ones a different mechanism is at work and it results to be topology independent.
Comprehensible Presentation of Topological Information
Weber, Gunther H. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Beketayev, Kenes [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Bremer, Peer-Timo [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Hamann, Bernd [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Haranczyk, Maciej [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Hlawitschka, Mario [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Pascucci, Valerio [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2012-03-05
Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.
Topology optimized permanent magnet systems
Bjørk, R; Insinga, A R
2016-01-01
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. First, the Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown, albeit with an increase of 3.8 pp. in field inhomogeneity - a value compared to the inhomogeneity in a 16 segmented Halbach cylinder. Following this a topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111% for the chosen dimensions. Finally, a permanent magnet with alternating high and low field regions is considered. Here a $\\Lambda_\\mathrm{cool}$ figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.
Streamline topology of axisymmetric flows
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 $v......$ is expanded in a Taylor series at a point on the axis, and the expansion coefficients are considered as bifurcation parameters. After a normal form transformation we easily obtain the most common bifurcations of the flow patterns. The use of non-linear normal forms provide a gross simplification, which...... 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...
Cartography – morphology – topology
Dinesen, Cort Ross; Peder Pedersen, Claus
2010-01-01
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...
Experimental Realizations of Magnetic Topological Insulator and Topological Crystalline Insulator
Xu, Suyang
2013-03-01
Over the past few years the experimental research on three-dimensional topological insulators have emerged as one of the most rapidly developing fields in condensed matter physics. In this talk, we report on two new developments in the field: The first part is on the dynamic interplay between ferromagnetism and the Z2 topological insulator state (leading to a magnetic topological insulator). We present our spin-resolved photoemission and magnetic dichroic experiments on MBE grown films where a hedgehog-like spin texture is revealed on the magnetically ordered surface of Mn-Bi2Se3 revealing a Berry's phase gradient in energy-momentum space of the crystal. A chemically/electrically tunable Berry's phase switch is further demonstrated via the tuning of the spin groundstate in Mn-Bi2Se3 revealed in our data (Nature Physics 8, 616 (2012)). The second part of this talk describes our experimental observation of a new topological phase of matter, namely a topological crystalline insulator where space group symmetries replace the role of time-reversal symmetry in an otherwise Z2 topological insulator predicted in theory. We experimentally investigate the possibility of a mirror symmetry protected topological phase transition in the Pb1-xSnxTe alloy system, which has long been known to contain an even number of band inversions based on band theory. Our experimental results show that at a composition below the theoretically predicted band inversion, the system is fully gapped, whereas in the band-inverted regime, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order (Nature Communications 3, 1192 (2012)) distinct from that observed in Z2 topological insulators. We discuss future experimental possibilities opened up by these new developments in topological insulators research. This work is in collaboration with M. Neupane, C. Liu, N. Alidoust, I. Belopolski, D. Qian, D.M. Zhang, A. Richardella, A. Marcinkova, Q
Topological Fidelity in Sensor Networks
Chintakunta, Harish; Krim, Hamid
2011-01-01
Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection ...
Williams, M; Thomas, C; Dijkstra, H; Nardulli, J; Spradlin, P
2011-01-01
The HLT2 topological lines have been redesigned to trigger inclusively on $n$-body B decays. They are able to maintain high signal selection efficiencies, while simultaneously providing a large background rejection factor (even at large $\\mu$). The timing performance of these lines is also impressive. This note discusses the current status and performance of the HLT2 topological lines, along with plans for future improvements.
Topological Fidelity in Sensor Networks
Chintakunta, Harish; Krim, Hamid
2011-01-01
Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection ...
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.
Momentum space topology of QCD
Zubkov, M A
2016-01-01
We discuss the possibility to consider quark matter as the topological material. In our consideration we concentrate on the hadronic phase (HP), on the quark - gluon plasma phase (QGP), and on the color - flavor locking (CFL) phase. In those phases we identify the relevant topological invariants in momentum space. The formalism is developed, which relates those invariants and massless fermions that reside on vortices and at the interphases. This formalism is illustrated by the example of vortices in the CFL phase.
Quantum gates with topological phases
Ionicioiu, R
2003-01-01
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.
Completely regular fuzzifying topological spaces
A. K. Katsaras
2005-12-01
Full Text Available Some of the properties of the completely regular fuzzifying topological spaces are investigated. It is shown that a fuzzifying topology ÃÂ„ is completely regular if and only if it is induced by some fuzzy uniformity or equivalently by some fuzzifying proximity. Also, ÃÂ„ is completely regular if and only if it is generated by a family of probabilistic pseudometrics.
Topology Optimized Photonic Wire Splitters
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.
Extracting labeled topological patterns from samples of networks.
Christoph Schmidt
Full Text Available An advanced graph theoretical approach is introduced that enables a higher level of functional interpretation of samples of directed networks with identical fixed pairwise different vertex labels that are drawn from a particular population. Compared to the analysis of single networks, their investigation promises to yield more detailed information about the represented system. Often patterns of directed edges in sample element networks are too intractable for a direct evaluation and interpretation. The new approach addresses the problem of simplifying topological information and characterizes such a sample of networks by finding its locatable characteristic topological patterns. These patterns, essentially sample-specific network motifs with vertex labeling, might represent the essence of the intricate topological information contained in all sample element networks and provides as well a means of differentiating network samples. Central to the accurateness of this approach is the null model and its properties, which is needed to assign significance to topological patterns. As a proof of principle the proposed approach has been applied to the analysis of networks that represent brain connectivity before and during painful stimulation in patients with major depression and in healthy subjects. The accomplished reduction of topological information enables a cautious functional interpretation of the altered neuronal processing of pain in both groups.
Topological Insulators from Group Cohomology
Alexandradinata, A.; Wang, Zhijun; Bernevig, B. Andrei
2016-04-01
We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations; i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as "piecewise topological," in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discover include a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently proposed KHgSb material class), and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.
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.
Topological Insulators from Group Cohomology
A. Alexandradinata
2016-04-01
Full Text Available We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations; i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as “piecewise topological,” in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discover include a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently proposed KHgSb material class, and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.
Instant topological relationships hidden in the reality
2007-01-01
In most applications of general topology, topology usually is not the first, primary structure, but the information which finally leads to the construction of the certain, for some purpose required topology, is filtered by more or less thick filter of the other mathematical structures. This fact has two main consequences: (1) Most important applied constructions may be done in the primary structure, bypassing the topology. (2) Some topologically important informatio...
Topological Defects in Liquid Crystal Films
DUAN Yi-Shi; ZHAO Li; ZHANG Xin-Hui; SI Tie-Yan
2007-01-01
A topological theory of liquid crystal films in the presence of defects is developed based on the φ-mapping topological current theory. By generalizing the free-energy density in "one-constant" approximation, a covariant freeenergy density is obtained, from which the U(1) gauge field and the unified topological current for monopoles and strings in liquid crystals are derived. The inner topological structure of these topological defects is characterized by the winding numbers of φ-mapping.
Lower and Upper Fuzzy Topological Subhypergroups
Irina CRISTEA; Jian Ming ZHAN
2013-01-01
This paper provides a new connection between algebraic hyperstructures and fuzzy sets.More specifically,using both properties of fuzzy topological spaces and those of fuzzy subhypergroups,we define the notions of lower (upper) fuzzy topological subhypergroups of a hypergroup endowed with a fuzzy topology.Some results concerning the image and the inverse image of a lower (upper) topological subhypergroup under a very good homomorphism of hypergroups (endowed with fuzzy topologies) are pointed out.
Convex integration theory solutions to the h-principle in geometry and topology
Spring, David
1998-01-01
This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, u...
Mixed methods for viscoelastodynamics and topology optimization
Giacomo Maurelli
2014-07-01
Full Text Available A truly-mixed approach for the analysis of viscoelastic structures and continua is presented. An additive decomposition of the stress state into a viscoelastic part and a purely elastic one is introduced along with an Hellinger-Reissner variational principle wherein the stress represents the main variable of the formulation whereas the kinematic descriptor (that in the case at hand is the velocity field acts as Lagrange multiplier. The resulting problem is a Differential Algebraic Equation (DAE because of the need to introduce static Lagrange multipliers to comply with the Cauchy boundary condition on the stress. The associated eigenvalue problem is known in the literature as constrained eigenvalue problem and poses several difficulties for its solution that are addressed in the paper. The second part of the paper proposes a topology optimization approach for the rationale design of viscoelastic structures and continua. Details concerning density interpolation, compliance problems and eigenvalue-based objectives are given. Worked numerical examples are presented concerning both the dynamic analysis of viscoelastic structures and their topology optimization.
Topological sequence entropy of continuous maps on topological spaces
Lei Liu
2013-12-01
Full Text Available In this paper we propose a new definition of topological sequence entropy for continuous maps on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required, investigate fundamental properties of the new sequence entropy, and compare the new sequence entropy with the existing ones. The defined sequence entropy generates that of Goodman. Yet, it holds various basic properties of Goodman’s sequence entropy, e.g., the sequence entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same sequence entropy, the sequence entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new sequence entropy coincides with Goodman’s sequence entropy for compact systems.
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.
Topological Strings and Integrable Hierarchies
Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht; Mariño, 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 -algebra symmetries which encode 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 an A-model topological string on P1 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.
Topological strings from quantum mechanics
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
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{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 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.
Toward A Nonperturbative Topological String
Neitzke, A
2005-01-01
We discuss three examples of nonperturbative phenomena in the topological string. First, we consider the computation of amplitudes in N = 4 super Yang-Mills theory using the B model topological string as proposed by Witten. We give an argument suggesting that the computations using connected or disconnected D-instantons of the B model are in fact equivalent. Second, we formulate a conjecture that the squared modulus of the open topological string partition function can be defined nonperturbatively as the partition function of a mixed ensemble of BPS states in d = 4. This conjecture is an extension of a recent proposal for the closed topological string. In a particular example involving a non-compact Calabi- Yau threefold, we show that the conjecture passes some basic checks, and that the square of the open topological string amplitude has a natural interpretation in terms of 2-dimensional Yang-Mills theory, again generalizing known results for the closed string case. Third, we discuss an action for an abel...
Topological Insulators at Room Temperature
Zhang, Haijun; /Beijing, Inst. Phys.; Liu, Chao-Xing; /Tsinghua U., Beijing; Qi, Xiao-Liang; /Stanford U., Phys. Dept.; Dai, Xi; Fang, Zhong; /Beijing, Inst. Phys.; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-25
Topological insulators are new states of quantum matter with surface states protected by the time-reversal symmetry. In this work, we perform first-principle electronic structure calculations for Sb{sub 2}Te{sub 3}, Sb{sub 2}Se{sub 3}, Bi{sub 2}Te{sub 3} and Bi{sub 2}Se{sub 3} crystals. Our calculations predict that Sb{sub 2}Te{sub 3}, Bi{sub 2}T e{sub 3} and Bi{sub 2}Se{sub 3} are topological insulators, while Sb{sub 2}Se{sub 3} is not. In particular, Bi{sub 2}Se{sub 3} has a topologically non-trivial energy gap of 0.3eV , suitable for room temperature applications. We present a simple and unified continuum model which captures the salient topological features of this class of materials. These topological insulators have robust surface states consisting of a single Dirac cone at the {Lambda} point.
NOVEL METHOD SOLVING NUMERICAL INSTABILITIES IN TOPOLOGY OPTIMIZATION
无
2002-01-01
Numerical instabilities are often encountered in FE solution of continuum topology optimization. The essence of the numerical instabilities is given from the inverse partial differential equation (PDE) point of view. On the basis of the strict mathematical theory, a novel method, named as window filter and multi-grid method, which solves the numerical instabilities, is proposed. Convergent analyses and a numerical example are presented.
Convergence for pseudo monotone semiflows on product ordered topological spaces
Yi, Taishan; Huang, Lihong
In this paper, we consider a class of pseudo monotone semiflows, which only enjoy some weak monotonicity properties and are defined on product-ordered topological spaces. Under certain conditions, several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium, which improve and extend some corresponding results already known. Some applications to delay differential equations are presented.
Tunneling Planar Hall Effect in Topological Insulators: Spin Valves and Amplifiers
Scharf, Benedikt; Matos-Abiague, Alex; Han, Jong E.; Hankiewicz, Ewelina M.; Žutić, Igor
2016-10-01
We investigate tunneling across a single ferromagnetic barrier on the surface of a three-dimensional topological insulator. In the presence of a magnetization component along the bias direction, a tunneling planar Hall conductance (TPHC), transverse to the applied bias, develops. Electrostatic control of the barrier enables a giant Hall angle, with the TPHC exceeding the longitudinal tunneling conductance. By changing the in-plane magnetization direction, it is possible to change the sign of both the longitudinal and transverse differential conductance without opening a gap in the topological surface state. The transport in a topological-insulator-ferromagnet junction can, thus, be drastically altered from a simple spin valve to an amplifier.
Airy Equation for the Topological String Partition Function in a Scaling Limit
Alim, Murad; Yau, Shing-Tung; Zhou, Jie
2016-06-01
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
Topological design of electromechanical actuators with robustness toward over- and under-etching
Qian, Xiaoping; Sigmund, Ole
2013-01-01
In this paper, we combine the recent findings in robust topology optimization formulations and Helmholtz partial differential equation based density filtering to improve the topological design of electromechanical actuators. For the electromechanical analysis, we adopt a monolithic formulation...... optimization, i.e. one-element wide structural parts or gaps. It thus leads to physically realizable designs that are robust against manufacturing imprecision such as over- and under-etching. © 2012 Elsevier B.V. All rights reserved....
Standard Model as the topological material
Volovik, G E
2016-01-01
Study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids and superconductors) opens the route for the investigation of the topological quantum vacua of relativistic fields. The symmetric phase of the Standard Model (SM), where both electroweak and chiral symmetry are not broken, represents the topological semimetal. The vacua of the SM (and its extensions) in the phases with broken Electroweak symmetry represent the topological insulators of different types. We discuss in details the topological invariants in both symmetric and broken phases and establish their relation to the stability of vacuum.
Dimensional Hierarchy of Fermionic Interacting Topological Phases
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-01
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d -dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Zn.
Dimensional Hierarchy of Fermionic Interacting Topological Phases.
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-11
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d-dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Z_{n}.
Topological mixing with ghost rods
Gouillart, Emmanuelle; Thiffeault, Jean-Luc; Finn, Matthew D.
2006-03-01
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call “ghost rods”, because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.
Topological Insulators from Electronic Superstructures
Sugita, Yusuke; Motome, Yukitoshi
2016-07-01
The possibility of realizing topological insulators by the spontaneous formation of electronic superstructures is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a triangular lattice. Using the mean-field approximation, we show that the model exhibits several different types of charge-ordered insulators, where the charge disproportionation forms a honeycomb or kagome superstructure. We find that the charge-ordered insulators in the presence of strong spin-orbit coupling can be topological insulators showing quantized spin Hall conductivity. Their band gap is dependent on electron correlations as well as the spin-orbit coupling, and even vanishes while showing the massless Dirac dispersion at the transition to a trivial charge-ordered insulator. Our results suggest a new route to realize and control topological states of quantum matter by the interplay between the spin-orbit coupling and electron correlations.
Topological Fidelity in Sensor Networks
Chintakunta, Harish
2011-01-01
Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection and Localization. We also note these solutions remain coordinate free as no priori localization information of the nodes is assumed. For the coverage hole problem, we follow a "divide and conquer approach", by strategically dissecting the network so that the overall topology is preserved, while efficiently pursuing the detection and localization of failures. The detection of holes, is enabled by first attributing a combinatorial object called a "Rips Complex" to each network segment, and by subsequently checking the exist...
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...
Quantum Capacitance in Topological Insulators
Xiu, Faxian; Meyer, Nicholas; Kou, Xufeng; He, Liang; Lang, Murong; Wang, Yong; Yu, Xinxin; Fedorov, Alexei V.; Zou, Jin; Wang, Kang L.
2012-01-01
Topological insulators show unique properties resulting from massless, Dirac-like surface states that are protected by time-reversal symmetry. Theory predicts that the surface states exhibit a quantum spin Hall effect with counter-propagating electrons carrying opposite spins in the absence of an external magnetic field. However, to date, the revelation of these states through conventional transport measurements remains a significant challenge owing to the predominance of bulk carriers. Here, we report on an experimental observation of Shubnikov-de Haas oscillations in quantum capacitance measurements, which originate from topological helical states. Unlike the traditional transport approach, the quantum capacitance measurements are remarkably alleviated from bulk interference at high excitation frequencies, thus enabling a distinction between the surface and bulk. We also demonstrate easy access to the surface states at relatively high temperatures up to 60 K. Our approach may eventually facilitate an exciting exploration of exotic topological properties at room temperature. PMID:22993694
On exponentiable soft topological spaces
Ghasem Mirhosseinkhani
2016-11-01
Full Text Available An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalization of the category $mathbf{Top}$. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also wegive the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.
Topological Groups and Dugundji Compacta
Uspenskiĭ, V. V.
1990-02-01
A compact space X is called a Dugundji compactum if for every compact Y containing X, there exists a linear extension operator \\Lambda:\\ C(X)\\to C(Y) which preserves nonnegativity and maps constants into constants. It is known that every compact group is a Dugundji compactum. In this paper we show that compacta connected in a natural way with topological groups enjoy the same property. For example, in each of the following cases, the compact space X is a Dugundji compactum:1) X is a retract of an arbitrary topological group;2) X=\\beta P, where P is a pseudocompact space on which some \\aleph_0-bounded topological group acts transitively and continuously.Bibliography: 57 titles.
Topology optimization of flexoelectric structures
Nanthakumar, S. S.; Zhuang, Xiaoying; Park, Harold S.; Rabczuk, Timon
2017-08-01
We present a mixed finite element formulation for flexoelectric nanostructures that is coupled with topology optimization to maximize their intrinsic material performance with regards to their energy conversion potential. Using Barium Titanate (BTO) as the model flexoelectric material, we demonstrate the significant enhancement in energy conversion that can be obtained using topology optimization. We also demonstrate that non-smooth surfaces can play a key role in the energy conversion enhancements obtained through topology optimization. Finally, we examine the relative benefits of flexoelectricity, and surface piezoelectricity on the energy conversion efficiency of nanobeams. We find that the energy conversion efficiency of flexoelectric nanobeams is comparable to the energy conversion efficiency obtained from nanobeams whose electromechanical coupling occurs through surface piezoelectricity, but are ten times thinner. Overall, our results not only demonstrate the utility and efficiency of flexoelectricity as a nanoscale energy conversion mechanism, but also its relative superiority as compared to piezoelectric or surface piezoelectric effects.
Inferring topologies via driving-based generalized synchronization of two-layer networks
Wang, Yingfei; Wu, Xiaoqun; Feng, Hui; Lu, Jun-an; Xu, Yuhua
2016-05-01
The interaction topology among the constituents of a complex network plays a crucial role in the network’s evolutionary mechanisms and functional behaviors. However, some network topologies are usually unknown or uncertain. Meanwhile, coupling delays are ubiquitous in various man-made and natural networks. Hence, it is necessary to gain knowledge of the whole or partial topology of a complex dynamical network by taking into consideration communication delay. In this paper, topology identification of complex dynamical networks is investigated via generalized synchronization of a two-layer network. Particularly, based on the LaSalle-type invariance principle of stochastic differential delay equations, an adaptive control technique is proposed by constructing an auxiliary layer and designing proper control input and updating laws so that the unknown topology can be recovered upon successful generalized synchronization. Numerical simulations are provided to illustrate the effectiveness of the proposed method. The technique provides a certain theoretical basis for topology inference of complex networks. In particular, when the considered network is composed of systems with high-dimension or complicated dynamics, a simpler response layer can be constructed, which is conducive to circuit design. Moreover, it is practical to take into consideration perturbations caused by control input. Finally, the method is applicable to infer topology of a subnetwork embedded within a complex system and locate hidden sources. We hope the results can provide basic insight into further research endeavors on understanding practical and economical topology inference of networks.
Tierny, Julien; Favelier, Guillaume; Levine, Joshua A; Gueunet, Charles; Michaux, Michael
2017-08-29
This system paper presents the Topology ToolKit (TTK), a software platform designed for the topological analysis of scalar data in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. TTK aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependency-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions
Yingzi Li
Full Text Available Regulation of cell growth and cell division has a fundamental role in tissue formation, organ development, and cancer progression. Remarkable similarities in the topological distributions were found in a variety of proliferating epithelia in both animals and plants. At the same time, there are species with significantly varied frequency of hexagonal cells. Moreover, local topology has been shown to be disturbed on the boundary between proliferating and quiescent cells, where cells have fewer sides than natural proliferating epithelia. The mechanisms of regulating these topological changes remain poorly understood. In this study, we use a mechanical model to examine the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells. We find that regardless of orientation of division plane, our model can reproduce the commonly observed topological distributions of cells in natural proliferating animal epithelia with the consideration of cell rearrangements. In addition, with different schemes of division plane, we are able to generate different frequency of hexagonal cells, which is consistent with experimental observations. In proliferating cells interfacing quiescent cells, our results show that differential proliferation alone is insufficient to reproduce the local changes in cell topology. Rather, increased tension on the boundary, in conjunction with differential proliferation, can reproduce the observed topological changes. We conclude that both division plane orientation and mechanical forces play important roles in cell topology in animal proliferating epithelia. Moreover, cell memory is also essential for generating specific topological distributions.
Li, Yingzi; Naveed, Hammad; Kachalo, Sema; Xu, Lisa X; Liang, Jie
2012-01-01
Regulation of cell growth and cell division has a fundamental role in tissue formation, organ development, and cancer progression. Remarkable similarities in the topological distributions were found in a variety of proliferating epithelia in both animals and plants. At the same time, there are species with significantly varied frequency of hexagonal cells. Moreover, local topology has been shown to be disturbed on the boundary between proliferating and quiescent cells, where cells have fewer sides than natural proliferating epithelia. The mechanisms of regulating these topological changes remain poorly understood. In this study, we use a mechanical model to examine the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells. We find that regardless of orientation of division plane, our model can reproduce the commonly observed topological distributions of cells in natural proliferating animal epithelia with the consideration of cell rearrangements. In addition, with different schemes of division plane, we are able to generate different frequency of hexagonal cells, which is consistent with experimental observations. In proliferating cells interfacing quiescent cells, our results show that differential proliferation alone is insufficient to reproduce the local changes in cell topology. Rather, increased tension on the boundary, in conjunction with differential proliferation, can reproduce the observed topological changes. We conclude that both division plane orientation and mechanical forces play important roles in cell topology in animal proliferating epithelia. Moreover, cell memory is also essential for generating specific topological distributions.
Locally minimal topological groups 1
Chasco, María Jesús; Dikranjan, Dikran N.; Außenhofer, Lydia; Domínguez, Xabier
2015-01-01
The aim of this paper is to go deeper into the study of local minimality and its connection to some naturally related properties. A Hausdorff topological group ▫$(G,tau)$▫ is called locally minimal if there exists a neighborhood ▫$U$▫ of 0 in ▫$tau$▫ such that ▫$U$▫ fails to be a neighborhood of zero in any Hausdorff group topology on ▫$G$▫ which is strictly coarser than ▫$tau$▫. Examples of locally minimal groups are all subgroups of Banach-Lie groups, all locally compact groups and all mini...
Topological Mixing with Ghost Rods
2005-01-01
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring...
Topology optimized RF MEMS switches
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...... optimization for an RF MEM capacitive switch. Extensive experimental data confirms that the switches perform as designed by the optimizations, and that our simulation models are accurate. A subset of measurements are presented here. Broader results have been submitted in full journal format....
Topology optimization of flow problems
Gersborg, Allan Roulund
2007-01-01
of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the thesis also contains examples with the 2D Navier-Stokes equation as well as an example with convection dominated....... Although the study of the FVM is carried out using a simple heat conduction problem, the work illuminates and discusses the technicalities of employing the FVM in connection with topology optimization. Finally, parallelized solution methods are investigated using the high performance computing facility...
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
Anguelova, Lilia [Michigan Center for Theoretical Physics, Randall Laboratory, University of Michigan, Ann Arbor, MI 48109-1120 (United States); Medeiros, Paul de [Michigan Center for Theoretical Physics, Randall Laboratory, University of Michigan, Ann Arbor, MI 48109-1120 (United States); Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2005-05-01
We consider the construction of a topological version of F-theory on a particular Spin(7) 8-manifold which is a Calabi-Yau 3-fold times a 2-torus. We write an action for this theory in eight dimensions and reduce it to lower dimensions using Hitchin's gradient flow method. A symmetry of the eight-dimensional theory which follows from modular transformations of the torus induces duality transformations of the variables of the topological A- and B-models. We also consider target space form actions in the presence of background fluxes in six dimensions.
Topological Lensing in Spherical Spaces
Gausmann, E; Luminet, Jean Pierre; Uzan, J P; Weeks, J; Gausmann, Evelise; Lehoucq, Roland; Luminet, Jean-Pierre; Uzan, Jean-Philippe; Weeks, Jeffrey
2001-01-01
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogs of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.
Anguelova, L; Sinkovics, A; Anguelova, Lilia; Medeiros, Paul de; Sinkovics, Annamaria
2005-01-01
We consider the construction of a topological version of F-theory on a particular $Spin(7)$ 8-manifold which is a Calabi-Yau 3-fold times a 2-torus. We write an action for this theory in eight dimensions and reduce it to lower dimensions using Hitchin's gradient flow method. A symmetry of the eight-dimensional theory which follows from modular transformations of the torus induces duality transformations of the variables of the topological A- and B-models. We also consider target space form actions in the presence of background fluxes in six dimensions.
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
Liu Lei [Department of Mathematics, Northwest University, Xian, Shaanxi 710069 (China)], E-mail: liugh105@163.com; Wang Yangeng [Department of Mathematics, Northwest University, Xian, Shaanxi 710069 (China)], E-mail: ygwang62@163.com; Wei Guo [Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372 (United States)], E-mail: guo.wei@uncp.edu
2009-01-15
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.
Of topology and low-dimensionality
2016-11-01
The 2016 Nobel Prize in Physics has been awarded to David Thouless, Duncan Haldane and Michael Kosterlitz ``for theoretical discoveries of topological phase transitions and topological phases of matter''.
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.
New Supersymmetric Localizations from Topological Gravity
Bae, Jinbeom; Rey, Soo-Jong; Rosa, Dario
2015-01-01
Supersymmetric field theories can be studied exactly on suitable off-shell supergravity backgrounds. We show that in two dimensions such backgrounds are identifiable with BRST invariant backgrounds of topological gravity coupled to an abelian topological gauge multiplet. This latter background is required for the consistent coupling of the topological `matter' YM theory to topological gravity. We make use of this topological point of view to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. The BRST invariant topological backgrounds are parametrized by both Killing vectors and $S^1$-equivariant cohomology of the 2-dimensional world-sheet. We reconstruct completely the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are "composite", i.e. they are non-linear functionals of them. We recover all the known localizing 2-dimensional backg...
Jakob Nielsen and His Contributions to Topology
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....
Experimental demonstration of topological error correction
2012-01-01
Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest known tolerable error rate for a local architecture. This scheme makes use of cluster states with topological properties and requires only nearest-neighbour interactions. Here we report the first experimental demonstration of topological error correction with a...
Majorana Fermions and Topology in Superconductors
Sato, Masatoshi; Fujimoto, Satoshi
2016-01-01
Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex cores of topological superconductors, Majorana fermions, which are particles identified with their own anti-particles, appear as Bogoliubov quasiparticles. The existence and stability of Majorana fermions are ensured by bulk topological invariants constrained by the symmetries of the systems. Majorana...
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces
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.
Topological Properties of Spatial Coherence Function
REN Ji-Rong; ZHU Tao; DUAN Yi-Shi
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.
Topology evolution in polymer modification
Kryven, I.; Iedema, P.D.
2013-01-01
A recent numerical method has opened new opportunities in multidimensional population balance modeling. Here, this method is applied to a full three-dimensional population balance model (PBM) describing branching topology evolution driven by chain end to backbone coupling. This process is typical fo
Topology optimization for acoustic problems
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 effects on string vacua
Loaiza-Brito, Oscar
2011-01-01
We review some topological effects on the construction of string flux-vacua. Specifically we study the effects of brane-flux transitions on the stability of D-branes on a generalized tori compactificaction, the transition that a black hole suffers in a background threaded with fluxes and the connections among some Minkowsky vacua solutions.
Topological freeness for Hilbert bimodules
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 and a s...
Topological Schr\\"odinger cats
Dziarmaga, Jacek; Zwolak, Michael
2011-01-01
Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences [1,2]. They are energetically costly (the energy density in their core reaches that of the prior symmetric vacuum) but topologically stable (the whole manifold would have to be rearranged to get rid of the defect). We show how, in a paradigmatic model of a quantum phase transition, a topological defect can be put in a non-local superposition, so that - in a region large compared to the size of its core - the order parameter of the system is "undecided" by being in a quantum superposition of conflicting choices of the broken symmetry. We demonstrate how to exhibit such a "Schr\\"odinger kink" by devising a version of a double-slit experiment suitable for topological defects. Coherence detectable in such experiments will be suppressed as a consequence of interaction with the environment. We analyze environment-induced ...
Magnetic field topology in jets
T. Gardiner
2000-01-01
Full Text Available Presentamos la topolog a del campo magn etico en un chorro pulsado y radia- tivo. Para campos inicialmente helicoidales y variaciones peri odicas de velocidad, encontramos que el campo a lo largo del chorro var a entre mayormente toroidal en los nudos a posiblemente poloidal en el resto de las regiones.
Topological Classification of Lagrangian Fibrations
Sepe, D
2009-01-01
We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of Lagrangian fibrations with base $\\rpr$ and fixed monodromy representation, generalising a construction due to Bates.
Topology of helical fluid flow
Andersen, Morten; Brøns, Morten
2014-01-01
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...
Topological Strings from Quantum Mechanics
Grassi, Alba; Marino, Marcos
2014-01-01
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 theta 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 P2, local P1xP1 and local F1. 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. Phys...
Topological conjugacy of circle diffeomorphisms
1995-01-01
The classical criterion for a circle diffeomorphism to be topologically conjugate to an irrational rigid rotation was given by A. Denjoy. In 1985, one of us (Sullivan) gave a new criterion. There is an example satisfying Denjoy's bounded variation condition rather than Sullivan's Zygmund condition and vice versa. This paper will give the third criterion which is implied by either of the above criteria.
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.
Topological Excitation in Skyrme Theory
DUAN Yi-Shi; ZHANG Xin-Hui; LIU Yu-Xiao
2007-01-01
Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes (splitting, merging, and intersection) during the evolution of the monopoles.
Elementary topology and universal computation
Petrus Potgieter
2008-09-01
Full Text Available This paper attempts to define a general framework for computability on an arbitrary topological space X . The elements of X are taken as primitives in this approach—also for the coding of functions — and, except when X = N, the natural numbers are not used directly.
Topological dynamics and definable groups
Pillay, Anand
2012-01-01
Following the works of Newelski we continue the study of the relations between abstract topological dynamics and generalized stable group theory. We show that the Ellis theory, applied to the action of G(M) on its type space, for G an fsg group in a NIP theory, and M any model, yields the quotient G/G^00.
Crystallographic topology and its applications
Johnson, C.K.; Burnett, M.N. [Oak Ridge National Lab., TN (United States); Dunbar, W.D. [Simon`s Rock Coll., Great Barrington, MA (United States). Div. of Natural Sciences and Mathematics
1996-10-01
Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.
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.
General Recursion and Formal Topology
Silvio Valentini
2010-12-01
Full Text Available It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In this work we propose a new approach to this problem based on the use of inductively generated formal topologies.
Topological design of torsional metamaterials
Vitelli, Vincenzo; Paulose, Jayson; Meeussen, Anne; Topological Mechanics Lab Team
Frameworks - stiff elements with freely hinged joints - model the mechanics of a wide range of natural and artificial structures, including mechanical metamaterials with auxetic and topological properties. The unusual properties of the structure depend crucially on the balance between degrees of freedom associated with the nodes, and the constraints imposed upon them by the connecting elements. Whereas networks of featureless nodes connected by central-force springs have been well-studied, many real-world systems such as frictional granular packings, gear assemblies, and flexible beam meshes incorporate torsional degrees of freedom on the nodes, coupled together with transverse shear forces exerted by the connecting elements. We study the consequences of such torsional constraints on the mechanics of periodic isostatic networks as a foundation for mechanical metamaterials. We demonstrate the existence of soft modes of topological origin, that are protected against disorder or small perturbations of the structure analogously to their counterparts in electronic topological insulators. We have built a lattice of gears connected by rigid beams that provides a real-world demonstration of a torsional metamaterial with topological edge modes and mechanical Weyl modes.
Topological transitions in Ising models
Jalal, Somenath; Lal, Siddhartha
2016-01-01
The thermal dynamics of the two-dimensional Ising model and quantum dynamics of the one-dimensional transverse-field Ising model (TFIM) are mapped to one another through the transfer-matrix formalism. We show that the fermionised TFIM undergoes a Fermi-surface topology-changing Lifshitz transition at its critical point. We identify the degree of freedom which tracks the Lifshitz transition via changes in topological quantum numbers (e.g., Chern number, Berry phase etc.). An emergent $SU(2)$ symmetry at criticality is observed to lead to a topological quantum number different from that which characterises the ordered phase. The topological transition is also understood via a spectral flow thought-experiment in a Thouless charge pump, revealing the bulk-boundary correspondence across the transition. The duality property of the phases and their entanglement content are studied, revealing a holographic relation with the entanglement at criticality. The effects of a non-zero longitudinal field and interactions tha...
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.
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.
Topology optimization of microfluidic mixers
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...
Approximate Reanalysis in Topology Optimization
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...
Probing topology by "heating": Quantized circular dichroism in ultracold atoms.
Tran, Duc Thanh; Dauphin, Alexandre; Grushin, Adolfo G; Zoller, Peter; Goldman, Nathan
2017-08-01
We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (ν) of the populated band: This "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient η0 = ν/ℏ(2), where h = 2π ℏ is Planck's constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter.
Imperfect two-dimensional topological insulator field-effect transistors
Vandenberghe, William G.; Fischetti, Massimo V.
2017-01-01
To overcome the challenge of using two-dimensional materials for nanoelectronic devices, we propose two-dimensional topological insulator field-effect transistors that switch based on the modulation of scattering. We model transistors made of two-dimensional topological insulator ribbons accounting for scattering with phonons and imperfections. In the on-state, the Fermi level lies in the bulk bandgap and the electrons travel ballistically through the topologically protected edge states even in the presence of imperfections. In the off-state the Fermi level moves into the bandgap and electrons suffer from severe back-scattering. An off-current more than two-orders below the on-current is demonstrated and a high on-current is maintained even in the presence of imperfections. At low drain-source bias, the output characteristics are like those of conventional field-effect transistors, at large drain-source bias negative differential resistance is revealed. Complementary n- and p-type devices can be made enabling high-performance and low-power electronic circuits using imperfect two-dimensional topological insulators. PMID:28106059
Fractional topological phase for entangled qudits
Oxman, L E
2010-01-01
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional topological phase for cyclic evolutions in the multiply connected space of maximally entangled states.
Compactness in L-Fuzzy Topological Spaces
Luna-Torres, Joaquin
2010-01-01
We give a definition of compactness in L-fuzzy topological spaces and provide a characterization of compact L-fuzzy topological spaces, where L is a complete quasi-monoidal lattice with some additional structures, and we present a version of Tychonoff's theorem within the category of L-fuzzy topological spaces.
Results on fuzzy soft topological spaces
Mahanta, J
2012-01-01
B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and fuzzy soft interior. Separation axioms and connectedness are introduced and investigated for fuzzy soft topological spaces.
Invertibility in L-Topological Spaces
Anjaly Jose
2014-03-01
Full Text Available In this paper, we extend the concept of invertibility to L-topological spaces and delineate its properties. Then, we study further completely invertible L-topological spaces and introduce two types of invertible L-topologies based on the inverting maps, studying their sums, subspaces and simple extensions.
Excitations in Topological Superfluids and Superconductors
Wu, Hao
In this thesis I present the theoretical work on Fermionic surface states, and %the bulk Bosonic collective excitations in topological superfluids and superconductors. Broken symmetries %Bulk-edge correspondence in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. (Abstract shortened by ProQuest.).
Dual-topology insertion of a dual-topology membrane protein.
Woodall, Nicholas B; Yin, Ying; Bowie, James U
2015-01-01
Some membrane transporters are dual-topology dimers in which the subunits have inverted transmembrane topology. How a cell manages to generate equal populations of two opposite topologies from the same polypeptide chain remains unclear. For the dual-topology transporter EmrE, the evidence to date remains consistent with two extreme models. A post-translational model posits that topology remains malleable after synthesis and becomes fixed once the dimer forms. A second, co-translational model, posits that the protein inserts in both topologies in equal proportions. Here we show that while there is at least some limited topological malleability, the co-translational model likely dominates under normal circumstances.
Traces of differential forms and Hochschild homology
Hübl, Reinhold
1989-01-01
This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.
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.
Topological Insulators in α-Graphyne
WANG Guo-Xiang; HOU Jing-Min
2013-01-01
In this paper,we investigate topological phases of α-graphyne with tight-binding method.By calculating the topological invariant Z2 and the edge states,we identify topological insulators.We present the phase diagrams of α-graphyne with different filling fractions as a function of spin-orbit interaction and the nearest-neighbor hopping energy.We find there exist topological insulators in α-graphyne.We analyze and discuss the characteristics of topological phases of α-graphyne.
Topological Quantum Information Processing Mediated Via Hybrid Topological Insulator Structures
2013-11-13
Matthew J. Gilbert, and Benjamin L. Lev, "Imaging Topologically Protected Transport with Quantum Degenerate Gases," Physical Review B 85 205422...from the Entanglement Spectrum," Physical Review B: Rapid Communications 86, 041401 (2012). 3 Qinglei Meng, Taylor L. Hughes, Matthew J. Gilbert...34 Physical Review B 86, 155110 (2012). 4 Qinglei Meng, Vasudha Shivamoggi, Taylor L. Hughes, Matthew J. Gilbert and S. Vishveshwara, "Fractional Spin
Remarks on the boundary curve of a constant mean curvature topological disc
Brander, David; Lopéz, Rafael
2017-01-01
We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the bo......We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature...
Topological susceptibility in 2-flavor lattice QCD with fixed topology
Chiu, T W; Fukaya, H; Hashimoto, S; Hsieh, T H; Kaneko, T; Matsufuru, H; Noaki, J; Ogawa, K; Onogi, T; Yamada, N
2008-01-01
We determine the topological susceptibility $ \\chi_t $ in the trivial topological sector generated by lattice simulations of two-flavor QCD with overlap Dirac fermion, on a $16^3 \\times 32$ lattice with lattice spacing $\\sim$ 0.12 fm, at six sea quark masses $m_q$ ranging from $m_s/6$ to $m_s$ (where $m_s$ is the physical strange quark mass). The $ \\chi_t $ is extracted from the plateau (at large time separation) of the time-correlation function of the flavor-singlet pseudoscalar meson ($\\eta'$), which arises from the finite size effect due to fixed topology. In the small $m_q$ regime, our result of $\\chi_t$ is proportional to $m_q$ as expected from chiral effective theory. Using the formula $\\chi_t=m_q\\Sigma/N_f$ by Leutwyler-Smilga, we obtain the chiral condensate in $N_f=2$ QCD as $\\Sigma^{\\bar{\\mathrm{MS}}}(\\mathrm{2 GeV})=[252(5)(10) \\mathrm{MeV}]^3 $, in good agreement with our previous result obtained in the $\\epsilon$-regime.
Topological effects on the magnetoconductivity in topological insulators
Sacksteder, Vincent E.; Arnardottir, Kristin Bjorg; Kettemann, Stefan; Shelykh, Ivan A.
2014-12-01
Three-dimensional strong topological insulators (TIs) guarantee the existence of a two-dimensional (2-D) conducting surface state which completely covers the surface of the TI. The TI surface state necessarily wraps around the TI's top, bottom, and two sidewalls, and is therefore topologically distinct from ordinary 2-D electron gases (2-DEGs) which are planar. This has several consequences for the magnetoconductivity Δ σ , a frequently studied measure of weak antilocalization which is sensitive to the quantum coherence time τϕ and to temperature. We show that conduction on the TI sidewalls systematically reduces Δ σ , multiplying it by a factor which is always less than one and decreases in thicker samples. In addition, we present both an analytical formula and numerical results for the tilted-field magnetoconductivity which has been measured in several experiments. Lastly, we predict that as the temperature is reduced Δ σ will enter a wrapped regime where it is sensitive to diffusion processes which make one or more circuits around the TI. In this wrapped regime the magnetoconductivity's dependence on temperature, typically 1 /T2 in 2-DEGs, disappears. We present numerical and analytical predictions for the wrapped regime at both small and large field strengths. The wrapped regime and topological signatures discussed here should be visible in the same samples and at the same temperatures where the Altshuler-Aronov-Spivak (AAS) effect has already been observed, when the measurements are repeated with the magnetic field pointed perpendicularly to the TI's top face.
Inversion-symmetric topological insulators
Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
2011-06-01
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer N, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is “topological.” We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion
The nature of the topological intuition
Sultanova L. B.
2016-01-01
Full Text Available 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-called heuristics, built on the basis of guesswork, obtained by intuition. The author substantiates the conclusion that topological intuition significantly specific compared to a traditional mathematical intuitions of Euclidean geometry. Today topology is a rapidly developing field of modern mathematics, integrates nicely with other sections of mathematical science. In its most general form of the topology can be defined as the branch of mathematics that studies the properties of spatial figures, does not change under deformations. The topological intuition is an instrument for development of topology on the basis of typological heuristics, which is the result of applying topological intuition to the objects topology. The author demonstrates in detail providing with the examples the specificity of topological heuristics and establishes its interconnection with Euclidean geometry. The author draws the conclusion about the fundamentality of topological intuition, and that it, perhaps, is primary in relation to traditionally understood mathematical intuition.
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...
Classical topological order in kagome ice
Macdonald, Andrew J; Melko, Roger G [Department of Physics and Astronomy, University of Waterloo, ON, N2L 3G1 (Canada); Holdsworth, Peter C W [Universite de Lyon, Laboratoire de Physique, Ecole Normale Superieure de Lyon, CNRS, 46 Allee d' Italie, 69364 Lyon Cedex 07 (France)
2011-04-27
We examine the onset of classical topological order in a nearest neighbour kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the ground state using a nonlocal cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related systems.
Universal Cyclic Topology in Polymer Networks.
Wang, Rui; Alexander-Katz, Alfredo; Johnson, Jeremiah A; Olsen, Bradley D
2016-05-01
Polymer networks invariably possess topological defects: loops of different orders which have profound effects on network properties. Here, we demonstrate that all cyclic topologies are a universal function of a single dimensionless parameter characterizing the conditions for network formation. The theory is in excellent agreement with both experimental measurements of hydrogel loop fractions and Monte Carlo simulations without any fitting parameters. We demonstrate the superposition of the dilution effect and chain-length effect on loop formation. The one-to-one correspondence between the network topology and primary loop fraction demonstrates that the entire network topology is characterized by measurement of just primary loops, a single chain topological feature. Different cyclic defects cannot vary independently, in contrast to the intuition that the densities of all topological species are freely adjustable. Quantifying these defects facilitates studying the correlations between the topology and properties of polymer networks, providing a key step in overcoming an outstanding challenge in polymer physics.
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.
Topological methods in the instability problem of Hamiltonian systems
Gidea, M
2005-01-01
We use topological methods to investigate some recently proposed mechanisms of instability (Arnol'd diffusion) in Hamiltonian systems. In these mechanisms, chains of heteroclinic connections between whiskered tori are constructed, based on the existence of a normally hyperbolic manifold $\\Lambda$, so that: (a) the manifold $\\Lambda$ is covered rather densely by transitive tori (possibly of different topology), (b) the manifolds $W^\\st_\\Lambda$, $W^\\un_\\Lambda$ intersect transversally, (c) the systems satisfies some explicit non-degeneracy assumptions, which hold generically. In this paper we use the method of correctly aligned windows to show that, under the assumptions (a), (b) (c), there are orbits that move a significant amount. As a matter of fact, the method presented here does not require that the tori are exactly invariant, only that they are approximately invariant. Hence, compared with the previous papers, we do not need to use KAM theory. This lowers the assumptions on differentiability. Also, the m...
Ultrasonic imaging in liquid sodium: topological energy for damages detection
Lubeigt, E.; Gobillot, G. [CEA, Cadarache (France); Mensah, S.; Chaix, J.F.; Rakotonarivo, S. [LMA, CNRS - UPR 70 51, Aix-en-Provence (France)
2015-07-01
Under-sodium imaging at high temperature is an important requirement in sodium cooled fast reactors during structural inspection. It aims at checking the integrity of immersed structures and assessing component degradation. The work presented in this paper focuses on designing an advanced ultrasound methodology for detecting damages such as deep crack defects. For that purpose, a topological imaging approach was implemented. This method takes advantage of all available prior knowledge about the environment through the integration of differential imaging and time reversal techniques. The quality of the topological energy distribution (the image) is further enhanced by applying a time gating related to each reconstructed pixel. Numerical and experimental results are presented using this method in order to confirm its reliability. These images are compared to a B-scan to emphasize the localization performances of this method. (authors)
Topological vortices in generalized Born-Infeld-Higgs electrodynamics
Casana, R; Rubiera-Garcia, D; Santos, C dos
2015-01-01
A consistent BPS formalism to study the existence of topological axially symmetric vortices in generalized versions of the Born-Infeld-Higgs electrodynamics is implemented. Such a generalization modifies the field dynamics via introduction of three non-negative functions depending only in the Higgs field, namely, $G(|\\phi|)$, $w(|\\phi|) $ and $V(|\\phi|)$. A set of first-order differential equations is attained when these functions satisfy a constraint related to the Ampere law. Such a constraint allows to minimize the system energy in such way that it becomes proportional to the magnetic flux. Our results provides an enhancement of topological vortex solutions in Born-Infeld-Higgs electrodynamics. Finally, we analyze a set of models such that a generalized version of Maxwell-Higgs electrodynamics is recovered in a certain limit of the theory.
Topological vortices in generalized Born-Infeld-Higgs electrodynamics
Casana, R.; Hora, E. da; Rubiera-Garcia, D.; Santos, C. dos
2015-08-01
A consistent BPS formalism to study the existence of topological axially symmetric vortices in generalized versions of the Born-Infeld-Higgs electrodynamics is implemented. Such a generalization modifies the field dynamics via the introduction of three nonnegative functions depending only in the Higgs field, namely, , , and . A set of first-order differential equations is attained when these functions satisfy a constraint related to the Ampère law. Such a constraint allows one to minimize the system's energy in such way that it becomes proportional to the magnetic flux. Our results provides an enhancement of the role of topological vortex solutions in Born-Infeld-Higgs electrodynamics. Finally, we analyze a set of models entailing the recovery of a generalized version of Maxwell-Higgs electrodynamics in a certain limit of the theory.
Formation of current singularity in a topologically constrained plasma
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Huang, Yi-Min [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China.; Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
2016-02-01
Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.
Topological vortices in generalized Born-Infeld-Higgs electrodynamics
Casana, R. [Universidade Federal do Maranhao, Departamento de Fisica, Sao Luis, Maranhao (Brazil); Hora, E. da [Universidade Federal do Maranhao, Departamento de Fisica, Sao Luis, Maranhao (Brazil); Universidade Federal do Maranhao, Coordenadoria Interdisciplinar de Ciencia e Tecnologia, Sao Luis, Maranhao (Brazil); Rubiera-Garcia, D. [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Santos, C. dos [Faculdade de Ciencias da Universidade do Porto, Centro de Fisica e Departamento de Fisica e Astronomia, Porto (Portugal)
2015-08-15
A consistent BPS formalism to study the existence of topological axially symmetric vortices in generalized versions of the Born-Infeld-Higgs electrodynamics is implemented. Such a generalization modifies the field dynamics via the introduction of three nonnegative functions depending only in the Higgs field, namely,G(vertical stroke φ vertical stroke), w(vertical stroke φ vertical stroke), and V (vertical stroke φ vertical stroke). A set of first-order differential equations is attained when these functions satisfy a constraint related to the Ampere law. Such a constraint allows one to minimize the system's energy in such way that it becomes proportional to the magnetic flux. Our results provides an enhancement of the role of topological vortex solutions in Born-Infeld-Higgs electrodynamics. Finally, we analyze a set of models entailing the recovery of a generalized version of Maxwell-Higgs electrodynamics in a certain limit of the theory. (orig.)
Tune the topology to create or destroy patterns
Asllani, Malbor; Fanelli, Duccio
2016-01-01
We consider the dynamics of a reaction-diffusion system on a multigraph. The species share the same set of nodes but can access different links to explore the embedding spatial support. By acting on the topology of the networks we can control the ability of the system to self-organise in macroscopic patterns, emerging as a symmetry breaking instability of an homogeneous fixed point. Two different cases study are considered: on the one side, we produce a global modification of the networks, starting from the limiting setting where species are hosted on the same graph. On the other, we consider the effect of inserting just one additional single link to differentiate the two graphs. In both cases, patterns can be generated or destroyed, as follows the imposed, small, topological perturbation. Approximate analytical formulae allows to grasp the essence of the phenomenon and can potentially inspire innovative control strategies to shape the macroscopic dynamics on multigraph networks
Streamline topologies near a fixed wall using normal forms
Hartnack, Johan
1999-01-01
Streamline patterns and their bifurcations in two-dimensional incompressible viscous flow in the vicinity of a fixed wall have been investigated from a topological point of view by Bakker [11]. Bakker's work is revisited in a more general setting allowing a curvature of the fixed wall and a time...... dependence of the streamlines. The velocity field is expanded at a point on the wall, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate changes results in a much simplified system of differential equations for the streamlines (a normal form......) encapsulating all the features of the original system. From this, a complete description of bifurcations up to codimension three close to a simple linear degeneracy is obtained. Further, the case of a non-simple degeneracy is considered. Finally the effect of the Navier-Stokes equations on the local topology...
Detecting topological phases in silicene by anomalous Nernst effect
Xu, Yafang; Zhou, Xingfei; Jin, Guojun
2016-05-01
Silicene undergoes various topological phases under the interplay of intrinsic spin-orbit coupling, perpendicular electric field, and off-resonant light. We propose that the abundant topological phases can be distinguished by measuring the Nernst conductivity even at room temperature, and their phase boundaries can be determined by differentiating the charge and spin Nernst conductivities. By modulating the electric and light fields, pure spin polarized, valley polarized, and even spin-valley polarized Nernst currents can be generated. As Nernst conductivity is zero for linear polarized light, silicene can act as an optically controlled spin and valley field-effect transistor. Similar investigations can be extended from silicene to germanene and stanene, and a comparison is made for the anomalous thermomagnetic figure of merits between them. These results will facilitate potential applications in spin and valley caloritronics.
Rings in random environments: sensing disorder through topology.
Michieletto, Davide; Baiesi, Marco; Orlandini, Enzo; Turner, Matthew S
2015-02-14
In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby generating a disordered environment. Changes in the microscopic structure of the gel are captured by measuring the electrophoretic mobility of ring polymers moving through the medium, while their linear counterparts provide a control system as we show they are insensitive to these changes. We show that ring polymers provide a novel, non-invasive way of exploiting topology to sense microscopic disorder. Finally, we compare the results from the simulations with an analytical model for the non-equilibrium differential mobility, and find a striking agreement between simulation and theory.
Streamline topologies and their bifurcations for mixed convective peristaltic flow
Z. Asghar
2015-09-01
Full Text Available In this work our focus is on streamlines patterns and their bifurcations for mixed convective peristaltic flow of Newtonian fluid with heat transfer. The flow is considered in a two dimensional symmetric channel and the governing equations are simplified under widely taken assumptions of large wavelength and low Reynolds number in a wave frame of reference. In order to study the streamlines patterns, a system of nonlinear autonomous differential equations are established and dynamical systems approach is used to discuss the local bifurcations and their topological changes. We have discussed all types of bifurcations and their topological changes are presented graphically. We found that the vortices contract along the vertical direction whereas they expand along horizontal direction. A global bifurcations diagram is used to summarize the bifurcations. The trapping and backward flow regions are mainly affected by increasing Grashof number and constant heat source parameter in such a way that trapping region increases whereas backward flow region shrinks.
Tune the topology to create or destroy patterns
Asllani, Malbor; Carletti, Timoteo; Fanelli, Duccio
2016-12-01
We consider the dynamics of a reaction-diffusion system on a multigraph. The species share the same set of nodes but can access different links to explore the embedding spatial support. By acting on the topology of the networks we can control the ability of the system to self-organise in macroscopic patterns, emerging as a symmetry breaking instability of an homogeneous fixed point. Two different cases study are considered: on the one side, we produce a global modification of the networks, starting from the limiting setting where species are hosted on the same graph. On the other, we consider the effect of inserting just one additional single link to differentiate the two graphs. In both cases, patterns can be generated or destroyed, as follows the imposed, small, topological perturbation. Approximate analytical formulae allow to grasp the essence of the phenomenon and can potentially inspire innovative control strategies to shape the macroscopic dynamics on multigraph networks.
Noncommutative topology and the world's simplest index theorem
van Erp, Erik
2010-01-01
This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how this theorem is a special case of a much more general index theorem for subelliptic operators on contact manifolds. Finally we discuss the noncommutative topology that is employed in the proof of this theorem. We present these results as an instance in which noncommutative topology is fruitful in proving a very explicit (analytic/geometric) classical result.
Topological open strings on orbifolds
Bouchard, Vincent; Marino, Marcos; Pasquetti, Sara
2008-01-01
We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest. We exemplify this procedure for the C^3/Z_3 orbifold point of local P^2, where we present results for topological string amplitudes for genus zero and up to three holes, and for the one-holed torus. These amplitudes can be understood as generating functions for either open orbifold Gromov-Witten invariants of C^3/Z_3, or correlation functions in the orbifold CFT involving insertions of both bulk and boundary operators.
Topological recursion and mirror curves
Bouchard, Vincent
2012-01-01
We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding Gromov-Witten invariants, which can be encoded in powers of the MacMahon function. As a result, we extend the scope of the "remodeling conjecture" to the full free energies, including the constant contributions. In the process we study how the pair of pants decomposition of the mirror curves plays an important role in the topological recursion. We also show that the free energies are not, strictly speaking, symplectic invariants, and that the recursive construction of the free energies does not commute with certain limits of mirror curves.
Interior Operators and Topological Categories
Luna-Torres, Joaquin
2010-01-01
The introduction of the categorical notion of closure operators has unified various important notions and has led to interesting examples and applications in diverse areas of mathematics (see for example, Dikranjan and Tholen (\\cite{DT})). For a topological space it is well-known that the associated closure and interior operators provide equivalent descriptions of the topology, but this is not true in general. So, it makes sense to define and study the notion of interior operators $I$ in the context of a category $\\mathfrak C$ and a fixed class $\\mathcal M$ of monomorphisms in $\\mathfrak C$ closed under composition in such a way that $\\mathfrak C$ is finitely $\\mathcal M$-complete and the inverse images of morphisms have both left and right adjoint, which is the purpose of this paper.
Topology Optimization for Additive Manufacturing
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......-portant AM-related manufacturing constraints are presented. These constraints are di-vided into directional and non-directional constraints. Non-directional constraints include minimum/uniform length scale and a cavity constraint. It is shown that modified filter boundary conditions are required in order...
Topics in Open Topological Strings
Prudenziati, Andrea
2010-01-01
This thesis is based on some selected topics in open topological string theory which I have worked on during my Ph.D. It comprises an introductory part where I have focused on the points most needed for the later chapters, trading completeness for conciseness and clarity. Then, following [12], we discuss tadpole cancellation for topological strings where we mainly show how its implementation is needed for ensuring the same "odd" moduli decoupling encountered in the closed theory. Next we move to analyse how the open and closed effective field theories for the B model interact writing the complete Lagrangian. We first check it deriving some already known tree level amplitudes in term of target space quantities, and then we extend the recipe to new results; later we implement open closed duality from a target field theory perspective. This last subject is also analysed from a worldsheet point of view extending the analysis of [13]. Some ideas for future research are briefly reported.
Reconfigurable Microwave Photonic Topological Insulator
Goryachev, Maxim; Tobar, Michael E.
2016-12-01
Using full 3D finite-element simulation and underlining Hamiltonian models, we demonstrate reconfigurable photonic analogues of topological insulators on a regular lattice of tunable posts in a reentrant 3D lumped element-type system. The tunability allows a dynamical in situ change of media chirality and other properties via the alteration of the same parameter for all posts, and as a result, great flexibility in the choice of bulk-edge configurations. Additionally, one-way photon transport without an external magnetic field is demonstrated. The ideas are illustrated by using both full finite-element simulation as well as simplified harmonic oscillator models. Dynamical reconfigurability of the proposed systems paves the way to a class of systems that can be employed for random access, topological signal processing, and sensing.
Reconfigurable Microwave Photonic Topological Insulator
Goryachev, Maxim
2016-01-01
We demonstrate reconfigurable photonic analogues of topological insulators on a regular lattice of tunable posts in a re-entrant 3D lumped element type system. The tunability allows dynamical {\\it in-situ} change of media chirality and other properties via change of a single post parameter, and as a result, great flexibility in choice of bulk/edge configurations. Additionally, one way photon transport without external magnetic field is demonstrated. The ideas are illustrated by using both full finite element simulation as well as simplified harmonic oscillator models. Reconfigurability of the proposed systems paves the wave to a new class of systems that can be employed for random access, topological signal processing and sensing.
A free topology safeguards network
Kadner, S.P.; Resnik, W.M. [Aquila Technologies Group, Inc., Albuquerque, NM (United States); Schurig, A. [Communications Foundation, Orem, UT (United States)
1995-12-31
Free Topology Network technology provides cost reduction benefits as well as flexibility in safeguards applications. Power line communications technologies have proven viability for transmission and reception of safeguards data, including surveillance photographs, the source of the largest data files. In the future, enhancements will be made to the technology that should boost both performance and flexibility. Work is already underway to achieve higher data rates over power line communications eventually, it should be possible to reach data rates of one million bits per second or higher. Also, the use of technologies such as Novell Embedded Systems Technology (NEST) and Echelon LON technology will allow a greater number of safeguards technologies to become resident on the Free Topology Safeguards Network.
Topological inflation with graceful exit
Marunović, Anja
2015-01-01
We investigate a class of models of topological inflation in which a super-Hubble-sized global monopole seeds inflation. These models are attractive since inflation starts from rather generic initial conditions, but their not so attractive feature is that, unless symmetry is again restored, inflation never ends. In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation. While the monopole core grows during inflation, the growth stops after inflation, such that the monopole eventually enters the Hubble radius, and shrinks to its Minkowski space size, rendering it immaterial for the subsequent Universe's dynamics. Furthermore, we find that our model can produce cosmological perturbations that source CMB temperature fluctuations and seed large scale structure statistically consistent (within one standard...
Topological Insulator Nanowires and Nanoribbons
Kong, D.S.
2010-06-02
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi{sub 2}Se{sub 3} 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 Bi{sub 2}Se{sub 3} nanomaterials with a variety of morphologies. The synthesis of Bi{sub 2}Se{sub 3} 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 [11-20] direction with a rectangular crosssection 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 {approx}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 orbitals 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.
Noncommutative Topological Theories of Gravity
García-Compéan, H; Ramírez, C; Sabido, M
2003-01-01
The possibility of noncommutative gravity arising in the same manner as Yang-Mills theory is explored. Using the Seiberg-Witten map we give a noncommutative version of topological gravity, from which the Euler characteristic and the signature are obtained, in both cases up to third order in the noncommutativity parameter. Finally, we discuss possible ways towards obtaining noncommutative gravitational instantons and to detect local and global gravitational anomalies within this context.
Topological sigma models on supermanifolds
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.
Topological sigma models on supermanifolds
Jia, Bei
2017-02-01
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.
Topology Optimization of Nanophotonic Devices
Yang, Lirong
are appropriate for problems where the power is to be maximized or minimized at a few frequencies, without regards on the detailed profile of the optical pulse or the need of large amount of frequency samplings. The design of slow light couplers connecting ridge waveguides and the photonic crystal waveguides...... 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....
Topological Sigma Models On Supermanifolds
Jia, Bei
2016-01-01
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.
Some Topological Properties of Anyons
CAO Zhen-Bin; LIU Yu-Xiao; DUAN Yi-Shi
2008-01-01
In this paper, starting with the well known U(1) Chern-Simons Lagrangian and the covariant derivative of a complex scalar matter field, we give a detailed discussion of some topological properties of anyons. We show that the "basic" charge carried by anyons has an inner structure and can be decomposed in terms of the Chern-Simons coupling and the gauge coupling constants of the theory. Also some incorrect results obtained in the literature are revised.
Time-Space Topology Optimization
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 expansion and boundary conditions
Eynard, Bertrand
2008-01-01
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.
Topology optimized electrothermal polysilicon microgrippers
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....... The accuracy of the finite element model is verified by comparison of simulated and measured displacement vs. bias voltage curves. A considerable improvement in the mechanical stiffness is indicated by AFM force measurements, being 9 times higher compared to the conventional three-beam actuator. (C) 2008...
New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem
Giordano, Paolo
2012-01-01
Based on the theory of Fermat reals we introduce new topologies on spaces of Colombeau generalized points and derive some of their fundamental properties. In particular, we obtain metric topologies on the space of near-standard generalized points that induce the standard Euclidean topology on the reals. We also give a new description of the sharp topology in terms of the natural extension of the absolute value (or of the defining semi-norms in the case of locally convex spaces) that allows to preserve a number of classical notions. Building on a new point value characterization of Colombeau generalized functions we prove a Fermat-Reyes theorem that forms the basis of an approach to differentiation on spaces of generalized functions close to the classical one.
Topological Quantization of k-Dimensional Topological Defects and Motion Equations
YANG Guo-Hong; JIANG Ying; DUAN Yi-Shi
2001-01-01
Using the φ-mapping method and kth-order topological tensor current theory, we present a unified theory of describing k-dimensional topological defects and obtain their topological quantization and motion equations. It is shown that the inner structure of the topological tensor current is just the dynamic form of the topological defects, which are generated from the zeros of the m-component order parameter vector field. In this dynamic form, the topological defects are topologically quantized naturally and the topological quantum numbers are determined by the Hopf indices and the Brouwer degrees. As the generalization of Nielsen's Lagrangian and Nambu's action for strings, the action and the motion equations of the topological defects are also derived.
Rigidity of the topological dual of spaces of formal series with respect to product topologies
Poinsot, Laurent
2010-01-01
Even in spaces of formal power series is required a topology in order to legitimate some operations, in particular to compute infinite summations. Many topologies can be exploited for different purposes. Combinatorists and algebraists may think to usual order topologies, or the product topology induced by a discrete coefficient field, or some inverse limit topologies. Analysists will take into account the valued field structure of real or complex numbers. As the main result of this paper we prove that the topological dual spaces of formal power series, relative to the class of product topologies with respect to Hausdorff field topologies on the coefficient field, are all the same, namely the space of polynomials. As a consequence, this kind of rigidity forces linear maps, continuous for any (and then for all) of those topologies, to be defined by very particular infinite matrices similar to row-finite matrices.
Is a color superconductor topological?
Nishida, Yusuke
2010-01-01
A fully gapped state of matter, whether insulator or superconductor, can be asked if it is topologically trivial or nontrivial. Here we investigate topological properties of superconducting Dirac fermions in 3D having a color superconductor as an application. In the chiral limit, when the pairing gap is parity even, the right-handed and left-handed sectors of the free space Hamiltonian have nontrivial topological charges with opposite signs. Accordingly, a vortex line in the superconductor supports localized gapless right-handed and left-handed fermions with the dispersion relations E=+/-vp_z (v is a parameter dependent velocity) and thus propagating in opposite directions along the vortex line. However, the presence of the fermion mass immediately opens up a mass gap for such localized fermions and the dispersion relations become E=+/-v(m^2+p_z^2)^(1/2). When the pairing gap is parity odd, the situation is qualitatively different. The right-handed and left-handed sectors of the free space Hamiltonian in the ...
Cai, Rong-Gen; Wu, Yue-Liang; Zhang, Yun-Long
2016-01-01
In this paper we investigate the $(2+1)$-dimensional topological non-Fermi liquid in strongly correlated electron system, which has a holographic dual description by Einstein gravity in $(3+1)$-dimensional anti-de Sitter (AdS) space-time. In a dyonic Reissner-Nordstrom black hole background, we consider a Dirac fermion coupled to the background $U(1)$ gauge theory and an intrinsic chiral gauge field $b_M$ induced by chiral anomaly. UV retarded Green's function of the charged fermion in the UV boundary from AdS$_4$ gravity is calculated, by imposing in-falling wave condition at the horizon. We also obtain IR correlation function of the charged fermion at the IR boundary arising from the near horizon geometry of the topological black hole with index $k=0,\\pm 1$. By using the UV retarded Green's function and IR correlation function, we analyze the low frequency behavior of the topological non-Fermi liquid at zero and finite temperatures, especially the relevant non-Fermi liquid behavior near the quantum critical...
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.
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: ...
Topology of the Electroweak Vacua
Gripaios, Ben
2016-01-01
In the Standard Model, the electroweak symmetry is broken by a complex, $SU(2)$-doublet Higgs field and the vacuum manifold $SU(2)\\times U(1)/U(1)$ has the topology of a 3-sphere. We remark that there exist alternative effective field theory descriptions that can be fully consistent with existing collider data, but in which the vacuum manifold is homeomorphic to an arbitrary non-trivial principal $U(1)$-bundle over a 2-sphere. These alternatives have non-trivial fundamental group and so lead to topologically-stable electroweak strings. Perhaps the most plausible alternative to $S^3$ is the manifold $\\mathbb{R}P^3$ (with fundamental group $\\mathbb{Z}/2$), since it allows custodial protection of gauge boson masses and their couplings to fermions. Searches for such strings may thus be regarded as independent, and qualitatively different, precision tests of the SM, in that they are (thus far) astrophysical in nature, and test the global topology, rather than the local geometry, of the electroweak vacua.
Integrated Differential Three-Level High-Voltage Pulser Output Stage for CMUTs
Llimos Muntal, Pere; Larsen, Dennis Øland; Jørgensen, Ivan Harald Holger;
2015-01-01
A new integrated differential three-level highvoltage pulser output stage to drive capacitive micromachined ultrasonic transducers (CMUTs) is proposed in this paper. A topology comparison between the new differential output stage and the most commonly used single-ended topology is performed...
Einstein Metrics, Four-Manifolds, and Differential Topology
2004-01-01
This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of Riemannian variational problems on 4-manifolds.
A convenient differential category
Blute, Richard; Tasson, Christine
2010-01-01
In this paper, we show that the category of Mackey-complete, separated, topological convex bornological vector spaces and bornological linear maps is a differential category. Such spaces were introduced by Fr\\"olicher and Kriegl, where they were called convenient vector spaces. While much of the structure necessary to demonstrate this observation is already contained in Fr\\"olicher and Kriegl's book, we here give a new interpretation of the category of convenient vector spaces as a model of the differential linear logic of Ehrhard and Regnier. Rather than base our proof on the abstract categorical structure presented by Fr\\"olicher and Kriegl, we prefer to focus on the bornological structure of convenient vector spaces. We believe bornological structures will ultimately yield a wide variety of models of differential logics.
Hyperbolic differential operators and related problems
Ancona, Vincenzo
2003-01-01
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the top
GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES
无
2011-01-01
This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.
Circuit topology of proteins and nucleic acids.
Mashaghi, Alireza; van Wijk, Roeland J; Tans, Sander J
2014-09-02
Folded biomolecules display a bewildering structural complexity and diversity. They have therefore been analyzed in terms of generic topological features. For instance, folded proteins may be knotted, have beta-strands arranged into a Greek-key motif, or display high contact order. In this perspective, we present a method to formally describe the topology of all folded linear chains and hence provide a general classification and analysis framework for a range of biomolecules. Moreover, by identifying the fundamental rules that intrachain contacts must obey, the method establishes the topological constraints of folded linear chains. We also briefly illustrate how this circuit topology notion can be applied to study the equivalence of folded chains, the engineering of artificial RNA structures and DNA origami, the topological structure of genomes, and the role of topology in protein folding.
Observation of photonic anomalous Floquet topological insulators
Maczewsky, Lukas J.; Zeuner, Julia M.; Nolte, Stefan; Szameit, Alexander
2017-01-01
Topological insulators are a new class of materials that exhibit robust and scatter-free transport along their edges -- independently of the fine details of the system and of the edge -- due to topological protection. To classify the topological character of two-dimensional systems without additional symmetries, one commonly uses Chern numbers, as their sum computed from all bands below a specific bandgap is equal to the net number of chiral edge modes traversing this gap. However, this is strictly valid only in settings with static Hamiltonians. The Chern numbers do not give a full characterization of the topological properties of periodically driven systems. In our work, we implement a system where chiral edge modes exist although the Chern numbers of all bands are zero. We employ periodically driven photonic waveguide lattices and demonstrate topologically protected scatter-free edge transport in such anomalous Floquet topological insulators.
Topological phase transitions in superradiance lattices
Wang, Da-Wei; Yuan, Luqi; Liu, Ren-Bao; Zhu, Shi-Yao
2015-01-01
The discovery of the quantum Hall effect (QHE) reveals a new class of matter phases, topological insulators (TI's), which have been extensively studied in solid-state materials and recently in photonic structures, time-periodic systems and optical lattices of cold atoms. All these topological systems are lattices in real space. Our recent study shows that Scully's timed Dicke states (TDS) can form a superradiance lattice (SL) in momentum space. Here we report the discovery of topological phase transitions in a two-dimensional SL in electromagnetically induced transparency (EIT). By periodically modulating the three EIT coupling fields, we can create a Haldane model with in-situ tunable topological properties. The Chern numbers of the energy bands and hence the topological properties of the SL manifest themselves in the contrast between diffraction signals emitted by superradiant TDS. The topological superradiance lattices (TSL) provide a controllable platform for simulating exotic phenomena in condensed matte...
Photonic simulation of topological excitations in metamaterials.
Tan, Wei; Sun, Yong; Chen, Hong; Shen, Shun-Qing
2014-01-23
Condensed matter systems with topological order and metamaterials with left-handed chirality have attracted recently extensive interests in the fields of physics and optics. So far the topological order and chirality of electromagnetic wave are two independent concepts, and there is no work to address their connection. Here we propose to establish the relation between the topological order in condensed matter systems and the chirality in metamaterials, by mapping explicitly Maxwell's equations to the Dirac equation in one dimension. We report an experimental implement of the band inversion in the Dirac equation, which accompanies change of chirality of electromagnetic wave in metamaterials, and the first microwave measurement of topological excitations and topological phases in one dimension. Our finding provides a proof-of-principle example that electromagnetic wave in the metamaterials can be used to simulate the topological order in condensed matter systems and quantum phenomena in relativistic quantum mechanics in a controlled laboratory environment.
Topological Thouless pumping of ultracold fermions
Nakajima, Shuta; Tomita, Takafumi; Taie, Shintaro; Ichinose, Tomohiro; Ozawa, Hideki; Wang, Lei; Troyer, Matthias; Takahashi, Yoshiro
2016-04-01
An electron gas in a one-dimensional periodic potential can be transported even in the absence of a voltage bias if the potential is slowly and periodically modulated in time. Remarkably, the transferred charge per cycle is sensitive only to the topology of the path in parameter space. Although this so-called Thouless charge pump was first proposed more than thirty years ago, it has not yet been realized. Here we report the demonstration of topological Thouless pumping using ultracold fermionic atoms in a dynamically controlled optical superlattice. We observe a shift of the atomic cloud as a result of pumping, and extract the topological invariance of the pumping process from this shift. We demonstrate the topological nature of the Thouless pump by varying the topology of the pumping path and verify that the topological pump indeed works in the quantum regime by varying the speed and temperature.
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...
Iron-Based Superconductors as topological matter
Hu, Jiangping
We show the existence of non-trivial topological properties in Iron-based superconductors. Several examples are provided, including (1) the single layer FeSe grown on SrTiO3 substrate, in which an topological insulator phase exists due to the band inversion at M point; (2) CaFeAs2, a staggered intercalation compound that integrates both quantum spin hall and superconductivity in which the nontrivial topology stems from the chain-like As layers away from FeAs layers; (3) the Fe(Te,Se) thin films in which the nontrivial Z2 topological invariance originates from the parity exchange at Γ point that is controlled by the Te(Se) height; (4 nontrivial topology that is driven by the nematic order in FeSe. These results lay ground for integrating high Tc superconductivity with topological properties to realize new emergent phenomena, such as majorana particles, in iron-based high temperature superconductors
Topological data analysis of biological aggregation models.
Topaz, Chad M; Ziegelmeier, Lori; Halverson, Tom
2015-01-01
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.
Fractals on IPv6 Network Topology
Bo Yang
2013-02-01
Full Text Available The coarse-grained renormalization and the fractal analysis of the Internet macroscopic topology can help people better understand the relationship between the part and whole of the Internet, and it is significant for people to understand the essence of the research object through a small amount of information. Aiming at the complexity of Internet IPv6 IP-level topology, we put forward a method of core-threshold coarse-grained to renormalize its topology. By analyzing the degree distribution and degree correlation characteristics in each k-core network topology, the scale invariance of the networks of coarse-grained renormalization was illustrated. The fractal dimension of Internet IPv6 IP-level topology was further computed which shows that the Internet IPv6 IP-level topology has got fractals.
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 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.
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...
On closed embeddings of free topological algebras
2012-01-01
Let $\\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\\mathcal E$ (which means that $\\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all completely regular topological $\\mathcal E$-algebras algebraically isomorphic to members of $\\mathcal K$). For a topological space $X$ by $F(X)$ we denote the free universal $\\mathcal E$-algebra over $X$ in the class $\\mathcal K$. Using some extension propert...
Stability of Topological Persistence for Domains
2006-02-01
University Press, 2002. [7] J. Milnor. Morse Theory. Princeton University Press, 1963. [8] Joseph J. Rotman . An Introduction to Algebraic Topology...groups For a topological space , the th homology group is an algebraic encoding of the connectivity of in the th dimension. For a good...persistence and simplification. In Proc. 41st Annu. IEEE Sympos. Found. Comput. Sci., pages 454–463, 2000. [6] A. Hatcher. Algebraic Topology. Cambridge
Analysis of topology changes in multibody systems
2009-01-01
Mechanical systems with time-varying topology appear frequently in natural or human-made artificial systems. The nature of topology transitions is a key characteristic in the functioning of such systems. In this paper, a concept to decouple kinematic and kinetic quantities at the time of topology transition is used. This approach is based on the use of impulsive bilateral constraints and it is a useful tool for the analysis of energy redistribution and velocity change when these constraint...
Transversality theorems for the weak topology
2011-01-01
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here we first discuss the Thom transversality theorem for the weak topology and then give a similiar kind of result for the weak topology, under very weak hypotheses. Recently sever...
Preimage entropy dimension of topological dynamical systems
Lei LIU; 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...
A Relational Localisation Theory for Topological Algebras
2012-01-01
In this thesis, we develop a relational localisation theory for topological algebras, i.e., a theory that studies local approximations of a topological algebra’s relational counterpart. In order to provide an appropriate framework for our considerations, we first introduce a general Galois theory between continuous functions and closed relations on an arbitrary topological space. Subsequently to this rather foundational discussion, we establish the desired localisation theory comprising the i...
Interval Valued Neutrosophic Soft Topological Spaces
Anjan Mukherjee
2014-12-01
Full Text Available In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology. We also define interval valued neutrosophic interior and closer of an interval valued neutrosophic soft set. Some theorems and examples are cites. Interval valued neutrosophic soft subspace topology are studied. Some examples and theorems regarding this concept are presented.
A Topological Model for Parallel Algorithm Design
1991-09-01
New York, 1989. 108. J. Dugundji . Topology . Allen and Bacon, Rockleigh, NJ, 1966. 109. R. Duncan. A Survey of Parallel Computer Architectures. IEEE...Approved for public release; distribition unlimited 4N1f-e AFIT/DS/ENG/91-02 A TOPOLOGICAL MODEL FOR PARALLEL ALGORITHM DESIGN DISSERTATION Presented to...DC 20503. 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS A Topological Model For Parallel Algorithm Design 6. AUTHOR(S) Jeffrey A Simmers, Captain, USAF 7
Signature of Topological Phases in Zitterbewegung
Ghosh, S.
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.
Simultaneous topology optimization of structures and supports
Buhl, Thomas
2002-01-01
The purpose of this paper is to demonstrate a method for and the benefits of simultaneously designing structure and support distribution using topology optimization. The support conditions are included in the topology optimization by introducing, a new set of design variables that represents...... cost of supports in a design domain. Other examples show that more efficient mechanisms are obtained by introducing the support conditions in the topology optimization problem....
Zhao, Y. X.; Wang, Z. D.
2014-02-01
A topology-intrinsic connection between the stabilities of Fermi surfaces (FSs) and topological insulators/superconductors (TIs/TSCs) is revealed. First, through revealing the topological difference of the roles played by the time-reversal (or particle-hole) symmetry respectively on FSs and TIs/TSCs, a one-to-one relation between the topological types of FSs and TIs/TSCs is rigorously derived by two distinct methods with one relying on the direct evaluation of topological invariants and the other on K theory. Secondly, we propose and prove a general index theorem that relates the topological charge of FSs on the natural boundary of a TI/TSC to its bulk topological number. In the proof, FSs of all codimensions for all symmetry classes and topological types are systematically constructed by Dirac matrices. Moreover, implications of the general index theorem on the boundary quasiparticles are also addressed.
Emergence of magnetic topological states in topological insulators doped with magnetic impurities
Tran, Minh-Tien; Nguyen, Hong-Son; Le, Duc-Anh
2016-04-01
Emergence of the topological invariant and the magnetic moment in topological insulators doped with magnetic impurities is studied based on a mutual cooperation between the spin-orbit coupling of electrons and the spin exchange of these electrons with magnetic impurity moments. The mutual cooperation is realized based on the Kane-Mele model in the presence of magnetic impurities. The topological invariants and the spontaneous magnetization are self-consistently determined within the dynamical mean-field theory. We find different magnetic topological phase transitions, depending on the electron filling. At half filling an antiferromagnetic topological insulator, which exhibits the quantum spin Hall effect, exists in the phase region between the paramagnetic topological insulator and the trivially topological antiferromagnetic insulator. At quarter and three-quarter fillings, a ferromagnetic topological insulator, which exhibits the quantum anomalous Hall effect, occurs in the strong spin-exchange regime.