Supersymmetric Quantum Mechanics and Topology

International Nuclear Information System (INIS)

Wasay, Muhammad Abdul

2016-01-01

Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.

Topological string partition functions as polynomials

International Nuclear Information System (INIS)

Yamaguchi, Satoshi; Yau Shingtung

2004-01-01

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus. (author)

Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Chekhov, Leonid O.; Penner, Robert

2013-01-01

and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given...... topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly for genera less than four....

Explicitly computing geodetic coordinates from Cartesian coordinates

Science.gov (United States)

Zeng, Huaien

2013-04-01

This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.

Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation

Directory of Open Access Journals (Sweden)

V. Kantser

2011-10-01

Full Text Available A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin braid group -- the mathematical basis of topological quantum computation (TQC. Vector spaces of TQC correspond to associated strings of particle interactions, and TQC operates its calculations on braided strings of special physical quasiparticles -- anyons -- with non-Abelian statistics. The physical platform of TQC is to use the topological quantum numbers of such small groups of anyons as qubits and to perform operations on these qubits by exchanging the anyons, both within the groups that form the qubits and, for multi-qubit gates, between groups. By braiding two or more anyons, they acquire up a topological phase or Berry phase similar to that found in the Aharonov-Bohm effect. Topological matter such as fractional quantum Hall systems and novel discovered topological insulators open the way to form system of anyons -- Majorana fermions -- with the unique property of encoding and processing quantum information in a naturally fault-tolerant way. In the topological insulators, due to its fundamental attribute of topological surface state occurrence of the bound, Majorana fermions are generated at its heterocontact with superconductors. One of the key operations of TQC -- braiding of non-Abelian anyons: it is illustrated how it can be implemented in one-dimensional topological isolator wire networks.

Mirror of the refined topological vertex from a matrix model

CERN Document Server

Eynard, B

2011-01-01

We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined vertex. With the same method we also find a matrix model for the strip geometry, and we find its mirror curve. The fact that there is a matrix model shows that the refined topological string amplitudes also satisfy the remodeling the B-model construction.

Architectural design for a topological cluster state quantum computer

International Nuclear Information System (INIS)

Devitt, Simon J; Munro, William J; Nemoto, Kae; Fowler, Austin G; Stephens, Ashley M; Greentree, Andrew D; Hollenberg, Lloyd C L

2009-01-01

The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly non-trivial problem. Scalability in quantum information processing is not just a problem of qubit manufacturing and control but it crucially depends on the ability to adapt advanced techniques in quantum information theory, such as error correction, to the experimental restrictions of assembling qubit arrays into the millions. In this paper, we introduce a feasible architectural design for large scale quantum computation in optical systems. We combine the recent developments in topological cluster state computation with the photonic module, a simple chip-based device that can be used as a fundamental building block for a large-scale computer. The integration of the topological cluster model with this comparatively simple operational element addresses many significant issues in scalable computing and leads to a promising modular architecture with complete integration of active error correction, exhibiting high fault-tolerant thresholds.

Computational Power of Symmetry-Protected Topological Phases.

Science.gov (United States)

Stephen, David T; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert

2017-07-07

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Lectures on the Topological Vertex

CERN Document Server

Mariño, M

2008-01-01

In this lectures, I will summarize the approach to Gromov–Witten invariants on toric Calabi–Yau threefolds based on large N dualities. Since the large N duality/topological vertex approach computes Gromov–Witten invariants in terms of Chern–Simons knot and link invariants, Sect. 2 is devoted to a review of these. Section 3 reviews topological strings and Gromov–Witten invariants, and gives some information about the open string case. Section 4 introduces the class of geometries we will deal with, namely toric (noncompact) Calabi–Yau manifolds, and we present a useful graphical way to represent these manifolds which constitutes the geometric core of the theory of the topological vertex. Finally, in Sect. 5, we define the vertex and present some explicit formulae for it and some simple applications. A brief Appendix contains useful information about symmetric polynomials. It has not been possible to present all the relevant background and physical derivations in this set of lectures. However, these...

An Invitation to the Mathematics of Topological Quantum Computation

International Nuclear Information System (INIS)

Rowell, E C

2016-01-01

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials. (paper)

A computational non-commutative geometry program for disordered topological insulators

CERN Document Server

Prodan, Emil

2017-01-01

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...

Computational proximity excursions in the topology of digital images

CERN Document Server

Peters, James F

2016-01-01

This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in ...

Boundary Hamiltonian Theory for Gapped Topological Orders

Science.gov (United States)

Hu, Yuting; Wan, Yidun; Wu, Yong-Shi

2017-06-01

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.

An explicit parametrization for casting constraints in gradient driven topology optimization

DEFF Research Database (Denmark)

Gersborg, Allan Roulund; Andreasen, Casper Schousboe

From a practical point of view it is often desirable to limit the complexity of a topology design such that casting/milling type manufacturing techniques can be applied. In the context of gradient driven topology optimization this work studies how castable designs can be obtained by use of a Heav......From a practical point of view it is often desirable to limit the complexity of a topology design such that casting/milling type manufacturing techniques can be applied. In the context of gradient driven topology optimization this work studies how castable designs can be obtained by use...

Universal quantum computing using (Zd) 3 symmetry-protected topologically ordered states

Science.gov (United States)

Chen, Yanzhu; Prakash, Abhishodh; Wei, Tzu-Chieh

2018-02-01

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically nontrivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016), 10.1038/npjqi.2016.36] recently constructed a particular Z2×Z2×Z2 symmetry-protected topological state on the Union Jack lattice and established its quantum-computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting (d -1 ) qudit nontrivial Zd×Zd×Zd symmetry-protected topological states are universal on the triangular lattice, for d being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.

Applications of Atomic Systems in Quantum Simulation, Quantum Computation and Topological Phases of Matter

Science.gov (United States)

Wang, Shengtao

The ability to precisely and coherently control atomic systems has improved dramatically in the last two decades, driving remarkable advancements in quantum computation and simulation. In recent years, atomic and atom-like systems have also been served as a platform to study topological phases of matter and non-equilibrium many-body physics. Integrated with rapid theoretical progress, the employment of these systems is expanding the realm of our understanding on a range of physical phenomena. In this dissertation, I draw on state-of-the-art experimental technology to develop several new ideas for controlling and applying atomic systems. In the first part of this dissertation, we propose several novel schemes to realize, detect, and probe topological phases in atomic and atom-like systems. We first theoretically study the intriguing properties of Hopf insulators, a peculiar type of topological insulators beyond the standard classification paradigm of topological phases. Using a solid-state quantum simulator, we report the first experimental observation of Hopf insulators. We demonstrate the Hopf fibration with fascinating topological links in the experiment, showing clear signals of topological phase transitions for the underlying Hamiltonian. Next, we propose a feasible experimental scheme to realize the chiral topological insulator in three dimensions. They are a type of topological insulators protected by the chiral symmetry and have thus far remained unobserved in experiment. We then introduce a method to directly measure topological invariants in cold-atom experiments. This detection scheme is general and applicable to probe of different topological insulators in any spatial dimension. In another study, we theoretically discover a new type of topological gapless rings, dubbed a Weyl exceptional ring, in three-dimensional dissipative cold atomic systems. In the second part of this dissertation, we focus on the application of atomic systems in quantum computation

Measurement-only topological quantum computation without forced measurements

International Nuclear Information System (INIS)

Zheng, Huaixiu; Dua, Arpit; Jiang, Liang

2016-01-01

We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al (2008 Phys. Rev. Lett. 101 010501) where the braiding operation is shown to be equivalent to a series of topological charge ‘forced measurements’ of anyons. In a forced measurement, the charge measurement is forced to yield the desired outcome (e.g. charge 0) via repeatedly measuring charges in different bases. This is a probabilistic process with a certain success probability for each trial. In practice, the number of measurements needed will vary from run to run. We show that such an uncertainty associated with forced measurements can be removed by simulating the braiding operation using a fixed number of three measurements supplemented by a correction operator. Furthermore, we demonstrate that in practice we can avoid applying the correction operator in hardware by implementing it in software. Our findings greatly simplify the MOTQC proposal and only require the capability of performing charge measurements to implement topologically protected transformations generated by braiding exchanges without physically moving anyons. (paper)

Element-topology-independent preconditioners for parallel finite element computations

Science.gov (United States)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Topological transformation of fractional optical vortex beams using computer generated holograms

Science.gov (United States)

Maji, Satyajit; Brundavanam, Maruthi M.

2018-04-01

Optical vortex beams with fractional topological charges (TCs) are generated by the diffraction of a Gaussian beam using computer generated holograms embedded with mixed screw-edge dislocations. When the input Gaussian beam has a finite wave-front curvature, the generated fractional vortex beams show distinct topological transformations in comparison to the integer charge optical vortices. The topological transformations at different fractional TCs are investigated through the birth and evolution of the points of phase singularity, the azimuthal momentum transformation, occurrence of critical points in the transverse momentum and the vorticity around the singular points. This study is helpful to achieve better control in optical micro-manipulation applications.

Computational topology and the Unique Games Conjecture

OpenAIRE

Grochow, Joshua A.; Tucker-Foltz, Jamie

2018-01-01

Covering spaces of graphs have long been useful for studying expanders (as "graph lifts") and unique games (as the "label-extended graph"). In this paper we advocate for the thesis that there is a much deeper relationship between computational topology and the Unique Games Conjecture. Our starting point is Linial's 2005 observation that the only known problems whose inapproximability is equivalent to the Unique Games Conjecture - Unique Games and Max-2Lin - are instances of Maximum Section of...

High-order computer-assisted estimates of topological entropy

Science.gov (United States)

Grote, Johannes

The concept of Taylor Models is introduced, which offers highly accurate C0-estimates for the enclosures of functional dependencies, combining high-order Taylor polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified interval arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly nonlinear dynamical systems. A method to obtain sharp rigorous enclosures of Poincare maps for certain types of flows and surfaces is developed and numerical examples are presented. Differential algebraic techniques allow the efficient and accurate computation of polynomial approximations for invariant curves of certain planar maps around hyperbolic fixed points. Subsequently we introduce a procedure to extend these polynomial curves to verified Taylor Model enclosures of local invariant manifolds with C0-errors of size 10-10--10 -14, and proceed to generate the global invariant manifold tangle up to comparable accuracy through iteration in Taylor Model arithmetic. Knowledge of the global manifold structure up to finite iterations of the local manifold pieces enables us to find all homoclinic and heteroclinic intersections in the generated manifold tangle. Combined with the mapping properties of the homoclinic points and their ordering we are able to construct a subshift of finite type as a topological factor of the original planar system to obtain rigorous lower bounds for its topological entropy. This construction is fully automatic and yields homoclinic tangles with several hundred homoclinic points. As an example rigorous lower bounds for the topological entropy of the Henon map are computed, which to the best knowledge of the authors yield the largest such estimates published so far.

Topology optimization based on spline-based meshfree method using topological derivatives

International Nuclear Information System (INIS)

Hur, Junyoung; Youn, Sung-Kie; Kang, Pilseong

2017-01-01

Spline-based meshfree method (SBMFM) is originated from the Isogeometric analysis (IGA) which integrates design and analysis through Non-uniform rational B-spline (NURBS) basis functions. SBMFM utilizes trimming technique of CAD system by representing the domain using NURBS curves. In this work, an explicit boundary topology optimization using SBMFM is presented with an effective boundary update scheme. There have been similar works in this subject. However unlike the previous works where semi-analytic method for calculating design sensitivities is employed, the design update is done by using topological derivatives. In this research, the topological derivative is used to derive the sensitivity of boundary curves and for the creation of new holes. Based on the values of topological derivatives, the shape of boundary curves is updated. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several compliance minimization problems.

Topology optimization based on spline-based meshfree method using topological derivatives

Energy Technology Data Exchange (ETDEWEB)

Hur, Junyoung; Youn, Sung-Kie [KAIST, Daejeon (Korea, Republic of); Kang, Pilseong [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of)

2017-05-15

Spline-based meshfree method (SBMFM) is originated from the Isogeometric analysis (IGA) which integrates design and analysis through Non-uniform rational B-spline (NURBS) basis functions. SBMFM utilizes trimming technique of CAD system by representing the domain using NURBS curves. In this work, an explicit boundary topology optimization using SBMFM is presented with an effective boundary update scheme. There have been similar works in this subject. However unlike the previous works where semi-analytic method for calculating design sensitivities is employed, the design update is done by using topological derivatives. In this research, the topological derivative is used to derive the sensitivity of boundary curves and for the creation of new holes. Based on the values of topological derivatives, the shape of boundary curves is updated. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several compliance minimization problems.

A short course in computational geometry and topology

CERN Document Server

Edelsbrunner, Herbert

2014-01-01

With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: tessellations, complexes, homology, persistence. To speak to the non-specialist, detailed formalisms are often avoided in favor of lively 2- and 3-dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world of shapes.

Dynamical topological invariant after a quantum quench

Science.gov (United States)

Yang, Chao; Li, Linhu; Chen, Shu

2018-02-01

We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

Topological gravity with minimal matter

International Nuclear Information System (INIS)

Li Keke

1991-01-01

Topological minimal matter, obtained by twisting the minimal N = 2 supeconformal field theory, is coupled to two-dimensional topological gravity. The free field formulation of the coupled system allows explicit representations of BRST charge, physical operators and their correlation functions. The contact terms of the physical operators may be evaluated by extending the argument used in a recent solution of topological gravity without matter. The consistency of the contact terms in correlation functions implies recursion relations which coincide with the Virasoro constraints derived from the multi-matrix models. Topological gravity with minimal matter thus provides the field theoretic description for the multi-matrix models of two-dimensional quantum gravity. (orig.)

An explicit parameterization for casting constraints in gradient driven topology optimization

DEFF Research Database (Denmark)

Gersborg, Allan Roulund; Andreasen, Casper Schousboe

2011-01-01

From a practical point of view it is often desirable to limit the complexity of a topology optimization design such that casting/milling type manufacturing techniques can be applied. In the context of gradient driven topology optimization this work studies how castable designs can be obtained...... by use of a Heaviside design parameterization in a specified casting direction. This reduces the number of design variables considerably and the approach is simple to implement....

Topological strings from quantum mechanics

International Nuclear Information System (INIS)

Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

2014-12-01

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

Analysis of stationary availability factor of two-level backbone computer networks with arbitrary topology

Science.gov (United States)

Rahman, P. A.

2018-05-01

This scientific paper deals with the two-level backbone computer networks with arbitrary topology. A specialized method, offered by the author for calculation of the stationary availability factor of the two-level backbone computer networks, based on the Markov reliability models for the set of the independent repairable elements with the given failure and repair rates and the methods of the discrete mathematics, is also discussed. A specialized algorithm, offered by the author for analysis of the network connectivity, taking into account different kinds of the network equipment failures, is also observed. Finally, this paper presents an example of calculation of the stationary availability factor for the backbone computer network with the given topology.

Robustness of Topological Superconductivity in Solid State Hybrid Structures

Science.gov (United States)

Sitthison, Piyapong

The non-Abelian statistics of Majorana fermions (MFs) makes them an ideal platform for implementing topological quantum computation. In addition to the fascinating fundamental physics underlying the emergence of MFs, this potential for applications makes the study of these quasiparticles an extremely popular subject in condensed matter physics. The commonly called `Majorana fermions' are zero-energy bound states that emerge near boundaries and defects in topological superconducting phases, which can be engineered, for example, by proximity coupling strong spin-orbit coupling semiconductor nanowires and ordinary s-wave superconductors. The stability of these bound states is determined by the stability of the underlying topological superconducting phase. Hence, understanding their stability (which is critical for quantum computation), involves studying the robustness of the engineered topological superconductors. This work addresses this important problem in the context of two types of hybrid structures that have been proposed for realizing topological superconductivity: topological insulator - superconductor (TI-SC) and semiconductor - superconductor (SM-SC) nanostructures. In both structures, electrostatic effects due to applied external potentials and interface-induced potentials are significant. This work focuses on developing a theoretical framework for understanding these effects, to facilitate the optimization of the nanostructures studied in the laboratory. The approach presented in this thesis is based on describing the low-energy physics of the hybrid structure using effective tight-binding models that explicitly incorporate the proximity effects emerging at interfaces. Generically, as a result of the proximity coupling to the superconductor, an induced gap emerges in the semiconductor (topological insulator) sub-system. The strength of the proximity-induced gap is determined by the transparency of the interface and by the amplitude of the low- energy SM

Algebraic Modeling of Topological and Computational Structures and Applications

CERN Document Server

Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis

2017-01-01

This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w...

Algebraic definition of topological W gravity

International Nuclear Information System (INIS)

Hosono, S.

1992-01-01

In this paper, the authors propose a definition of the topological W gravity using some properties of the principal three-dimensional subalgebra of a simple Lie algebra due to Kostant. In the authors' definition, structures of the two-dimensional topological gravity are naturally embedded in the extended theories. In accordance with the definition, the authors will present some explicit calculations for the W 3 gravity

Few remarks on chiral theories with sophisticated topology

International Nuclear Information System (INIS)

Golo, V.L.; Perelomov, A.M.

1978-01-01

Two classes of the two-dimensional Euclidean chiral field theoreties are singled out: 1) the field phi(x) takes the values in the compact Hermitiam symmetric space 2) the field phi(x) takes the values in an orbit of the adjoint representation of the comcompact Lie group. The theories have sophisticated topological and rich analytical structures. They are considered with the help of topological invariants (topological charges). Explicit formulae for the topological charges are indicated, and the lower bound extimate for the action is given

On a characterization of path connected topological fields

OpenAIRE

Caicedo, Xavier; Mantilla-Soler, Guillermo

2017-01-01

The aim of this paper is to give a characterization of path connected topological fields, inspired by the classic Gelfand's correspondence between a compact Hausdorff topological space $X$ and the space of maximal ideals on the ring of real valued continuous functions $C(X,\\mathbb{R})$. More explicitly, our motivation is the following question: What is the essential property of the topological field $F=\\mathbb{R}$ that makes such correspondence valid for all compact Hausdorff spaces? It turns...

Quark-parton model from dual topological unitarization

International Nuclear Information System (INIS)

Cohen-Tannoudji, G.; El Hassouni, A.; Kalinowski, J.; Peschanski, R.

1979-01-01

Topology, which occurs in the topological expansion of quantum chromodynamics (QCD) and in the dual topological unitarization (DTU) schemes, allows us to establish a quantitative correspondence between QCD and the dual S-matrix approaches. This topological correspondence, proposed by Veneziano and made more explicit in a recent paper for current-induced reactions, provides a clarifying and unifying quark-parton interpretation of soft inclusive processes. Precise predictions for inclusive cross sections in hadron-hadron collisions, structure functions of hadrons, and quark fragmentation functions including absolute normalizations are shown to agree with data. On a more theoretical ground the proposed scheme suggests a new approach to the confinement problem

EXAFS Phase Retrieval Solution Tracking for Complex Multi-Component System: Synthesized Topological Inverse Computation

International Nuclear Information System (INIS)

Lee, Jay Min; Yang, Dong-Seok; Bunker, Grant B

2013-01-01

Using the FEFF kernel A(k,r), we describe the inverse computation from χ(k)-data to g(r)-solution in terms of a singularity regularization method based on complete Bayesian statistics process. In this work, we topologically decompose the system-matched invariant projection operators into two distinct types, (A + AA + A) and (AA + AA + ), and achieved Synthesized Topological Inversion Computation (STIC), by employing a 12-operator-closed-loop emulator of the symplectic transformation. This leads to a numerically self-consistent solution as the optimal near-singular regularization parameters are sought, dramatically suppressing instability problems connected with finite precision arithmetic in ill-posed systems. By statistically correlating a pair of measured data, it was feasible to compute an optimal EXAFS phase retrieval solution expressed in terms of the complex-valued χ(k), and this approach was successfully used to determine the optimal g(r) for a complex multi-component system.

Machine learning topological states

Science.gov (United States)

Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.

2017-11-01

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.

Explicit Interaction

DEFF Research Database (Denmark)

Löwgren, Jonas; Eriksen, Mette Agger; Linde, Per

2006-01-01

We report an ongoing study of palpable computing to support surgical rehabilitation, in the general field of interaction design for ubiquitous computing. Through explorative design, fieldwork and participatory design techniques, we explore the design principle of explicit interaction as an interp...

Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies.

Science.gov (United States)

Deng, Nanjie; Zhang, Bin W; Levy, Ronald M

2015-06-09

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.

Disorder effect in two-dimensional topological insulators

International Nuclear Information System (INIS)

Zhang Xianglin; Feng Shiping; Guo Huaiming

2012-01-01

We conduct a systematic study on the disorder effect in two-dimensional (2D) topological insulators by calculating the Z 2 topological invariant. Starting from the trivial and nontrivial topological phases of the model describing HgTe/CdTe quantum wells (QWs), we introduce three different kinds of disorder into the system, including the fluctuations in the on-site potential, the hopping amplitude and the topological mass. These kinds of disorder commonly exist in HgTe/CdTe QWs grown experimentally. By explicit numerical calculations, we show that all three kinds of disorder have the similar effect: the topological phase in the system is not only robust to them, but also can be brought about by introducing them to the trivial insulator phase. These results make a further confirmation and extendability of the study on the interplay between the disorder and the topological phase.

Identifying Two-Dimensional Z 2 Antiferromagnetic Topological Insulators

Science.gov (United States)

Bègue, F.; Pujol, P.; Ramazashvili, R.

2018-01-01

We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z 2 topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.

Topological methods in gauge theory

International Nuclear Information System (INIS)

Sarukkai, S.R.

1992-01-01

The author begins with an overview of the important topological methods used in gauge theory. In the first chapter, the author discusses the general structure of fiber bundles and associated mathematical concepts and briefly discuss their application in gauge theory. The second chapter deals with the study of instantons in both gauge and gravity theories. These self-dual solutions are presented. This chapter is also a broad introduction to certain topics in gravitational physics. Gravity and gauge theory are unified in Kaluza-Klein theory as discussed in the third chapter. Of particular interest is the physics of the U(1) bundles over non-trivial manifolds. The radius of the fifth dimension is undetermined classically in the Kaluza-Klein theory. A mechanism is described using topological information to derive the functional form of the radius of the fifth dimension and show that it is possible classically to derive expressions for the radius as a consequence of topology. The behavior of the radius is dependent on the information present in the base metric. Results are computed for three gravitational instantons. Consequences of this mechanism are discussed. The description is studied of instantons in terms of projector valued fields and universal bundles. The results of the previous chapter and this are connected via the study of universal bundles. Projector valued transformations are defined and their consequences discussed. With the solutions of instantons in this formalism, it is shown explicitly that there can be solutions which allow for a Sp(n) instanton to be transformed to a Sp(k) instanton, thus showing that there can be interpolations which carry one instanton with a rank n to another characterized by rank k with different topological numbers

Topological orbifold models and quantum cohomology rings

International Nuclear Information System (INIS)

Zaslow, E.

1993-01-01

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of CP 1 by the dihedral group D 4 , how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral CP 1 orbifolds. We then consider CP 2 /D 4 , and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds. (orig.)

Topology and computational performance of attractor neural networks

International Nuclear Information System (INIS)

McGraw, Patrick N.; Menzinger, Michael

2003-01-01

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world, and scale-free topologies. The random configuration is the most efficient for storage and retrieval of patterns by the network as a whole. However, in the scale-free case retrieval errors are not distributed uniformly among the nodes. The portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. The implications of these findings for brain function and social dynamics are suggestive

Anomalous Symmetry Fractionalization and Surface Topological Order

Directory of Open Access Journals (Sweden)

Xie Chen

2015-10-01

Full Text Available In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain “anomalous” SETs can only occur on the surface of a 3D symmetry-protected topological (SPT phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H^{4}(G,U(1, which also precisely labels the set of 3D SPT phases, with symmetry group G. An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U(1_{2}] topological order with a reduced symmetry Z_{2}×Z_{2}⊂SO(3, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.

Knot topology in QCD

International Nuclear Information System (INIS)

Zou, L.P.; Zhang, P.M.; Pak, D.G.

2013-01-01

We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N) (N=2,3) under the action of maximal Abelian stability group. Starting with explicit vacuum knot configurations we study possible exact classical solutions. Exact analytic non-static knot solution in a simple CP 1 model in Euclidean space–time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new solutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space–time can be naturally obtained from knot solitons in integrable CP 1 models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is proposed

Constructing a logical, regular axis topology from an irregular topology

Science.gov (United States)

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.

Computer Based Porosity Design by Multi Phase Topology Optimization

Science.gov (United States)

Burblies, Andreas; Busse, Matthias

2008-02-01

A numerical simulation technique called Multi Phase Topology Optimization (MPTO) based on finite element method has been developed and refined by Fraunhofer IFAM during the last five years. MPTO is able to determine the optimum distribution of two or more different materials in components under thermal and mechanical loads. The objective of optimization is to minimize the component's elastic energy. Conventional topology optimization methods which simulate adaptive bone mineralization have got the disadvantage that there is a continuous change of mass by growth processes. MPTO keeps all initial material concentrations and uses methods adapted from molecular dynamics to find energy minimum. Applying MPTO to mechanically loaded components with a high number of different material densities, the optimization results show graded and sometimes anisotropic porosity distributions which are very similar to natural bone structures. Now it is possible to design the macro- and microstructure of a mechanical component in one step. Computer based porosity design structures can be manufactured by new Rapid Prototyping technologies. Fraunhofer IFAM has applied successfully 3D-Printing and Selective Laser Sintering methods in order to produce very stiff light weight components with graded porosities calculated by MPTO.

A hybrid computational model to explore the topological characteristics of epithelial tissues.

Science.gov (United States)

González-Valverde, Ismael; García-Aznar, José Manuel

2017-11-01

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue. Copyright © 2017 John Wiley & Sons, Ltd.

Explicitly represented polygon wall boundary model for the explicit MPS method

Science.gov (United States)

Mitsume, Naoto; Yoshimura, Shinobu; Murotani, Kohei; Yamada, Tomonori

2015-05-01

This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.

Braiding knots with topological strings

International Nuclear Information System (INIS)

Gu, Jie

2015-08-01

For an arbitrary knot in a three-sphere, the Ooguri-Vafa conjecture associates to it a unique stack of branes in type A topological string on the resolved conifold, and relates the colored HOMFLY invariants of the knot to the free energies on the branes. For torus knots, we use a modified version of the topological recursion developed by Eynard and Orantin to compute the free energies on the branes from the Aganagic-Vafa spectral curves of the branes, and find they are consistent with the known colored HOMFLY knot invariants a la the Ooguri-Vafa conjecture. In addition our modified topological recursion can reproduce the correct closed string free energies, which encode the information of the background geometry. We conjecture the modified topological recursion is applicable for branes associated to hyperbolic knots as well, encouraged by the observation that the modified topological recursion yields the correct planar closed string free energy from the Aganagic-Vafa spectral curves of hyperbolic knots. This has implications for the knot theory concerning distinguishing mutant knots with colored HOMFLY invariants. Furthermore, for hyperbolic knots, we present methods to compute colored HOMFLY invariants in nonsymmetric representations of U(N). The key step in this computation is computing quantum 6j-symbols in the quantum group U q (sl N ).

Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems

Directory of Open Access Journals (Sweden)

Maissam Barkeshli

2014-11-01

Full Text Available The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be used as robust “topological qubits” to store and process quantum information. In this paper, we propose a new experimental setup that can realize topological qubits in a simple bilayer fractional quantum Hall system with proper electric gate configurations. Our proposal is accessible with current experimental techniques, involves well-established topological states, and, moreover, can realize a large class of topological qubits, generalizing the Majorana zero modes studied in recent literature to more computationally powerful possibilities. We propose three tunneling and interferometry experiments to detect the existence and nonlocal topological properties of the topological qubits.

OPTIMAL NETWORK TOPOLOGY DESIGN

Science.gov (United States)

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.

A computational study of the topology of vortex breakdown

Science.gov (United States)

Spall, Robert E.; Gatski, Thomas B.

1991-01-01

A fully three-dimensional numerical simulation of vortex breakdown using the unsteady, incompressible Navier-Stokes equations has been performed. Solutions to four distinct types of breakdown are identified and compared with experimental results. The computed solutions include weak helical, double helix, spiral, and bubble-type breakdowns. The topological structure of the various breakdowns as well as their interrelationship are studied. The data reveal that the asymmetric modes of breakdown may be subject to additional breakdowns as the vortex core evolves in the streamwise direction. The solutions also show that the freestream axial velocity distribution has a significant effect on the position and type of vortex breakdown.

Topological mirror superconductivity.

Science.gov (United States)

Zhang, Fan; Kane, C L; Mele, E J

2013-08-02

We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

Interactive Topology Optimization

DEFF Research Database (Denmark)

Nobel-Jørgensen, Morten

Interactivity is the continuous interaction between the user and the application to solve a task. Topology optimization is the optimization of structures in order to improve stiffness or other objectives. The goal of the thesis is to explore how topology optimization can be used in applications...... on theory of from human-computer interaction which is described in Chapter 2. Followed by a description of the foundations of topology optimization in Chapter 3. Our applications for topology optimization in 2D and 3D are described in Chapter 4 and a game which trains the human intuition of topology...... optimization is presented in Chapter 5. Topology optimization can also be used as an interactive modeling tool with local control which is presented in Chapter 6. Finally, Chapter 7 contains a summary of the findings and concludes the dissertation. Most of the presented applications of the thesis are available...

Quantized Hall conductance as a topological invariant

International Nuclear Information System (INIS)

Niu, Q.; Thouless, Ds.J.; Wu, Y.S.

1984-10-01

Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references

Error Correction for Non-Abelian Topological Quantum Computation

Directory of Open Access Journals (Sweden)

James R. Wootton

2014-03-01

Full Text Available The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of D(S_{3}. This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, _q) and PGL(2, _q)

International Nuclear Information System (INIS)

Roche, Ph.

2016-01-01

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, _q) and PGL(2, _q). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Chiral topological insulator on Nambu 3-algebraic geometry

Directory of Open Access Journals (Sweden)

Kazuki Hasebe

2014-09-01

Full Text Available Chiral topological insulator (AIII-class with Landau levels is constructed based on the Nambu 3-algebraic geometry. We clarify the geometric origin of the chiral symmetry of the AIII-class topological insulator in the context of non-commutative geometry of 4D quantum Hall effect. The many-body groundstate wavefunction is explicitly derived as a (l,l,l−1 Laughlin–Halperin type wavefunction with unique K-matrix structure. Fundamental excitation is identified with anyonic string-like object with fractional charge 1/(2(l−12+1. The Hall effect of the chiral topological insulators turns out be a color version of Hall effect, which exhibits a dual property of the Hall and spin-Hall effects.

Relational topology

CERN Document Server

Schmidt, Gunther

2018-01-01

This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.

Grassmannian topological Kazama-Suzuki models and cohomology

International Nuclear Information System (INIS)

Blau, M.; Hussain, F.; Thompson, G.

1995-10-01

We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann odd scalars of the theory) coincides with the classical cohomology ring of the Grassmanian for all values of the level k. We also analyze the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an Abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP(2) model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,K + 2), thus realizing the level-rank duality between this model and the G(2, k + 2) model at level one. (author). 28 refs

Planck 2015 results. XVIII. Background geometry & topology

CERN Document Server

Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; De Rosa, A.; De Zotti, G.; Delabrouille, J.; Désert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Feeney, S.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McEwen, J.D.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Tent, F. Van; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-01-01

Full-sky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $\\chi_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at log-likelihood-ratio $\\Delta\\ln{L}>-5$ relative to a simply-connected flat Planck best-fit model) are $R_i>0.97\\chi_{rec}$ for the cubic torus and $R_i>0.56\\chi_{rec}$ for the slab. The limit for the cubic torus from the matched-circles search is numerically equivalent, $R_i>0.97\\chi_{rec}...

Generalized Mathai-Quillen Topological Sigma Models

OpenAIRE

Llatas, Pablo M.

1995-01-01

A simple field theoretical approach to Mathai-Quillen topological field theories of maps $X: M_I \\to M_T$ from an internal space to a target space is presented. As an example of applications of our formalism we compute by applying our formulas the action and Q-variations of the fields of two well known topological systems: Topological Quantum Mechanics and type-A topological Sigma Model.

Using heteroclinic orbits to quantify topological entropy in fluid flows

International Nuclear Information System (INIS)

Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.

2016-01-01

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Computational Topology Based Quantification Of Hepatocytes Nuclei In Lipopolysaccharide-Induced Liver Injury In Mice

Directory of Open Access Journals (Sweden)

Rodrigo Rojas Moraleda

2016-06-01

The computational topology approach proposed successfully detected hepatocyte cells under several natural variations. We evaluated on a per-pixel basis how the segmentation performs on: i all nuclei in the images, ii big round nuclei considered belonging to hepatocytes cells (accuracy 87.2%, recall 80.3%, and iii nuclei regarded to non-parenchymal cells.  

Decorrelating topology with HMC

International Nuclear Information System (INIS)

Lippert, Th.; Alles, B.; Bali, G.; D'Elia, M.; Di Giacomo, A.; Eicker, N.; Guesken, S.; Schilling, K.; Spitz, A.; Struckmann, T.; Ueberholz, P.; Viehoff, J.

1999-01-01

The investigation of the decorrelation efficiency of the HMC algorithm with respect to vacuum topology is a prerequisite for trustworthy full QCD simulations, in particular for the computation of topology sensitive quantities. We demonstrate that for ((m π )/(m ρ ))-ratios ≥ 0.69 sufficient tunneling between the topological sectors can be achieved, for two flavours of dynamical Wilson fermions close to the scaling region (β 5.6). Our results are based on time series of length 5000 trajectories

1992 Trieste lectures on topological gauge theory and Yang-Mills theory

International Nuclear Information System (INIS)

Thompson, G.

1993-05-01

In these lecture notes we explain a connection between Yang-Mills theory on arbitrary Riemann surfaces and two types of topological field theory, the so called BF and cohomological theories. The quantum Yang-Mills theory is solved exactly using path integral techniques. Explicit expressions, in terms of group representation theory, are obtained for the partition function and various correlation functions. In a particular limit the Yang-Mills theory devolves to the topological models and the previously determined correlation functions give topological information about the moduli spaces of flat connections. In particular, the partition function yields the volume of the moduli space for which an explicit expression is derived. These notes are self contained, with a basic introduction to the various ideas underlying the topological field theories. This includes some relatively new work on handling problems that arise in the presence of reducible connections, which in turn, forms the bridge between the various models under consideration. These notes are identical to those made available to participants of the 1992 summer school in Trieste, except for one or two additions added circa January 1993. (author). 52 refs, 6 figs

Inclusion of Topological Measurements into Analytic Estimates of Effective Permeability in Fractured Media

Science.gov (United States)

Sævik, P. N.; Nixon, C. W.

2017-11-01

We demonstrate how topology-based measures of connectivity can be used to improve analytical estimates of effective permeability in 2-D fracture networks, which is one of the key parameters necessary for fluid flow simulations at the reservoir scale. Existing methods in this field usually compute fracture connectivity using the average fracture length. This approach is valid for ideally shaped, randomly distributed fractures, but is not immediately applicable to natural fracture networks. In particular, natural networks tend to be more connected than randomly positioned fractures of comparable lengths, since natural fractures often terminate in each other. The proposed topological connectivity measure is based on the number of intersections and fracture terminations per sampling area, which for statistically stationary networks can be obtained directly from limited outcrop exposures. To evaluate the method, numerical permeability upscaling was performed on a large number of synthetic and natural fracture networks, with varying topology and geometry. The proposed method was seen to provide much more reliable permeability estimates than the length-based approach, across a wide range of fracture patterns. We summarize our results in a single, explicit formula for the effective permeability.

Optimization of Network Topology in Computer-Aided Detection Schemes Using Phased Searching with NEAT in a Time-Scaled Framework.

Science.gov (United States)

Tan, Maxine; Pu, Jiantao; Zheng, Bin

2014-01-01

In the field of computer-aided mammographic mass detection, many different features and classifiers have been tested. Frequently, the relevant features and optimal topology for the artificial neural network (ANN)-based approaches at the classification stage are unknown, and thus determined by trial-and-error experiments. In this study, we analyzed a classifier that evolves ANNs using genetic algorithms (GAs), which combines feature selection with the learning task. The classifier named "Phased Searching with NEAT in a Time-Scaled Framework" was analyzed using a dataset with 800 malignant and 800 normal tissue regions in a 10-fold cross-validation framework. The classification performance measured by the area under a receiver operating characteristic (ROC) curve was 0.856 ± 0.029. The result was also compared with four other well-established classifiers that include fixed-topology ANNs, support vector machines (SVMs), linear discriminant analysis (LDA), and bagged decision trees. The results show that Phased Searching outperformed the LDA and bagged decision tree classifiers, and was only significantly outperformed by SVM. Furthermore, the Phased Searching method required fewer features and discarded superfluous structure or topology, thus incurring a lower feature computational and training and validation time requirement. Analyses performed on the network complexities evolved by Phased Searching indicate that it can evolve optimal network topologies based on its complexification and simplification parameter selection process. From the results, the study also concluded that the three classifiers - SVM, fixed-topology ANN, and Phased Searching with NeuroEvolution of Augmenting Topologies (NEAT) in a Time-Scaled Framework - are performing comparably well in our mammographic mass detection scheme.

On RNA-RNA interaction structures of fixed topological genus.

Science.gov (United States)

Fu, Benjamin M M; Han, Hillary S W; Reidys, Christian M

2015-04-01

Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and a linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of a bicellular map directly, or to lose connectivity by decomposing the complex into a pair of single stranded RNA structures. Our main result is proved bijectively. It provides an explicit algorithm of how to rewire the corresponding complexes and an unambiguous decomposition grammar. Using the concept of genus induction, we construct bicellular maps of fixed topological genus g uniformly in linear time. We present various statistics on these topological RNA complexes and compare our findings with biological complexes. Furthermore we show how to construct loop-energy based complexes using our decomposition grammar. Copyright © 2015 Elsevier Inc. All rights reserved.

Explicitly-correlated ring-coupled-cluster-doubles theory: Including exchange for computations on closed-shell systems

Energy Technology Data Exchange (ETDEWEB)

Hehn, Anna-Sophia; Holzer, Christof; Klopper, Wim, E-mail: klopper@kit.edu

2016-11-10

Highlights: • Ring-coupled-cluster-doubles approach now implemented with exchange terms. • Ring-coupled-cluster-doubles approach now implemented with F12 functions. • Szabo–Ostlund scheme (SO2) implemented for use in SAPT. • Fast convergence to the limit of a complete basis. • Implementation in the TURBOMOLE program system. - Abstract: Random-phase-approximation (RPA) methods have proven to be powerful tools in electronic-structure theory, being non-empirical, computationally efficient and broadly applicable to a variety of molecular systems including small-gap systems, transition-metal compounds and dispersion-dominated complexes. Applications are however hindered due to the slow basis-set convergence of the electron-correlation energy with the one-electron basis. As a remedy, we present approximate explicitly-correlated RPA approaches based on the ring-coupled-cluster-doubles formulation including exchange contributions. Test calculations demonstrate that the basis-set convergence of correlation energies is drastically accelerated through the explicitly-correlated approach, reaching 99% of the basis-set limit with triple-zeta basis sets. When implemented in close analogy to early work by Szabo and Ostlund [36], the new explicitly-correlated ring-coupled-cluster-doubles approach including exchange has the perspective to become a valuable tool in the framework of symmetry-adapted perturbation theory (SAPT) for the computation of dispersion energies of molecular complexes of weakly interacting closed-shell systems.

Topological field theory: zero-modes and renormalization

International Nuclear Information System (INIS)

Ouvry, S.; Thompson, G.

1989-09-01

We address the issue of the non-triviality of the observables in various Topological Field Theories by means of the explicit introduction of the zero-modes into the BRST algebra. Supersymmetric quantum mechanics and Topological Yang-Mills theory are dealt with in detail. It is shown that due to the presence of fermionic zero-modes the BRST algebra may be dynamically broken leading to non trivial observables albeit the local cohomology being trivial. However the metric and coupling constant independence of the observables are still valid. A renormalization procedure is given that correctly incorporates the zero-modes. Particular attention is given to the conventional gauge fixing in Topological Yang-Mills theories, with emphasis on the geometrical character of the fields and their role in the non-triviality of the observables

Topological string theory, modularity and non-perturbative physics

Energy Technology Data Exchange (ETDEWEB)

Rauch, Marco

2011-09-15

In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group {gamma}(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P{sup 2} and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in

Topological string theory, modularity and non-perturbative physics

International Nuclear Information System (INIS)

Rauch, Marco

2011-09-01

In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group Γ(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P 2 and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in turn is

Aeroelastic Wingbox Stiffener Topology Optimization

Science.gov (United States)

Stanford, Bret K.

2017-01-01

This work considers an aeroelastic wingbox model seeded with run-out blade stiffeners along the skins. Topology optimization is conducted within the shell webs of the stiffeners, in order to add cutouts and holes for mass reduction. This optimization is done with a global-local approach in order to moderate the computational cost: aeroelastic loads are computed at the wing-level, but the topology and sizing optimization is conducted at the panel-level. Each panel is optimized separately under stress, buckling, and adjacency constraints, and periodically reassembled to update the trimmed aeroelastic loads. The resulting topology is baselined against a design with standard full-depth solid stiffener blades, and found to weigh 7.43% less.

Operator Product Formulas in the Algebraic Approach of the Refined Topological Vertex

International Nuclear Information System (INIS)

Cai Li-Qiang; Wang Li-Fang; Wu Ke; Yang Jie

2013-01-01

The refined topological vertex of Iqbal—Kozçaz—Vafa has been investigated from the viewpoint of the quantum algebra of type W 1+∞ by Awata, Feigin, and Shiraishi. They introduced the trivalent intertwining operator Φ which is normal ordered along with some prefactors. We manage to establish formulas from the infinite operator product of the vertex operators and the generalized ones to restore this prefactor, and obtain an explicit formula for the vertex realization of the topological vertex as well as the refined topological vertex

Combined shape and topology optimization for minimization of maximal von Mises stress

DEFF Research Database (Denmark)

Lian, Haojie; Christiansen, Asger Nyman; Tortorelli, Daniel A.

2017-01-01

This work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology....... By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy....

Topology optimization under stochastic stiffness

Science.gov (United States)

Asadpoure, Alireza

Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations

Topology optimization for acoustic-structure interaction problems

DEFF Research Database (Denmark)

Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole

2006-01-01

We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz...... to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz......-dimensional acoustic-structure interaction problems are optimized to show the validity of the proposed method....

Real topological string amplitudes

Energy Technology Data Exchange (ETDEWEB)

Narain, K.S. [The Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Piazzalunga, N. [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794-3636 (United States); International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy); Tanzini, A. [International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy)

2017-03-15

We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G{sub χ}, at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g{sup ′}=−χ+1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F{sub g}.

Combined shape and topology optimization for minimization of maximal von Mises stress

International Nuclear Information System (INIS)

Lian, Haojie; Christiansen, Asger N.; Tortorelli, Daniel A.; Sigmund, Ole; Aage, Niels

2017-01-01

Here, this work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology. By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy.

A Conclusive Test of Abelian Dominance Hypothesis for Topological Charge in the QCD Vacuum

OpenAIRE

Sasaki, Shoichi; Miyamura, Osamu

1998-01-01

We study the topological feature in the QCD vacuum based on the hypothesis of abelian dominance. The topological charge $Q_{\\rm SU(2)}$ can be explicitly represented in terms of the monopole current in the abelian dominated system. To appreciate its justification, we directly measure the corresponding topological charge $Q_{\\rm Mono}$, which is reconstructed only from the monopole current and the abelian component of gauge fields, by using the Monte Carlo simulation on SU(2) lattice. We find ...

Explicit time integration of finite element models on a vectorized, concurrent computer with shared memory

Science.gov (United States)

Gilbertsen, Noreen D.; Belytschko, Ted

1990-01-01

The implementation of a nonlinear explicit program on a vectorized, concurrent computer with shared memory is described and studied. The conflict between vectorization and concurrency is described and some guidelines are given for optimal block sizes. Several example problems are summarized to illustrate the types of speed-ups which can be achieved by reprogramming as compared to compiler optimization.

Topological constraints and their breakdown in dynamical evolution

International Nuclear Information System (INIS)

Goldstein, Raymond E; Moffatt, H Keith; Pesci, Adriana I

2012-01-01

A variety of physical and biological systems exhibit dynamical behaviour that has some explicit or implicit topological features. Here, the term ‘topological’ is meant to convey the idea of structures, e.g. physical knots, links or braids, that have some measure of invariance under continuous deformation. Dynamical evolution is then subject to the topological constraints that express this invariance. The simplest problem arising in these systems is the determination of minimum-energy structures (and routes towards these structures) permitted by such constraints, and elucidation of mechanisms by which the constraints may be broken. In more complex nonequilibrium cases there can be recurring singularities associated with topological rearrangements driven by continuous injection of energy. In this brief overview, motivated by an upcoming program on ‘Topological Dynamics in the Physical and Biological Sciences’ at the Isaac Newton Institute for Mathematical Sciences, we present a summary of this class of dynamical systems and discuss examples of important open problems. (invited articles)

Signatures of topological superconductivity

Energy Technology Data Exchange (ETDEWEB)

Peng, Yang

2017-07-19

The prediction and experimental discovery of topological insulators brought the importance of topology in condensed matter physics into the limelight. Topology hence acts as a new dimension along which more and more new states of matter start to emerge. One of these topological states of matter, namely topological superconductors, comes into the focus because of their gapless excitations. These gapless excitations, especially in one dimensional topological superconductors, are Majorana zero modes localized at the ends of the superconductor and exhibit exotic nonabelian statistics, which can be potentially applied to fault-tolerant quantum computation. Given their highly interesting physical properties and potential applications to quantum computation, both theorists and experimentalists spend great efforts to realize topological supercondoctors and to detect Majoranas. In two projects within this thesis, we investigate the properties of Majorana zero modes in realistic materials which are absent in simple theoretical models. We find that the superconducting proximity effect, an essential ingredient in all existing platforms for topological superconductors, plays a significant role in determining the localization property of the Majoranas. Strong proximity coupling between the normal system and the superconducting substrate can lead to strongly localized Majoranas, which can explain the observation in a recent experiment. Motivated by experiments in Molenkamp's group, we also look at realistic quantum spin Hall Josephson junctions, in which charge puddles acting as magnetic impurities are coupled to the helical edge states. We find that with this setup, the junction generically realizes an exotic 8π periodic Josephson effect, which is absent in a pristine Josephson junction. In another two projects, we propose more pronounced signatures of Majoranas that are accessible with current experimental techniques. The first one is a transport measurement, which uses

Crashworthiness design of transient frame structures using topology optimization

DEFF Research Database (Denmark)

Pedersen, Claus B. Wittendorf

2004-01-01

The aim of this paper is to present topology optimization as a method to obtain conceptual designs for crash-worthiness. The topology optimization formulation uses rigorously computed sensitivities. The large displacements and plasticity of the 2D beam elements are modelled with the co-rotational......The aim of this paper is to present topology optimization as a method to obtain conceptual designs for crash-worthiness. The topology optimization formulation uses rigorously computed sensitivities. The large displacements and plasticity of the 2D beam elements are modelled with the co...

Efficient physical embedding of topologically complex information processing networks in brains and computer circuits.

Directory of Open Access Journals (Sweden)

Danielle S Bassett

2010-04-01

Full Text Available Nervous systems are information processing networks that evolved by natural selection, whereas very large scale integrated (VLSI computer circuits have evolved by commercially driven technology development. Here we follow historic intuition that all physical information processing systems will share key organizational properties, such as modularity, that generally confer adaptivity of function. It has long been observed that modular VLSI circuits demonstrate an isometric scaling relationship between the number of processing elements and the number of connections, known as Rent's rule, which is related to the dimensionality of the circuit's interconnect topology and its logical capacity. We show that human brain structural networks, and the nervous system of the nematode C. elegans, also obey Rent's rule, and exhibit some degree of hierarchical modularity. We further show that the estimated Rent exponent of human brain networks, derived from MRI data, can explain the allometric scaling relations between gray and white matter volumes across a wide range of mammalian species, again suggesting that these principles of nervous system design are highly conserved. For each of these fractal modular networks, the dimensionality of the interconnect topology was greater than the 2 or 3 Euclidean dimensions of the space in which it was embedded. This relatively high complexity entailed extra cost in physical wiring: although all networks were economically or cost-efficiently wired they did not strictly minimize wiring costs. Artificial and biological information processing systems both may evolve to optimize a trade-off between physical cost and topological complexity, resulting in the emergence of homologous principles of economical, fractal and modular design across many different kinds of nervous and computational networks.

The Topological Vertex

CERN Document Server

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.

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

International Nuclear Information System (INIS)

Groote, S.; Koerner, J.G.; Pivovarov, A.A.

2007-01-01

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D 0 for different values of dimensions including the most important practical cases D 0 = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added

Streamline topology of axisymmetric flows

DEFF Research Database (Denmark)

Brøns, Morten

Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....

Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics

International Nuclear Information System (INIS)

Oezis, Turgut; Aslan, Imail

2009-01-01

With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered. (general)

Topological data analysis for scientific visualization

CERN Document Server

Tierny, Julien

2017-01-01

Combining theoretical and practical aspects of topology, this book delivers a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a thorough but intuitive manner, with many high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in details, and their application is carefully illustrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis, for lecturers, students and researchers.

Topological fluid mechanics of Axisymmetric Flow

DEFF Research Database (Denmark)

Brøns, Morten

1998-01-01

Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...

Entanglement entropy of ABJM theory and entropy of topological black hole

Science.gov (United States)

Nian, Jun; Zhang, Xinyu

2017-07-01

In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

QCD topological susceptibility from the nonlocal chiral quark model

Science.gov (United States)

Nam, Seung-Il; Kao, Chung-Wen

2017-06-01

We investigate the quantum chromodynamics (QCD) topological susceptibility χ by using the semi-bosonized nonlocal chiral-quark model (SB-NLχQM) for the leading large- N c contributions. This model is based on the liquid-instanton QCD-vacuum configuration, in which SU(3) flavor symmetry is explicitly broken by the finite current-quark mass ( m u,d, m s) ≈ (5, 135) MeV. To compute χ, we derive the local topological charge-density operator Q t( x) from the effective action of SB-NLχQM. We verify that the derived expression for χ in our model satisfies the Witten- Veneziano (WV) and the Leutwyler-Smilga (LS) formulae, and the Crewther theorem in the chiral limit by construction. Once the average instanton size and the inter-instanton distance are fixed with ρ¯ = 1/3 fm and R¯ = 1 fm, respectively, all the other parameters are determined self-consistently within the model. We obtain χ = (167.67MeV)4, which is comparable with the empirical value χ = (175±5MeV)4 whereas it turns out that χ QL = (194.30MeV)4 in the quenched limit. Thus, we conclude that the value of χ will be reduced around 10 20% by the dynamical-quark contribution.

Investigation of Turbulent Hydrogen Premixed Flame Topologies at Different Combustion Regimes Using Computational Singular Perturbation

Science.gov (United States)

Tingas, Efstathios-Alexandros; Hernandez Perez, Francisco; Im, Hong

2017-11-01

The investigation of turbulent flames at higher Reynolds and Karlovitz numbers has been gaining research interest, due to the advances in the computational power that has facilitated the use of direct numerical simulations (DNS). One of the additional challenges associated with highly turbulent premixed flames is the difficulties in identifying the turbulent flame topologies as the flame structures become severely corrugated or even disrupted by the small scale turbulent eddies. In these conditions, the conventional methods using a scalar iso-surface may lead to uncertainties in describing the flame front dynamics. In this study, the computational singular perturbation (CSP) is utilized as an automated tool to identify the flame front topologies based on the dynamical time scales and eigenvalues. In particular, the tangential stretch rate (TSR) approach, an extended generalized method to depict the dynamics of chemical and transport processes, is used for the flame front identification. The CSP/TSR approach and tools are used to compare the flame fronts of two turbulent H2/air premixed flames and to identify their similarities/differences, from a dynamical point of view. The results for two different combustion regimes are analyzed and compared.

Quadratic stabilisability of multi-agent systems under switching topologies

Science.gov (United States)

Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long

2014-12-01

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

Morse theory interpretation of topological quantum field theories

International Nuclear Information System (INIS)

Labastida, J.M.F.

1989-01-01

Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)

Renormalization of topological field theory

International Nuclear Information System (INIS)

Birmingham, D.; Rakowski, M.; Thompson, G.

1988-11-01

One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs

Topology optimization aided structural design: Interpretation, computational aspects and 3D printing.

Science.gov (United States)

Kazakis, Georgios; Kanellopoulos, Ioannis; Sotiropoulos, Stefanos; Lagaros, Nikos D

2017-10-01

Construction industry has a major impact on the environment that we spend most of our life. Therefore, it is important that the outcome of architectural intuition performs well and complies with the design requirements. Architects usually describe as "optimal design" their choice among a rather limited set of design alternatives, dictated by their experience and intuition. However, modern design of structures requires accounting for a great number of criteria derived from multiple disciplines, often of conflicting nature. Such criteria derived from structural engineering, eco-design, bioclimatic and acoustic performance. The resulting vast number of alternatives enhances the need for computer-aided architecture in order to increase the possibility of arriving at a more preferable solution. Therefore, the incorporation of smart, automatic tools in the design process, able to further guide designer's intuition becomes even more indispensable. The principal aim of this study is to present possibilities to integrate automatic computational techniques related to topology optimization in the phase of intuition of civil structures as part of computer aided architectural design. In this direction, different aspects of a new computer aided architectural era related to the interpretation of the optimized designs, difficulties resulted from the increased computational effort and 3D printing capabilities are covered here in.

The topological entropy of iterated piecewise affine maps is uncomputable

Directory of Open Access Journals (Sweden)

Pascal Koiran

2001-12-01

Full Text Available We show that it is impossible to compute (or even to approximate the topological entropy of a continuous piecewise affine function in dimension four. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real number can be obtained as the topological entropy of a piecewise affine function. It seems that these two questions are also open for cellular automata.

Layer Construction of 3D Topological States and String Braiding Statistics

Directory of Open Access Journals (Sweden)

Chao-Ming Jian

2014-12-01

Full Text Available While the topological order in two dimensions has been studied extensively since the discovery of the integer and fractional quantum Hall systems, topological states in three spatial dimensions are much less understood. In this paper, we propose a general formalism for constructing a large class of three-dimensional topological states by stacking layers of 2D topological states and introducing coupling between them. Using this construction, different types of topological states can be obtained, including those with only surface topological order and no bulk topological quasiparticles, and those with topological order both in the bulk and at the surface. For both classes of states, we study its generic properties and present several explicit examples. As an interesting consequence of this construction, we obtain example systems with nontrivial braiding statistics between string excitations. In addition to studying the string-string braiding in the example system, we propose a topological field-theory description for the layer-constructed systems, which captures not only the string-particle braiding statistics but also the string-string braiding statistics when the coupling is twisted. Last, we provide a proof of a general identity for Abelian string statistics and discuss an example system with non-Abelian strings.

The character of free topological groups II

Directory of Open Access Journals (Sweden)

Peter Nickolas

2005-04-01

Full Text Available A systematic analysis is made of the character of the free and free abelian topological groups on metrizable spaces and compact spaces, and on certain other closely related spaces. In the first case, it is shown that the characters of the free and the free abelian topological groups on X are both equal to the “small cardinal” d if X is compact and metrizable, but also, more generally, if X is a non-discrete k!-space all of whose compact subsets are metrizable, or if X is a non-discrete Polish space. An example is given of a zero-dimensional separable metric space for which both characters are equal to the cardinal of the continuum. In the case of a compact space X, an explicit formula is derived for the character of the free topological group on X involving no cardinal invariant of X other than its weight; in particular the character is fully determined by the weight in the compact case. This paper is a sequel to a paper by the same authors in which the characters of the free groups were analysed under less restrictive topological assumptions.

Geometric entanglement in topologically ordered states

International Nuclear Information System (INIS)

Orús, Román; Wei, Tzu-Chieh; Buerschaper, Oliver; Nest, Maarten Van den

2014-01-01

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically ordered systems such as the toric code, double semion, colour code and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks and a contribution quantifying the underlying pattern of long-range entanglement of the topologically ordered state. This topological contribution is also present in the case of single-spin blocks in most cases, and constitutes an alternative characterization of topological order for these quantum states based on a multipartite entanglement measure. In particular, we see that the topological term for the two-dimensional colour code is twice as much as the one for the toric code, in accordance with recent renormalization group arguments (Bombin et al 2012 New J. Phys. 14 073048). Motivated by these results, we also derive a general formalism to obtain upper- and lower-bounds to the geometric entanglement of states with a non-Abelian group symmetry, and which we explicitly use to analyse quantum double models. Furthermore, we also provide an analysis of the robustness of the topological contribution in terms of renormalization and perturbation theory arguments, as well as a numerical estimation for small systems. Some of the results in this paper rely on the ability to disentangle single sites from the quantum state, which is always possible for the systems that we consider. Additionally we relate our results to the behaviour of the relative entropy of entanglement in topologically ordered systems, and discuss a number of numerical approaches based on tensor networks that could be

On the topology of real algebraic plane curves

DEFF Research Database (Denmark)

Cheng, Jinsan; Lazard, Sylvain; Peñaranda, Luis

2010-01-01

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given...... and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition...

Planck 2015 results: XVIII. Background geometry and topology of the Universe

DEFF Research Database (Denmark)

Ade, P. A R; Aghanim, N.; Arnaud, M.

2016-01-01

and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology...... the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), both via a direct scan for matched circular patterns at the intersections...... with a scale below the diameter of the last-scattering surface. The limits on the radius i of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ>-5 relative to a simply-connected flat Planck best-fit model) are: i > 0.97 χrec for the T3 cubic torus; and i > 0.56 χrec for the T...

(d -2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States

Science.gov (United States)

Song, Zhida; Fang, Zhong; Fang, Chen

2017-12-01

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d =2 , 3). We show that in both cases nontrivial topology is manifested by the presence of the (d -2 )-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through the explicit construction of microscopic models having robust (d -2 )-dimensional edge states.

Probing the moduli dependence of refined topological amplitudes

Directory of Open Access Journals (Sweden)

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.

Scalar-tensor approach to the construction of theory of topological transformations

International Nuclear Information System (INIS)

Konstantinov, M.Yu.

1985-01-01

Problem of construction of the classical gravitational theory, which solutions in the explicit form contain description of topological transformations, is under study. With this object in view, the scalar-tensor formalism is considered based on a representation of some subclass of space-like hypersurfaces as surfaces of a smooth function level in four-dimensional manifolds. Solutions of the theory along with the Lorentz space-time structure and space-like surface topology define some reference system, but the type of topological transformations is not dependent on the reference system option. All these facts prove the above approach correctness. Two variants of the scalar-tensor theory of topological transformations are considered as an example; one of them is reduced to the Einstein gravitational theory in the regular space region and another represents a nontrivial modification of the Brans-Dikker theory

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

Science.gov (United States)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Bosonization of fermions coupled to topologically massive gravity

Science.gov (United States)

Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.

2014-03-01

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space-time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space-time.

Bosonization of fermions coupled to topologically massive gravity

International Nuclear Information System (INIS)

Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.

2014-01-01

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space–time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy–momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space–time.

Bosonization of fermions coupled to topologically massive gravity

Energy Technology Data Exchange (ETDEWEB)

Fradkin, Eduardo [Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080 (United States); Moreno, Enrique F. [Department of Physics, Northeastern University, Boston, MA 02115 (United States); Schaposnik, Fidel A. [Departamento de Física, Universidad Nacional de La Plata, Instituto de Física La Plata, C.C. 67, 1900 La Plata (Argentina)

2014-03-07

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space–time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy–momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space–time.

Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions

Science.gov (United States)

Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi

2015-01-01

In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452

Topological zero modes in Monte Carlo simulations

International Nuclear Information System (INIS)

Dilger, H.

1994-08-01

We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly. (orig.)

Topology optimization using the finite volume method

DEFF Research Database (Denmark)

Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole

2005-01-01

in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix $\\mathbf K$ and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression $ c = \\mathbf u^\\T \\tilde{\\mathbf K} \\mathbf u...... the arithmetic and harmonic average with the latter being the well known Reuss lower bound. [1] Bendsøe, MP and Sigmund, O 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, HK and Malalasekera, W 1995: An introduction to Computational Fluid Dynamics...

Topology optimization using the finite volume method

DEFF Research Database (Denmark)

in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix K and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression c = u^\\T \\tilde{K}u $, where \\tilde{K} is different from K...... the well known Reuss lower bound. [1] Bendsøe, M.P.; Sigmund, O. 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, H. K.; W. Malalasekera 1995: An introduction to Computational Fluid Dynamics: the Finite Volume Method. London: Longman...

Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains

Science.gov (United States)

Cao, Ting; Zhao, Fangzhou; Louie, Steven G.

2017-08-01

We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1 /2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

On topological RNA interaction structures.

Science.gov (United States)

Qin, Jing; Reidys, Christian M

2013-07-01

Recently a folding algorithm of topological RNA pseudoknot structures was presented in Reidys et al. (2011). This algorithm folds single-stranded γ-structures, that is, RNA structures composed by distinct motifs of bounded topological genus. In this article, we set the theoretical foundations for the folding of the two backbone analogues of γ structures: the RNA γ-interaction structures. These are RNA-RNA interaction structures that are constructed by a finite number of building blocks over two backbones having genus at most γ. Combinatorial properties of γ-interaction structures are of practical interest since they have direct implications for the folding of topological interaction structures. We compute the generating function of γ-interaction structures and show that it is algebraic, which implies that the numbers of interaction structures can be computed recursively. We obtain simple asymptotic formulas for 0- and 1-interaction structures. The simplest class of interaction structures are the 0-interaction structures, which represent the two backbone analogues of secondary structures.

Topology Optimization of Large Scale Stokes Flow Problems

DEFF Research Database (Denmark)

Aage, Niels; Poulsen, Thomas Harpsøe; Gersborg-Hansen, Allan

2008-01-01

This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.......This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs....

Tight Network Topology Dependent Bounds on Rounds of Communication

OpenAIRE

Chattopadhyay, Arkadev; Langberg, Michael; Li, Shi; Rudra, Atri

2016-01-01

We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems. Our main contri...

Computer-aided topological analysis of Nd-Fe-B ternary system

International Nuclear Information System (INIS)

Liu, G.; Xu, P.; Zhang, W.

1993-01-01

A three-dimensional partially matrixed topological model of the Nd-Fe-B ternary phase diagram has been established based on experimental results assessed comprehensively with the aid of a computer-aided design and graphic and graphics software, AutoCAD (R10), and application programs developed in this work. Vertical sections at 5.88 at.% B, Nd:B = 1:1, Fe-Nd/sub 2/Fe/sub 14/B-Nd, Nd/sub 2/Fe/sub 17/-Nd/sub 2/Fe/sub 7/B/sub 6/ have been cut out from the model and the corresponding phase relationships have been analyzed. Among them, those on the Nd-rich protons of both the sections at 5.88 at.% B and Nd:B = 2:1 and those on the Nd/sub 2/Fe/sub 14/B-Nd section are given for the first time. (author)

Search for Majorana fermions in topological superconductors.

Energy Technology Data Exchange (ETDEWEB)

Pan, Wei [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shi, Xiaoyan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hawkins, Samuel D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Klem, John Frederick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-10-01

The goal of this project is to search for Majorana fermions (a new quantum particle) in a topological superconductor (a new quantum matter achieved in a topological insulator proximitized by an s-wave superconductor). Majorana fermions (MFs) are electron-like particles that are their own anti-particles. MFs are shown to obey non-Abelian statistics and, thus, can be harnessed to make a fault-resistant topological quantum computer. With the arrival of topological insulators, novel schemes to create MFs have been proposed in hybrid systems by combining a topological insulator with a conventional superconductor. In this LDRD project, we will follow the theoretical proposals to search for MFs in one-dimensional (1D) topological superconductors. 1D topological superconductor will be created inside of a quantum point contact (with the metal pinch-off gates made of conventional s-wave superconductors such as niobium) in a two-dimensional topological insulator (such as inverted type-II InAs/GaSb heterostructure).

On physical states in 2d (topological) gravity

International Nuclear Information System (INIS)

Bouwknegt, P.; McCarthy, J.; Pilch, K.

1993-01-01

We review the BRST computation of physical states in various 2d gravity theories. First we discuss the cohomology relevant for 2d gravity coupled to c ≤ 1 conformal matter. We then use these results to compute the cohomology of a c=26 βγ-system, i.e. restricted 2d topological gravity. We also comment on the cohomology for the complete 2d topological gravity. (author). 39 refs

Real tunneling geometries and the large-scale topology of the universe

International Nuclear Information System (INIS)

Gibbons, G.W.; Hartle, J.B.

1990-01-01

If the topology and geometry of spacetime are quantum-mechanically variable, then the particular classical large-scale topology and geometry observed in our universe must be statistical predictions of its initial condition. This paper examines the predictions of the ''no boundary'' initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein's equation are important for such predictions. These consist of compact Riemannian (Euclidean) geometries joined to a Lorentzian cosmological geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable large-scale spacetime predicted by the real tunneling solutions of the ''no-boundary'' initial condition has the topology RxS 3 with the de Sitter metric

Topology optimization of fluid mechanics problems

DEFF Research Database (Denmark)

Gersborg-Hansen, Allan

While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...... processing tool. Prior to design manufacturing this allows the engineer to quantify the performance of the computed topology design using standard, credible analysis tools with a body-fitted mesh. [1] Borrvall and Petersson (2003) "Topology optimization of fluids in Stokes flow", Int. J. Num. Meth. Fluids...

Synthesis of hydrocode and finite element technology for large deformation Lagrangian computation

International Nuclear Information System (INIS)

Goudreau, G.L.; Hallquist, J.O.

1979-08-01

Large deformation engineering analysis at Lawrence Livermore Laboratory has benefited from a synthesis of computational technology from the finite difference hydrocodes of the scientific weapons community and the structural finite element methodology of engineering. Two- and three-dimensional explicit and implicit Lagrangian continuum codes have been developed exploiting the strengths of each. The explicit methodology primarily exploits the primitive constant stress (or one point integration) brick element. Similarity and differences with the integral finite difference method are discussed. Choice of stress and finite strain measures, and selection of hour glass viscosity are also considered. The implicit codes also employ a Cauchy formulation, with Newton iteration and a symmetric tangent matrix. A library of finite strain material routines includes hypoelastic/plastic, hyperelastic, viscoelastic, as well as hydrodynamic behavior. Arbitrary finite element topology and a general slide-line treatment significantly extends Lagrangian hydrocode application. Computational experience spans weapons and non-weapons applications

Parallel Computation on Multicore Processors Using Explicit Form of the Finite Element Method and C++ Standard Libraries

Directory of Open Access Journals (Sweden)

Rek Václav

2016-11-01

Full Text Available In this paper, the form of modifications of the existing sequential code written in C or C++ programming language for the calculation of various kind of structures using the explicit form of the Finite Element Method (Dynamic Relaxation Method, Explicit Dynamics in the NEXX system is introduced. The NEXX system is the core of engineering software NEXIS, Scia Engineer, RFEM and RENEX. It has the possibilities of multithreaded running, which can now be supported at the level of native C++ programming language using standard libraries. Thanks to the high degree of abstraction that a contemporary C++ programming language provides, a respective library created in this way can be very generalized for other purposes of usage of parallelism in computational mechanics.

Two-dimensional topological photonic systems

Science.gov (United States)

Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

2017-09-01

The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

Twisted quantum double model of topological order with boundaries

Science.gov (United States)

Bullivant, Alex; Hu, Yuting; Wan, Yidun

2017-10-01

We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group G and a 3-cocycle in the third cohomology group of G over U (1 ) , a boundary Hamiltonian can be defined by a subgroup K of G and a 2-cochain in the second cochain group of K over U (1 ) . The consistency between the bulk and boundary Hamiltonians is dictated by what we call the Frobenius condition that constrains the 2-cochain given the 3-cocyle. We offer a closed-form formula computing the ground-state degeneracy of the model on a cylinder in terms of the input data only, which can be naturally generalized to surfaces with more boundaries. We also explicitly write down the ground-state wave function of the model on a disk also in terms of the input data only.

Optimal Network-Topology Design

Science.gov (United States)

Li, Victor O. K.; Yuen, Joseph H.; Hou, Ting-Chao; Lam, Yuen Fung

1987-01-01

Candidate network designs tested for acceptability and cost. Optimal Network Topology Design computer program developed as part of study on topology design and analysis of performance of Space Station Information System (SSIS) network. Uses efficient algorithm to generate candidate network designs consisting of subsets of set of all network components, in increasing order of total costs and checks each design to see whether it forms acceptable network. Technique gives true cost-optimal network and particularly useful when network has many constraints and not too many components. Program written in PASCAL.

On topological properties of sierpinski networks

International Nuclear Information System (INIS)

Imran, Muhammad; Sabeel-e-Hafi; Gao, Wei; Reza Farahani, Mohammad

2017-01-01

Sierpinski graphs constitute an extensively studied class of graphs of fractal nature applicable in topology, mathematics of Tower of Hanoi, computer science, and elsewhere. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, biological activity, etc. are determined by the chemical applications of graph theory. These properties can be characterized by certain graph invariants referred to as topological indices. In QRAR/QSPR study these graph invariants has played a vital role. In this paper, we study the molecular topological properties of Sierpinski networks and derive the analytical closed formulas for the atom-bond connectivity (ABC) index, geometric-arithmetic (GA) index, and fourth and fifth version of these topological indices for Sierpinski networks denoted by S(n, k).

Topological Substituent Descriptors

Directory of Open Access Journals (Sweden)

Mircea V. DIUDEA

2002-12-01

Full Text Available Motivation. Substituted 1,3,5-triazines are known as useful herbicidal substances. In view of reducing the cost of biological screening, computational methods are carried out for evaluating the biological activity of organic compounds. Often a class of bioactives differs only in the substituent attached to a basic skeleton. In such cases substituent descriptors will give the same prospecting results as in case of using the whole molecule description, but with significantly reduced computational time. Such descriptors are useful in describing steric effects involved in chemical reactions. Method. Molecular topology is the method used for substituent description and multi linear regression analysis as a statistical tool. Results. Novel topological descriptors, XLDS and Ws, based on the layer matrix of distance sums and walks in molecular graphs, respectively, are proposed for describing the topology of substituents linked on a chemical skeleton. They are tested for modeling the esterification reaction in the class of benzoic acids and herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino-1,3,5-triazines. Conclusions. Ws substituent descriptor, based on walks in graph, satisfactorily describes the steric effect of alkyl substituents behaving in esterification reaction, with good correlations to the Taft and Charton steric parameters, respectively. Modeling the herbicidal activity of the seo of 1,3,5-triazines exceeded the models reported in literature, so far.

Critical phenomena in communication/computation networks with various topologies and suboptimal to optimal resource allocation

Science.gov (United States)

Cogoni, Marco; Busonera, Giovanni; Anedda, Paolo; Zanetti, Gianluigi

2015-01-01

We generalize previous studies on critical phenomena in communication networks [1,2] by adding computational capabilities to the nodes. In our model, a set of tasks with random origin, destination and computational structure is distributed on a computational network, modeled as a graph. By varying the temperature of a Metropolis Montecarlo, we explore the global latency for an optimal to suboptimal resource assignment at a given time instant. By computing the two-point correlation function for the local overload, we study the behavior of the correlation distance (both for links and nodes) while approaching the congested phase: a transition from peaked to spread g(r) is seen above a critical (Montecarlo) temperature Tc. The average latency trend of the system is predicted by averaging over several network traffic realizations while maintaining a spatially detailed information for each node: a sharp decrease of performance is found over Tc independently of the workload. The globally optimized computational resource allocation and network routing defines a baseline for a future comparison of the transition behavior with respect to existing routing strategies [3,4] for different network topologies.

Performance analysis and acceleration of explicit integration for large kinetic networks using batched GPU computations

Energy Technology Data Exchange (ETDEWEB)

Shyles, Daniel [University of Tennessee (UT); Dongarra, Jack J. [University of Tennessee, Knoxville (UTK); Guidry, Mike W. [ORNL; Tomov, Stanimire Z. [ORNL; Billings, Jay Jay [ORNL; Brock, Benjamin A. [ORNL; Haidar Ahmad, Azzam A. [ORNL

2016-09-01

Abstract—We demonstrate the systematic implementation of recently-developed fast explicit kinetic integration algorithms that solve efficiently N coupled ordinary differential equations (subject to initial conditions) on modern GPUs. We take representative test cases (Type Ia supernova explosions) and demonstrate two or more orders of magnitude increase in efficiency for solving such systems (of realistic thermonuclear networks coupled to fluid dynamics). This implies that important coupled, multiphysics problems in various scientific and technical disciplines that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible. As examples of such applications we present the computational techniques developed for our ongoing deployment of these new methods on modern GPU accelerators. We show that similarly to many other scientific applications, ranging from national security to medical advances, the computation can be split into many independent computational tasks, each of relatively small-size. As the size of each individual task does not provide sufficient parallelism for the underlying hardware, especially for accelerators, these tasks must be computed concurrently as a single routine, that we call batched routine, in order to saturate the hardware with enough work.

Study of Dendrimers by Topological Indices

Directory of Open Access Journals (Sweden)

Soleimani Najmeh

2017-12-01

Full Text Available In this paper, five degree based topological indices, the first Zagreb (M1, second Zagreb (M2, first multiple Zagreb (PM1, second multiple Zagreb (PM2, and the hyper Zagreb (HM indices of two types of dendrimers are studied. In addition, two distance based topological indices, the total eccentricity (θ and eccentric connectivity (ξc indices of these dendrimers are computed.

Architecture and data processing alternatives for the TSE computer. Volume 2: Extraction of topological information from an image by the Tse computer

Science.gov (United States)

Jones, J. R.; Bodenheimer, R. E.

1976-01-01

A simple programmable Tse processor organization and arithmetic operations necessary for extraction of the desired topological information are described. Hardware additions to this organization are discussed along with trade-offs peculiar to the tse computing concept. An improved organization is presented along with the complementary software for the various arithmetic operations. The performance of the two organizations is compared in terms of speed, power, and cost. Software routines developed to extract the desired information from an image are included.

Topology-Based Methods in Visualization 2015

CERN Document Server

Garth, Christoph; Weinkauf, Tino

2017-01-01

This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volum...

An improved genetic algorithm with dynamic topology

International Nuclear Information System (INIS)

Cai Kai-Quan; Tang Yan-Wu; Zhang Xue-Jun; Guan Xiang-Min

2016-01-01

The genetic algorithm (GA) is a nature-inspired evolutionary algorithm to find optima in search space via the interaction of individuals. Recently, researchers demonstrated that the interaction topology plays an important role in information exchange among individuals of evolutionary algorithm. In this paper, we investigate the effect of different network topologies adopted to represent the interaction structures. It is found that GA with a high-density topology ends up more likely with an unsatisfactory solution, contrarily, a low-density topology can impede convergence. Consequently, we propose an improved GA with dynamic topology, named DT-GA, in which the topology structure varies dynamically along with the fitness evolution. Several experiments executed with 15 well-known test functions have illustrated that DT-GA outperforms other test GAs for making a balance of convergence speed and optimum quality. Our work may have implications in the combination of complex networks and computational intelligence. (paper)

Persistent topological features of dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Maletić, Slobodan, E-mail: slobodan@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia); Zhao, Yi, E-mail: zhao.yi@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Rajković, Milan, E-mail: milanr@vinca.rs [Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia)

2016-05-15

Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.

Topology for statistical modeling of petascale data.

Energy Technology Data Exchange (ETDEWEB)

Pascucci, Valerio (University of Utah, Salt Lake City, UT); Mascarenhas, Ajith Arthur; Rusek, Korben (Texas A& M University, College Station, TX); Bennett, Janine Camille; Levine, Joshua (University of Utah, Salt Lake City, UT); Pebay, Philippe Pierre; Gyulassy, Attila (University of Utah, Salt Lake City, UT); Thompson, David C.; Rojas, Joseph Maurice (Texas A& M University, College Station, TX)

2011-07-01

This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.

Torsional Topological Invariants (and their relevance for real life)

CERN Document Server

Chandia, O; Chandia, Osvaldo; Zanelli, Jorge

1997-01-01

The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or SU(N) connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the Chern/Pontryagin invariants: they can be expressed as integrals over the manifold of local densities and take integer values on compact spaces without boundary; their spectrum is determined by the homotopy groups determined by the connection bundle but depend also on the bundle of local orthonormal frames on the tangent space of the manifold. It is shown that in spacetimes with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. Explicit examples of topologically stable configurations carrying nonvanishing instanton number in four and eight dimensions are given, and they can be conjectured to exist in dimension $4k$. It is also shown that the chiral anomaly in a spacetime with torsion rece...

TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

Science.gov (United States)

2017-01-01

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969

Topological order, entanglement, and quantum memory at finite temperature

International Nuclear Information System (INIS)

Mazáč, Dalimil; Hamma, Alioscia

2012-01-01

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement–deconfinement transitions in the corresponding Z 2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed. - Highlights: ► We calculate the topological entropy of a general toric code in any dimension. ► We find phase transitions in the topological entropy. ► The phase transitions coincide with the appearance of quantum/classical memory.

Taming the cosmological constant in 2D causal quantum gravity with topology change

NARCIS (Netherlands)

Loll, R.; Westra, W.; Zohren, S.

2005-01-01

As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of Causal Dy- namical Triangulations in two dimensions. In this paper we derive a complete ana- lytical solution of the quantum continuum

The new protein topology graph library web server.

Science.gov (United States)

Schäfer, Tim; Scheck, Andreas; Bruneß, Daniel; May, Patrick; Koch, Ina

2016-02-01

We present a new, extended version of the Protein Topology Graph Library web server. The Protein Topology Graph Library describes the protein topology on the super-secondary structure level. It allows to compute and visualize protein ligand graphs and search for protein structural motifs. The new server features additional information on ligand binding to secondary structure elements, increased usability and an application programming interface (API) to retrieve data, allowing for an automated analysis of protein topology. The Protein Topology Graph Library server is freely available on the web at http://ptgl.uni-frankfurt.de. The website is implemented in PHP, JavaScript, PostgreSQL and Apache. It is supported by all major browsers. The VPLG software that was used to compute the protein ligand graphs and all other data in the database is available under the GNU public license 2.0 from http://vplg.sourceforge.net. tim.schaefer@bioinformatik.uni-frankfurt.de; ina.koch@bioinformatik.uni-frankfurt.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Topological insulators/superconductors: Potential future electronic materials

International Nuclear Information System (INIS)

Hor, Y. S.

2014-01-01

A new material called topological insulator has been discovered and becomes one of the fastest growing field in condensed matter physics. Topological insulator is a new quantum phase of matter which has Dirac-like conductivity on its surface, but bulk insulator through its interior. It is considered a challenging problem for the surface transport measurements because of dominant internal conductance due to imperfections of the existing crystals of topological insulators. By a proper method, the internal bulk conduction can be suppressed in a topological insulator, and permit the detection of the surface currents which is necessary for future fault-tolerant quantum computing applications. Doped topological insulators have depicted a large variety of bulk physical properties ranging from magnetic to superconducting behaviors. By chemical doping, a TI can change into a bulk superconductor. Nb x Bi 2 Se 3 is shown to be a superconductor with T c ∼ 3.2 K, which could be a potential candidate for a topological superconductor

Hybrid MPI/OpenMP parallelization of the explicit Volterra integral equation solver for multi-core computer architectures

KAUST Repository

Al Jarro, Ahmed

2011-08-01

A hybrid MPI/OpenMP scheme for efficiently parallelizing the explicit marching-on-in-time (MOT)-based solution of the time-domain volume (Volterra) integral equation (TD-VIE) is presented. The proposed scheme equally distributes tested field values and operations pertinent to the computation of tested fields among the nodes using the MPI standard; while the source field values are stored in all nodes. Within each node, OpenMP standard is used to further accelerate the computation of the tested fields. Numerical results demonstrate that the proposed parallelization scheme scales well for problems involving three million or more spatial discretization elements. © 2011 IEEE.

Topological insulators and topological superconductors

CERN Document Server

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...

Globally symmetric topological phase: from anyonic symmetry to twist defect

International Nuclear Information System (INIS)

Teo, Jeffrey C Y

2016-01-01

Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics. These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and statistical properties. Anyonic symmetries associate topological defects or fluxes in topological phases. As the symmetries are global and static, these extrinsic defects are semiclassical objects that behave disparately from conventional quantum anyons. Remarkably, even when the topological states supporting them are Abelian, they are generically non-Abelian and powerful enough for topological quantum computation. In this article, I review the most recent theoretical developments on symmetries and defects in topological phases. (topical review)

Duo gating on a 3D topological insulator - independent tuning of both topological surface states

Science.gov (United States)

Li, Chuan; de Ronde, Bob; Snelder, Marieke; Stehno, Martin; Huang, Yingkai; Golden, Mark; Brinkman, Alexander; ICE Team; IOP Collaboration

ABSTRACT: Topological insulators are associated with a trove of exciting physics, such as the ability to host robust anyons, Majorana Bound States, which can be used for quantum computation. For future Majorana devices it is desirable to have the Fermi energy tuned as close as possible to the Dirac point of the topological surface state. Based on previous work on gating BSTS, we report the experimental progress towards gate-tuning of the top and bottom topological surface states of BiSbTeSe2 crystal flakes. When the Fermi level is moved across the Dirac point conduction is shown to change from electron dominated transport to hole dominated transport independently for either surface. In the high magnetic field, one can tune the system precisely between the different landau levels of both surfaces, thus a full gating map of the possible landau levels combination is established. In addition, we provide a simple capacitance model to explain the general hysteresis behaviors in topological insulator systems.

Solving topological field theories on mapping tori

International Nuclear Information System (INIS)

Blau, M.; Jermyn, I.; Thompson, G.

1996-05-01

Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1 modul 1) model of Rozansky and Saleur on Σ x S 1 , both directly and using equivalent two-dimensional theories. We also derive the partition function on a certain non-abelian generalization of the U(1 modul 1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two- dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold. (author). 20 refs

On Certain Topological Indices of Boron Triangular Nanotubes

Science.gov (United States)

Aslam, Adnan; Ahmad, Safyan; Gao, Wei

2017-08-01

The topological index gives information about the whole structure of a chemical graph, especially degree-based topological indices that are very useful. Boron triangular nanotubes are now replacing usual carbon nanotubes due to their excellent properties. We have computed general Randić (Rα), first Zagreb (M1) and second Zagreb (M2), atom-bond connectivity (ABC), and geometric-arithmetic (GA) indices of boron triangular nanotubes. Also, we have computed the fourth version of atom-bond connectivity (ABC4) and the fifth version of geometric-arithmetic (GA5) indices of boron triangular nanotubes.

Topologically-based visualization of large-scale volume data

International Nuclear Information System (INIS)

Takeshima, Y.; Tokunaga, M.; Fujishiro, I.; Takahashi, S.

2004-01-01

Due to the recent progress in the performance of computing/measurement environments and the advent of ITBL environments, volume datasets have become larger and more complicated. Although computer visualization is one of the tools to analyze such datasets effectively, it is almost impossible to adjust the visualization parameter value by trial and error without taking the feature of a given volume dataset into consideration. In this article, we introduce a scheme of topologically-based volume visualization, which is intended to choose appropriate visualization parameter values automatically through topological volume skeletonization. (author)

A study of topological quantum phase transition and Majorana localization length for the interacting helical liquid system

International Nuclear Information System (INIS)

Dey, Dayasindhu; Saha, Sudip Kumar; Deo, P. Singha; Kumar, Manoranjan; Sarkar, Sujit

2017-01-01

We study the topological quantum phase transition and also the nature of this transition using the density matrix renormalization group method. We observe the existence of topological quantum phase transition for repulsive interaction, however this phase is more stable for the attractive interaction. The length scale dependent study shows many new and important results and we show explicitly that the major contribution to the excitation comes from the edge of the system when the system is in the topological state. We also show the dependence of Majorana localization length for various values of chemical potential. (author)

Computational multiobjective topology optimization of silicon anode structures for lithium-ion batteries

Science.gov (United States)

Mitchell, Sarah L.; Ortiz, Michael

2016-09-01

This study utilizes computational topology optimization methods for the systematic design of optimal multifunctional silicon anode structures for lithium-ion batteries. In order to develop next generation high performance lithium-ion batteries, key design challenges relating to the silicon anode structure must be addressed, namely the lithiation-induced mechanical degradation and the low intrinsic electrical conductivity of silicon. As such this work considers two design objectives, the first being minimum compliance under design dependent volume expansion, and the second maximum electrical conduction through the structure, both of which are subject to a constraint on material volume. Density-based topology optimization methods are employed in conjunction with regularization techniques, a continuation scheme, and mathematical programming methods. The objectives are first considered individually, during which the influence of the minimum structural feature size and prescribed volume fraction are investigated. The methodology is subsequently extended to a bi-objective formulation to simultaneously address both the structural and conduction design criteria. The weighted sum method is used to derive the Pareto fronts, which demonstrate a clear trade-off between the competing design objectives. A rigid frame structure was found to be an excellent compromise between the structural and conduction design criteria, providing both the required structural rigidity and direct conduction pathways. The developments and results presented in this work provide a foundation for the informed design and development of silicon anode structures for high performance lithium-ion batteries.

Topological susceptibility in the SU(3) gauge theory

DEFF Research Database (Denmark)

Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio

2004-01-01

We compute the topological susceptibility for the SU(3) Yang--Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 +/- 5 MeV)^4 if F_K is used to set...

Topology Optimization Using Multiscale Finite Element Method for High-Contrast Media

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov

2014-01-01

The focus of this paper is on the applicability of multiscale finite element coarse spaces for reducing the computational burden in topology optimization. The coarse spaces are obtained by solving a set of local eigenvalue problems on overlapping patches covering the computational domain. The app......The focus of this paper is on the applicability of multiscale finite element coarse spaces for reducing the computational burden in topology optimization. The coarse spaces are obtained by solving a set of local eigenvalue problems on overlapping patches covering the computational domain...

Topology optimization for nano-photonics

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard; Sigmund, Ole

2011-01-01

Topology optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics...... applications. Topology optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion....... The optimization problem is efficiently solved using mathematical programming-based optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind topology optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices...

How to model wireless mesh networks topology

International Nuclear Information System (INIS)

Sanni, M L; Hashim, A A; Anwar, F; Ali, S; Ahmed, G S M

2013-01-01

The specification of network connectivity model or topology is the beginning of design and analysis in Computer Network researches. Wireless Mesh Networks is an autonomic network that is dynamically self-organised, self-configured while the mesh nodes establish automatic connectivity with the adjacent nodes in the relay network of wireless backbone routers. Researches in Wireless Mesh Networks range from node deployment to internetworking issues with sensor, Internet and cellular networks. These researches require modelling of relationships and interactions among nodes including technical characteristics of the links while satisfying the architectural requirements of the physical network. However, the existing topology generators model geographic topologies which constitute different architectures, thus may not be suitable in Wireless Mesh Networks scenarios. The existing methods of topology generation are explored, analysed and parameters for their characterisation are identified. Furthermore, an algorithm for the design of Wireless Mesh Networks topology based on square grid model is proposed in this paper. The performance of the topology generated is also evaluated. This research is particularly important in the generation of a close-to-real topology for ensuring relevance of design to the intended network and validity of results obtained in Wireless Mesh Networks researches

Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

Science.gov (United States)

Kumar, A.; Rudy, D. H.; Drummond, J. P.; Harris, J. E.

1982-01-01

Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

Energy Technology Data Exchange (ETDEWEB)

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr [Université Montpellier 2, CNRS, L2C, IMAG, Montpellier (France)

2016-03-15

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Ring-array processor distribution topology for optical interconnects

Science.gov (United States)

Li, Yao; Ha, Berlin; Wang, Ting; Wang, Sunyu; Katz, A.; Lu, X. J.; Kanterakis, E.

1992-01-01

The existing linear and rectangular processor distribution topologies for optical interconnects, although promising in many respects, cannot solve problems such as clock skews, the lack of supporting elements for efficient optical implementation, etc. The use of a ring-array processor distribution topology, however, can overcome these problems. Here, a study of the ring-array topology is conducted with an aim of implementing various fast clock rate, high-performance, compact optical networks for digital electronic multiprocessor computers. Practical design issues are addressed. Some proof-of-principle experimental results are included.

Topology Optimization of Lightweight Lattice Structural Composites Inspired by Cuttlefish Bone

Science.gov (United States)

Hu, Zhong; Gadipudi, Varun Kumar; Salem, David R.

2018-03-01

Lattice structural composites are of great interest to various industries where lightweight multifunctionality is important, especially aerospace. However, strong coupling among the composition, microstructure, porous topology, and fabrication of such materials impedes conventional trial-and-error experimental development. In this work, a discontinuous carbon fiber reinforced polymer matrix composite was adopted for structural design. A reliable and robust design approach for developing lightweight multifunctional lattice structural composites was proposed, inspired by biomimetics and based on topology optimization. Three-dimensional periodic lattice blocks were initially designed, inspired by the cuttlefish bone microstructure. The topologies of the three-dimensional periodic blocks were further optimized by computer modeling, and the mechanical properties of the topology optimized lightweight lattice structures were characterized by computer modeling. The lattice structures with optimal performance were identified.

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

International Nuclear Information System (INIS)

Ablinger, J.; Schneider, C.; Manteuffel, A. von

2015-09-01

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element A Qg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

Science.gov (United States)

Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

2016-05-01

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

Topological expansion of the chain of matrices

International Nuclear Information System (INIS)

Eynard, B.; Ferrer, A. Prats

2009-01-01

We solve the loop equations to all orders in 1/N 2 , for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large N asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).

Topological Phases in the Real World

Science.gov (United States)

Hsu, Yi-Ting

The experimental discovery and subsequent theoretical understanding of the integer quantum Hall effect, the first known topological phase, has started a revolutionary breakthrough in understanding states of matter since its discovery four decades ago. Topological phases are predicted to have many generic signatures resulting from their underlying topological nature, such as quantized Hall transport, robust boundary states, and possible fractional excitations. The intriguing nature of these signatures and their potential applications in quantum computation has intensely fueled the efforts of the physics community to materialize topological phases. Among various topological phases initially predicted on theoretical grounds, chiral topological superconductors and time-reversal symmetric topological insulators (TI) in three dimension (3D) are two promising candidates for experimental realization and application. The family of materials, Bi2X3 (X = Se, Te), has been predicted and shown experimentally to be time-reversal symmetric 3D TIs through the observation of robust Dirac surface states with Rashba-type spin-winding. Due to their robust surface states with spin-windings, these 3D TIs are expected to be promising materials for producing large spin-transfer torques which are advantageous for spintronics application. As for topological superconductors, despite the exotic excitations that have been extensively proposed as qubits for topological quantum computing, materials hosting topological superconductivity are rare to date and the leading candidate in two dimensions (2D), Sr 2RuO4, has a low transition temperature (Tc ). The goal of my phd study is to push forward the current status of realization of topological phases by materializing higher Tc topological superconductors and investigating the stability of Dirac surface states in 3D TIs. In the first part of this thesis, I will discuss our double-pronged objective for topological superconductors: to propose how to

Topological susceptibility for the SU(3) Yang--Mills theory

DEFF Research Database (Denmark)

Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio

2004-01-01

We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi...

Combinatorial-topological framework for the analysis of global dynamics

Science.gov (United States)

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Combinatorial-topological framework for the analysis of global dynamics.

Science.gov (United States)

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Characteristics and Classification of Topological Spatial Relations in 3-D Cadasters

Directory of Open Access Journals (Sweden)

Lili Fu

2018-03-01

Full Text Available The application of a 3-D topology to cadasters is becoming increasingly important as 3-D cadasters continue to develop and cadastral data applications increase. This study discusses spatial topological relations related to 3-D cadasters, the geometric objects used in 3-D cadastral spatial modelling, and the characteristics of the spatial data. The characteristics of the topological relations for a 3-D cadaster are summarized, and a classification method is proposed. Research on the classification of topological spatial relations in 3-D cadasters provides guidance for the analysis and computation of the topological spatial relations, changing of cadastral parcels, and topological consistency in cadastral spatial data.

On certain topological indices of boron triangular nanotubes

Energy Technology Data Exchange (ETDEWEB)

Aslam, Adnan [Univ. of Engineering and Technology, Lahore (Pakistan). Dept. of Natural Sciences and Humanities; Ahmad, Safyan [GC Univ. Lahore (Pakistan). Abdus Salam School of Mathematical Sciences; Gao, Wei [Yunnan Normal Univ., Kunming (China). School of Information Science and Technology

2017-11-01

The topological index gives information about the whole structure of a chemical graph, especially degree-based topological indices that are very useful. Boron triangular nanotubes are now replacing usual carbon nanotubes due to their excellent properties. We have computed general Randic (R{sub a}), first Zagreb (M{sub 1}) and second Zagreb (M{sub 2}), atom-bond connectivity (ABC), and geometric-arithmetic (GA) indices of boron triangular nanotubes. Also, we have computed the fourth version of atom-bond connectivity (ABC{sub 4}) and the fifth version of geometric-arithmetic (GA{sub 5}) indices of boron triangular nanotubes.

Robust quantum network architectures and topologies for entanglement distribution

Science.gov (United States)

Das, Siddhartha; Khatri, Sumeet; Dowling, Jonathan P.

2018-01-01

Entanglement distribution is a prerequisite for several important quantum information processing and computing tasks, such as quantum teleportation, quantum key distribution, and distributed quantum computing. In this work, we focus on two-dimensional quantum networks based on optical quantum technologies using dual-rail photonic qubits for the building of a fail-safe quantum internet. We lay out a quantum network architecture for entanglement distribution between distant parties using a Bravais lattice topology, with the technological constraint that quantum repeaters equipped with quantum memories are not easily accessible. We provide a robust protocol for simultaneous entanglement distribution between two distant groups of parties on this network. We also discuss a memory-based quantum network architecture that can be implemented on networks with an arbitrary topology. We examine networks with bow-tie lattice and Archimedean lattice topologies and use percolation theory to quantify the robustness of the networks. In particular, we provide figures of merit on the loss parameter of the optical medium that depend only on the topology of the network and quantify the robustness of the network against intermittent photon loss and intermittent failure of nodes. These figures of merit can be used to compare the robustness of different network topologies in order to determine the best topology in a given real-world scenario, which is critical in the realization of the quantum internet.

Topology Design for Directional Range Extension Networks with Antenna Blockage

Science.gov (United States)

2017-03-19

this is equivalent to the Hamiltonian Path Problem, which is NP- hard . More work on computationally efficient topology formation and maintenance... formation and maintenance of low-degree air topologies. 1 I. INTRODUCTION Tactical military networks both on land and at sea often have restricted...constraints on the number of antenna beams that a pod can support, a string topology formation and maintenance algorithm may be the best design choice

Conjugate gradient based projection - A new explicit methodology for frictional contact

Science.gov (United States)

Tamma, Kumar K.; Li, Maocheng; Sha, Desong

1993-01-01

With special attention towards the applicability to parallel computation or vectorization, a new and effective explicit approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focussed towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non-negative constraint condition; this direction is then applied to the Fletcher-Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction.

Thesaurus Racks - Categorical racks and applications in the algebraic topology of Lie racks

OpenAIRE

Grøsfjeld, Tobias

2016-01-01

Group objects of categories have been heavily studied in a general setting, but racks are mostly treated explicitly. Since rack structures are more general than groups, this thesis aims to explore the properties of general rack objects and use the tools of category theory to put topological racks in a new light.

Approximate Reanalysis in Topology Optimization

DEFF Research Database (Denmark)

Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

2009-01-01

In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

Topology in Molecular Biology

CERN Document Server

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.

Broadcasting Topology and Routing Information in Computer Networks

Science.gov (United States)

1985-05-01

DOWN\\ linki inki FIgwre 1.2.1: Topology Problem Example messages from node 2 before receiving the first DOWN message from node 3. Now assume that before...node to each of the link’s end nodes. 54 link.1 cc 4 1 -. distances to linki Figue 3.4.2: SPTA Port Distance Table Example An example of these

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

DEFF Research Database (Denmark)

Sun, Jialiang; Tian, Qiang; Hu, Haiyan

2018-01-01

Recent years have witnessed the application of topology optimization to flexible multibody systems (FMBS) so as to enhance their dynamic performances. In this study, an explicit topology optimization approach is proposed for an FMBS with variable-length bodies via the moving morphable components...... (MMC). Using the arbitrary Lagrangian–Eulerian (ALE) formulation, the thin plate elements of the absolute nodal coordinate formulation (ANCF) are used to describe the platelike bodies with variable length. For the thin plate element of ALE–ANCF, the elastic force and additional inertial force, as well...

Photoinduced Topological Phase Transitions in Topological Magnon Insulators.

Science.gov (United States)

Owerre, S A

2018-03-13

Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagomé ferromagnet Cu(1-3, bdc), and they also possess protected magnon edge modes. These topological magnetic materials can transport heat as well as spin currents, hence they can be useful for spintronic applications. Moreover, as magnons are charge-neutral spin-1 bosonic quasiparticles with a magnetic dipole moment, topological magnon materials can also interact with electromagnetic fields through the Aharonov-Casher effect. In this report, we study photoinduced topological phase transitions in intrinsic topological magnon insulators in the kagomé ferromagnets. Using magnonic Floquet-Bloch theory, we show that by varying the light intensity, periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with different sign of the Berry curvatures and the thermal Hall conductivity. We further show that, under certain conditions, periodically driven gapped topological magnon insulators can also be tuned to synthetic gapless topological magnon semimetals with Dirac-Weyl magnon cones. We envision that this work will pave the way for interesting new potential practical applications in topological magnetic materials.

Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework

DEFF Research Database (Denmark)

Aage, Niels; Andreassen, Erik; Lazarov, Boyan Stefanov

2015-01-01

This paper presents a flexible framework for parallel and easy-to-implement topology optimization using the Portable and Extendable Toolkit for Scientific Computing (PETSc). The presented framework is based on a standardized, and freely available library and in the published form it solves...

An explicit method in non-linear soil-structure interaction

International Nuclear Information System (INIS)

Kunar, R.R.

1981-01-01

The explicit method of analysis in the time domain is ideally suited for the solution of transient dynamic non-linear problems. Though the method is not new, its application to seismic soil-structure interaction is relatively new and deserving of public discussion. This paper describes the principles of the explicit approach in soil-structure interaction and it presents a simple algorithm that can be used in the development of explicit computer codes. The paper also discusses some of the practical considerations like non-reflecting boundaries and time steps. The practicality of the method is demonstrated using a computer code, PRESS, which is used to compare the treatment of strain-dependent properties using average strain levels over the whole time history (the equivalent linear method) and using the actual strain levels at every time step to modify the soil properties (non-linear method). (orig.)

The topological Anderson insulator phase in the Kane-Mele model

Science.gov (United States)

Orth, Christoph P.; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L.

2016-04-01

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.

Topology and boundary shape optimization as an integrated design tool

Science.gov (United States)

Bendsoe, Martin Philip; Rodrigues, Helder Carrico

1990-01-01

The optimal topology of a two dimensional linear elastic body can be computed by regarding the body as a domain of the plane with a high density of material. Such an optimal topology can then be used as the basis for a shape optimization method that computes the optimal form of the boundary curves of the body. This results in an efficient and reliable design tool, which can be implemented via common FEM mesh generator and CAD type input-output facilities.

Topology

CERN Document Server

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

Derivation of the Time-Reversal Anomaly for (2 +1 )-Dimensional Topological Phases

Science.gov (United States)

Tachikawa, Yuji; Yonekura, Kazuya

2017-09-01

We prove an explicit formula conjectured recently by Wang and Levin for the anomaly of time-reversal symmetry in (2 +1 )-dimensional fermionic topological quantum field theories. The crucial step is to determine the cross-cap state in terms of the modular S matrix and T2 eigenvalues, generalizing the recent analysis by Barkeshli et al. in the bosonic case.

Topological hierarchy matters — topological matters with superlattices of defects

International Nuclear Information System (INIS)

He Jing; Kou Su-Peng

2016-01-01

Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states. In this paper, we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters. We find that both topological defects (quantized vortices) and non topological defects (vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects. These topological mid-gap states have nontrivial topological properties, including the nonzero Chern number and the gapless edge states. Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters. (topical review)

An alternative low-loss stack topology for vanadium redox flow battery: Comparative assessment

Science.gov (United States)

Moro, Federico; Trovò, Andrea; Bortolin, Stefano; Del, Davide, , Col; Guarnieri, Massimo

2017-02-01

Two vanadium redox flow battery topologies have been compared. In the conventional series stack, bipolar plates connect cells electrically in series and hydraulically in parallel. The alternative topology consists of cells connected in parallel inside stacks by means of monopolar plates in order to reduce shunt currents along channels and manifolds. Channelled and flat current collectors interposed between cells were considered in both topologies. In order to compute the stack losses, an equivalent circuit model of a VRFB cell was built from a 2D FEM multiphysics numerical model based on Comsol®, accounting for coupled electrical, electrochemical, and charge and mass transport phenomena. Shunt currents were computed inside the cells with 3D FEM models and in the piping and manifolds by means of equivalent circuits solved with Matlab®. Hydraulic losses were computed with analytical models in piping and manifolds and with 3D numerical analyses based on ANSYS Fluent® in the cell porous electrodes. Total losses in the alternative topology resulted one order of magnitude lower than in an equivalent conventional battery. The alternative topology with channelled current collectors exhibits the lowest shunt currents and hydraulic losses, with round-trip efficiency higher by about 10%, as compared to the conventional topology.

Computing Z-top

International Nuclear Information System (INIS)

Kashani-Poor, A.K.

2014-01-01

The topological string presents an arena in which many features of string theory proper, such as the interplay between world-sheet and target space descriptions or open-closed duality, can be distilled into computational techniques which yield results beyond perturbation theory. In this thesis, I will summarize my research activity in this area. The presentation is organized around computations of the topological string partition function Z-top based on various perspectives on the topological string. (author)

Three-dimensional topological insulators and bosonization

Energy Technology Data Exchange (ETDEWEB)

Cappelli, Andrea [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Randellini, Enrico [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Dipartimento di Fisica e Astronomia, Università di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Sisti, Jacopo [Scuola Internazionale Superiore di Studi Avanzati (SISSA),Via Bonomea 265, 34136 Trieste (Italy)

2017-05-25

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

Protein structure: geometry, topology and classification

Energy Technology Data Exchange (ETDEWEB)

Taylor, William R.; May, Alex C.W.; Brown, Nigel P.; Aszodi, Andras [Division of Mathematical Biology, National Institute for Medical Research, London (United Kingdom)

2001-04-01

The structural principals of proteins are reviewed and analysed from a geometric perspective with a view to revealing the underlying regularities in their construction. Computer methods for the automatic comparison and classification of these structures are then reviewed with an analysis of the statistical significance of comparing different shapes. Following an analysis of the current state of the classification of proteins, more abstract geometric and topological representations are explored, including the occurrence of knotted topologies. The review concludes with a consideration of the origin of higher-level symmetries in protein structure. (author)

Higher dimensional quantum Hall effect as A-class topological insulator

Energy Technology Data Exchange (ETDEWEB)

Hasebe, Kazuki, E-mail: khasebe@stanford.edu

2014-09-15

We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for higher dimensional fuzzy spheres: the ordinary commutator formulation and quantum Nambu bracket formulation. Corresponding to these formulations, we introduce two kinds of monopole gauge fields: non-abelian gauge field and antisymmetric tensor gauge field, which respectively realize the non-commutative geometry of fuzzy sphere in the lowest Landau level. We establish connection between the two types of monopole gauge fields through Chern–Simons term, and derive explicit form of tensor monopole gauge fields with higher string-like singularity. The connection between two types of monopole is applied to generalize the concept of flux attachment in quantum Hall effect to A-class topological insulator. We propose tensor type Chern–Simons theory as the effective field theory for membranes in A-class topological insulators. Membranes turn out to be fractionally charged objects and the phase entanglement mediated by tensor gauge field transforms the membrane statistics to be anyonic. The index theorem supports the dimensional hierarchy of A-class topological insulator. Analogies to D-brane physics of string theory are discussed too.

Topological Signals of Singularities in Ricci Flow

Directory of Open Access Journals (Sweden)

Paul M. Alsing

2017-08-01

Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.

Topological Characterization of Fractured Coal

Science.gov (United States)

Jing, Yu; Armstrong, Ryan T.; Ramandi, Hamed L.; Mostaghimi, Peyman

2017-12-01

Coal transport properties are highly dependent on the underlying fractured network, known as cleats, which are characterized by geometrical and topological properties. X-ray microcomputed tomography (micro-CT) has been widely applied to obtain 3-D digital representations of the cleat network. However, segmentation of 3-D data is often problematic due to image noise, which will result in inaccurate estimation of coal properties (e.g., porosity and specific surface area). To circumvent this issue, a discrete fracture network (DFN) model is proposed. We develop a characterization framework to determine if the developed DFN models can preserve the topological properties of the coal cleat network found in micro-CT data. We compute the Euler characteristic, fractal dimension, and percolation quantities to analyze the topology locally and globally and compare the results between micro-CT data (before denoising), filtered micro-CT data (after denoising), and the DFN model. We find that micro-CT data with noise have extensive connectivity while filtered micro-CT data and DFN models have similar topology both globally and locally. It is concluded that the topology of the DFN models are closer to that of the realistic cleat network that do not have segmentation-induced pores. In addition, micro-CT imaging always struggles with the trade-off between sample size and resolution, while the presented DFN models are not restricted by imaging resolution and thus can be constructed with extended domain size. Overall, the presented DFN model is a reliable alternative with realistic cleat topology, extended domain size and favorable data format for direct numerical simulations.

Topological quantum error correction in the Kitaev honeycomb model

Science.gov (United States)

Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.

2017-08-01

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.

Higgsless superconductivity from topological defects in compact BF terms

Directory of Open Access Journals (Sweden)

M. Cristina Diamantini

2015-02-01

Full Text Available We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalisable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D−1-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D−2-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2 and the topological order (4 are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realised as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.

W-symmetry, topological vertex and affine Yangian

Energy Technology Data Exchange (ETDEWEB)

Procházka, Tomáš [Arnold Sommerfeld Center for Theoretical Physics, Ludwig Maximilian University of Munich,Theresienstr. 37, D-80333 München (Germany); Institute of Physics AS CR,Na Slovance 2, Prague 8 (Czech Republic)

2016-10-14

We discuss the representation theory of the non-linear chiral algebra W{sub 1+∞} of Gaberdiel and Gopakumar and its connection to the Yangian of (u(1))-hat whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of W{sub 1+∞} are given by the topological vertex. The Yangian picture provides an infinite number of commuting charges which can be explicitly diagonalized in W{sub 1+∞} highest weight representations. Many properties that are difficult to study in the W{sub 1+∞} picture turn out to have a simple combinatorial interpretation, once translated to the Yangian picture.

Unified Generic Geometric-Decompositions for Consensus or Flocking Systems of Cooperative Agents and Fast Recalculations of Decomposed Subsystems Under Topology-Adjustments.

Science.gov (United States)

Li, Wei

2016-06-01

This paper considers a unified geometric projection approach for: 1) decomposing a general system of cooperative agents coupled via Laplacian matrices or stochastic matrices and 2) deriving a centroid-subsystem and many shape-subsystems, where each shape-subsystem has the distinct properties (e.g., preservation of formation and stability of the original system, sufficiently simple structures and explicit formation evolution of agents, and decoupling from the centroid-subsystem) which will facilitate subsequent analyses. Particularly, this paper provides an additional merit of the approach: considering adjustments of coupling topologies of agents which frequently occur in system design (e.g., to add or remove an edge, to move an edge to a new place, and to change the weight of an edge), the corresponding new shape-subsystems can be derived by a few simple computations merely from the old shape-subsystems and without referring to the original system, which will provide further convenience for analysis and flexibility of choice. Finally, such fast recalculations of new subsystems under topology adjustments are provided with examples.

Efficient Reanalysis Procedures in Structural Topology Optimization

DEFF Research Database (Denmark)

Amir, Oded

This thesis examines efficient solution procedures for the structural analysis problem within topology optimization. The research is motivated by the observation that when the nested approach to structural optimization is applied, most of the computational effort is invested in repeated solutions...... on approximate reanalysis. For cases where memory limitations require the utilization of iterative equation solvers, we suggest efficient procedures based on alternative termination criteria for such solvers. These approaches are tested on two- and three-dimensional topology optimization problems including...

Explicit Content Caching at Mobile Edge Networks with Cross-Layer Sensing

Science.gov (United States)

Chen, Lingyu; Su, Youxing; Luo, Wenbin; Hong, Xuemin; Shi, Jianghong

2018-01-01

The deployment density and computational power of small base stations (BSs) are expected to increase significantly in the next generation mobile communication networks. These BSs form the mobile edge network, which is a pervasive and distributed infrastructure that can empower a variety of edge/fog computing applications. This paper proposes a novel edge-computing application called explicit caching, which stores selective contents at BSs and exposes such contents to local users for interactive browsing and download. We formulate the explicit caching problem as a joint content recommendation, caching, and delivery problem, which aims to maximize the expected user quality-of-experience (QoE) with varying degrees of cross-layer sensing capability. Optimal and effective heuristic algorithms are presented to solve the problem. The theoretical performance bounds of the explicit caching system are derived in simplified scenarios. The impacts of cache storage space, BS backhaul capacity, cross-layer information, and user mobility on the system performance are simulated and discussed in realistic scenarios. Results suggest that, compared with conventional implicit caching schemes, explicit caching can better exploit the mobile edge network infrastructure for personalized content dissemination. PMID:29565313

Explicit Content Caching at Mobile Edge Networks with Cross-Layer Sensing.

Science.gov (United States)

Chen, Lingyu; Su, Youxing; Luo, Wenbin; Hong, Xuemin; Shi, Jianghong

2018-03-22

The deployment density and computational power of small base stations (BSs) are expected to increase significantly in the next generation mobile communication networks. These BSs form the mobile edge network, which is a pervasive and distributed infrastructure that can empower a variety of edge/fog computing applications. This paper proposes a novel edge-computing application called explicit caching, which stores selective contents at BSs and exposes such contents to local users for interactive browsing and download. We formulate the explicit caching problem as a joint content recommendation, caching, and delivery problem, which aims to maximize the expected user quality-of-experience (QoE) with varying degrees of cross-layer sensing capability. Optimal and effective heuristic algorithms are presented to solve the problem. The theoretical performance bounds of the explicit caching system are derived in simplified scenarios. The impacts of cache storage space, BS backhaul capacity, cross-layer information, and user mobility on the system performance are simulated and discussed in realistic scenarios. Results suggest that, compared with conventional implicit caching schemes, explicit caching can better exploit the mobile edge network infrastructure for personalized content dissemination.

Topological recursion for Gaussian means and cohomological field theories

Science.gov (United States)

Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.

2015-12-01

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.

Topology influences performance in the associative memory neural networks

International Nuclear Information System (INIS)

Lu Jianquan; He Juan; Cao Jinde; Gao Zhiqiang

2006-01-01

To explore how topology affects performance within Hopfield-type associative memory neural networks (AMNNs), we studied the computational performance of the neural networks with regular lattice, random, small-world, and scale-free structures. In this Letter, we found that the memory performance of neural networks obtained through asynchronous updating from 'larger' nodes to 'smaller' nodes are better than asynchronous updating in random order, especially for the scale-free topology. The computational performance of associative memory neural networks linked by the above-mentioned network topologies with the same amounts of nodes (neurons) and edges (synapses) were studied respectively. Along with topologies becoming more random and less locally disordered, we will see that the performance of associative memory neural network is quite improved. By comparing, we show that the regular lattice and random network form two extremes in terms of patterns stability and retrievability. For a network, its patterns stability and retrievability can be largely enhanced by adding a random component or some shortcuts to its structured component. According to the conclusions of this Letter, we can design the associative memory neural networks with high performance and minimal interconnect requirements

Topological strings on compact Calabi-Yau's

Energy Technology Data Exchange (ETDEWEB)

Hollands, Lotte, E-mail: lhollands@science.uva.nl

2007-09-15

Some steps towards solving topological string amplitudes on Calabi-Yau spaces have been taken lately: all-genus amplitudes have been computed for non-compact toric Calabi-Yau threefolds, local Riemann surfaces and K3-fibrations, while progression has been made for the Fermat quintic threefold. However, the building blocks of all-genus topological string amplitudes for general compact Calabi-Yau's remain unknown. We study some aspects of the underlying geometry and discuss difficulties.

C*-algebras over topological spaces

DEFF Research Database (Denmark)

Meyer, Ralf; Nest, Ryszard

2012-01-01

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral...

Wide baseline stereo matching based on double topological relationship consistency

Science.gov (United States)

Zou, Xiaohong; Liu, Bin; Song, Xiaoxue; Liu, Yang

2009-07-01

Stereo matching is one of the most important branches in computer vision. In this paper, an algorithm is proposed for wide-baseline stereo vision matching. Here, a novel scheme is presented called double topological relationship consistency (DCTR). The combination of double topological configuration includes the consistency of first topological relationship (CFTR) and the consistency of second topological relationship (CSTR). It not only sets up a more advanced model on matching, but discards mismatches by iteratively computing the fitness of the feature matches and overcomes many problems of traditional methods depending on the powerful invariance to changes in the scale, rotation or illumination across large view changes and even occlusions. Experimental examples are shown where the two cameras have been located in very different orientations. Also, epipolar geometry can be recovered using RANSAC by far the most widely method adopted possibly. By the method, we can obtain correspondences with high precision on wide baseline matching problems. Finally, the effectiveness and reliability of this method are demonstrated in wide-baseline experiments on the image pairs.

Holonomic quantum computation based on the scalar Aharonov–Bohm effect for neutral particles and linear topological defects

International Nuclear Information System (INIS)

Bakke, Knut; Furtado, Claudio

2012-01-01

We discuss holonomic quantum computation based on the scalar Aharonov–Bohm effect for a neutral particle. We show that the interaction between the magnetic dipole moment and external fields yields a non-abelian quantum phase allowing us to make any arbitrary rotation on a one-qubit. Moreover, we show that the interaction between the magnetic dipole moment and a magnetic field in the presence of a topological defect yields an analogue effect of the scalar Aharonov–Bohm effect for a neutral particle, and a new way of building one-qubit quantum gates. - Highlights: ► Holonomic quantum computation for neutral particles. ► Implementation of one-qubit quantum gates based on the Anandan quantum phase. ► Implementation of one-qubit quantum gates based on the scalar Aharonov–Bohm effect.

On the Hardness of Topology Inference

Science.gov (United States)

Acharya, H. B.; Gouda, M. G.

Many systems require information about the topology of networks on the Internet, for purposes like management, efficiency, testing of new protocols and so on. However, ISPs usually do not share the actual topology maps with outsiders; thus, in order to obtain the topology of a network on the Internet, a system must reconstruct it from publicly observable data. The standard method employs traceroute to obtain paths between nodes; next, a topology is generated such that the observed paths occur in the graph. However, traceroute has the problem that some routers refuse to reveal their addresses, and appear as anonymous nodes in traces. Previous research on the problem of topology inference with anonymous nodes has demonstrated that it is at best NP-complete. In this paper, we improve upon this result. In our previous research, we showed that in the special case where nodes may be anonymous in some traces but not in all traces (so all node identifiers are known), there exist trace sets that are generable from multiple topologies. This paper extends our theory of network tracing to the general case (with strictly anonymous nodes), and shows that the problem of computing the network that generated a trace set, given the trace set, has no general solution. The weak version of the problem, which allows an algorithm to output a "small" set of networks- any one of which is the correct one- is also not solvable. Any algorithm guaranteed to output the correct topology outputs at least an exponential number of networks. Our results are surprisingly robust: they hold even when the network is known to have exactly two anonymous nodes, and every node as well as every edge in the network is guaranteed to occur in some trace. On the basis of this result, we suggest that exact reconstruction of network topology requires more powerful tools than traceroute.

Explicit dissipative structures

International Nuclear Information System (INIS)

Roessler, O.E.

1987-01-01

Dissipative structures consisting of a few macrovariables arise out of a sea of reversible microvariables. Unexpected residual effects of the massive underlying reversibility, on the macrolevel, cannot therefore be excluded. In the age of molecular-dynamics simulations, explicit dissipative structures like excitable systems (explicit observers) can be generated in a computer from first reversible principles. A class of classical, 1-D Hamiltonian systems of chaotic type is considered which has the asset that the trajectorial behavior in phase space can be understood geometrically. If, as nuatural, the number of particle types is much smaller than that of particles, the Gibbs symmetry must be taken into account. The permutation invariance drastically changes the behavior in phase space (quasi-periodization). The explicity observer becomes effectively reversible on a short time scale. In consequence, his ability to measure microscopic motions is suspended in a characteristic fashion. Unlike quantum mechanics whose holistic nature cannot be transcended, the present holistic (internal-interface) effects - mimicking the former to some extent - can be understood fully in principle

Topological susceptibility from twisted mass fermions using spectral projectors

Energy Technology Data Exchange (ETDEWEB)

Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, E. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Shindler, A. [Forschungszentrum Juelich (Germany). IAS; Forschungszentrum Juelich (Germany). IKP; Forschungszentrum Juelich (Germany). JCHP; Collaboration: European Twisted Mass Collaboration

2013-12-15

We discuss the computation of the topological susceptibility using the method of spectral projectors and dynamical twisted mass fermions. We present our analysis concerning the O(a)- improvement of the topological susceptibility and we show numerical results for N{sub f}=2 and N{sub f}=2+1+1 flavours, performing a study of the quark mass dependence in terms of leading order chiral perturbation theory.

M-Polynomials and Topological Indices of Dominating David Derived Networks

Directory of Open Access Journals (Sweden)

Kang Shin Min

2018-03-01

Full Text Available There is a strong relationship between the chemical characteristics of chemical compounds and their molecular structures. Topological indices are numerical values associated with the chemical molecular graphs that help to understand the physical features, chemical reactivity, and biological activity of chemical compound. Thus, the study of the topological indices is important. M-polynomial helps to recover many degree-based topological indices for example Zagreb indices, Randic index, symmetric division idex, inverse sum index etc. In this article we compute M-polynomials of dominating David derived networks of the first type, second type and third type of dimension n and find some topological properties by using these M-polynomials. The results are plotted using Maple to see the dependence of topological indices on the involved parameters.

Induced topological pressure for topological dynamical systems

International Nuclear Information System (INIS)

Xing, Zhitao; Chen, Ercai

2015-01-01

In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure

CCTOP: a Consensus Constrained TOPology prediction web server.

Science.gov (United States)

Dobson, László; Reményi, István; Tusnády, Gábor E

2015-07-01

The Consensus Constrained TOPology prediction (CCTOP; http://cctop.enzim.ttk.mta.hu) server is a web-based application providing transmembrane topology prediction. In addition to utilizing 10 different state-of-the-art topology prediction methods, the CCTOP server incorporates topology information from existing experimental and computational sources available in the PDBTM, TOPDB and TOPDOM databases using the probabilistic framework of hidden Markov model. The server provides the option to precede the topology prediction with signal peptide prediction and transmembrane-globular protein discrimination. The initial result can be recalculated by (de)selecting any of the prediction methods or mapped experiments or by adding user specified constraints. CCTOP showed superior performance to existing approaches. The reliability of each prediction is also calculated, which correlates with the accuracy of the per protein topology prediction. The prediction results and the collected experimental information are visualized on the CCTOP home page and can be downloaded in XML format. Programmable access of the CCTOP server is also available, and an example of client-side script is provided. © The Author(s) 2015. Published by Oxford University Press on behalf of Nucleic Acids Research.

Topological superconductivity, topological confinement, and the vortex quantum Hall effect

International Nuclear Information System (INIS)

Diamantini, M. Cristina; Trugenberger, Carlo A.

2011-01-01

Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.

Designing Structure-Dependent MPC-Based AGC Schemes Considering Network Topology

Directory of Open Access Journals (Sweden)

Young-Sik Jang

2015-04-01

Full Text Available This paper presents the important features of structure-dependent model predictive control (MPC-based approaches for automatic generation control (AGC considering network topology. Since power systems have various generators under different topologies, it is necessary to reflect the characteristics of generators in power networks and the control system structures in order to improve the dynamic performance of AGC. Specifically, considering control system structures is very important because not only can the topological problems be reduced, but also a computing system for AGC in a bulk-power system can be realized. Based on these considerations, we propose new schemes in the proposed controller for minimizing inadvertent line flows and computational burden, which strengthen the advantages of MPC-based approach for AGC. Analysis and simulation results in the IEEE 39-bus model system show different dynamic behaviors among structure-dependent control schemes and possible improvements in computational burden via the proposed control scheme while system operators in each balancing area consider physical load reference ramp constraints among generators.

Topological order and memory time in marginally-self-correcting quantum memory

Science.gov (United States)

Siva, Karthik; Yoshida, Beni

2017-03-01

We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.

Pure spinor formalism as an N = 2 topological string

International Nuclear Information System (INIS)

Berkovits, Nathan

2005-01-01

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted c-circumflex = 3 N = 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action

Topological susceptibility from the twisted mass Dirac operator spectrum

Energy Technology Data Exchange (ETDEWEB)

Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration

2013-12-15

We present results of our computation of the topological susceptibility with N{sub f}=2 and N{sub f}= +1+1 flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants Z{sub P}/Z{sub S}.

Topological susceptibility from the twisted mass Dirac operator spectrum

International Nuclear Information System (INIS)

Cichy, Krzysztof; Jansen, Karl; Cyprus Univ., Nicosia

2013-12-01

We present results of our computation of the topological susceptibility with N f =2 and N f = +1+1 flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants Z P /Z S .

Topological phases in the Haldane model with spin–spin on-site interactions

Science.gov (United States)

Rubio-García, A.; García-Ripoll, J. J.

2018-04-01

Ultracold atom experiments allow the study of topological insulators, such as the non-interacting Haldane model. In this work we study a generalization of the Haldane model with spin–spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long-range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the non-interacting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases.

Hyperswitch Network For Hypercube Computer

Science.gov (United States)

Chow, Edward; Madan, Herbert; Peterson, John

1989-01-01

Data-driven dynamic switching enables high speed data transfer. Proposed hyperswitch network based on mixed static and dynamic topologies. Routing header modified in response to congestion or faults encountered as path established. Static topology meets requirement if nodes have switching elements that perform necessary routing header revisions dynamically. Hypercube topology now being implemented with switching element in each computer node aimed at designing very-richly-interconnected multicomputer system. Interconnection network connects great number of small computer nodes, using fixed hypercube topology, characterized by point-to-point links between nodes.

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

A fast finite-difference algorithm for topology optimization of permanent magnets

Science.gov (United States)

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

2017-09-01

We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

Black holes in quasi-topological gravity and conformal couplings

Science.gov (United States)

Chernicoff, Mariano; Fierro, Octavio; Giribet, Gaston; Oliva, Julio

2017-02-01

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS5 analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R 3 and R 4 terms. In this paper, we investigate AdS5 black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS5 which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

Black holes in quasi-topological gravity and conformal couplings

International Nuclear Information System (INIS)

Chernicoff, Mariano; Fierro, Octavio; Giribet, Gaston; Oliva, Julio

2017-01-01

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS 5 analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R 3 and R 4 terms. In this paper, we investigate AdS 5 black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS 5 which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

Black holes in quasi-topological gravity and conformal couplings

Energy Technology Data Exchange (ETDEWEB)

Chernicoff, Mariano [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México,A.P. 70-542, México D.F. 04510 (Mexico); Fierro, Octavio [Departamento de Matemática y Física Aplicadas,Universidad Católica de la Santísima Concepción,Alonso de Rivera 2850, Concepción (Chile); Giribet, Gaston [Martin Fisher School of Physics, Brandeis University,Waltham, Massachusetts 02453 (United States); Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile)

2017-02-02

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS{sub 5} analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R{sup 3} and R{sup 4} terms. In this paper, we investigate AdS{sub 5} black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS{sub 5} which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

Effects of standard and explicit cognitive bias modification and computer-administered cognitive-behaviour therapy on cognitive biases and social anxiety.

Science.gov (United States)

Mobini, Sirous; Mackintosh, Bundy; Illingworth, Jo; Gega, Lina; Langdon, Peter; Hoppitt, Laura

2014-06-01

This study examines the effects of a single session of Cognitive Bias Modification to induce positive Interpretative bias (CBM-I) using standard or explicit instructions and an analogue of computer-administered CBT (c-CBT) program on modifying cognitive biases and social anxiety. A sample of 76 volunteers with social anxiety attended a research site. At both pre- and post-test, participants completed two computer-administered tests of interpretative and attentional biases and a self-report measure of social anxiety. Participants in the training conditions completed a single session of either standard or explicit CBM-I positive training and a c-CBT program. Participants in the Control (no training) condition completed a CBM-I neutral task matched the active CBM-I intervention in format and duration but did not encourage positive disambiguation of socially ambiguous or threatening scenarios. Participants in both CBM-I programs (either standard or explicit instructions) and the c-CBT condition exhibited more positive interpretations of ambiguous social scenarios at post-test and one-week follow-up as compared to the Control condition. Moreover, the results showed that CBM-I and c-CBT, to some extent, changed negative attention biases in a positive direction. Furthermore, the results showed that both CBM-I training conditions and c-CBT reduced social anxiety symptoms at one-week follow-up. This study used a single session of CBM-I training, however multi-sessions intervention might result in more endurable positive CBM-I changes. A computerised single session of CBM-I and an analogue of c-CBT program reduced negative interpretative biases and social anxiety. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

On topology optimization of plates with prestress

DEFF Research Database (Denmark)

Pedersen, Niels Leergaard

2001-01-01

of the sensitivities is complicated because of the initial stress stiffness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using the solid isotropic material with penalization (SIMP) method in combination with method of moving asymptotes (MMA......In this work, topology optimization is used to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the original stiffness matrix. The calculation...

Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy

International Nuclear Information System (INIS)

Aoyama, S.; Kodama, Y.

1996-01-01

Based on the dispersionless KP (dKP) theory, we study a topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form treating all the primaries in an equal basis, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having a finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formula for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space. (orig.)

General topology

CERN Document Server

Willard, Stephen

2004-01-01

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: ""continuous topology,"" represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and ""geometric topology,"" covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340

Topology optimum design of compliant mechanisms using modified ant colony optimization

Energy Technology Data Exchange (ETDEWEB)

Yoo, Kwang Seon; Han, Seog Young [Hanyang University, Seoul (Korea, Republic of)

2015-08-15

A Modified ant colony optimization (MACO) algorithm was suggested for topology optimal design of compliant mechanisms since standard ACO cannot provide an appropriate optimal topology. In order to improve computational efficiency and suitability of standard ACO algorithm in topology optimization for compliant mechanisms, a continuous variable, called the 'Element contribution significance (ECS),'is employed, which serves to replace the positions of ants in the standard ACO algorithm, and assess the importance of each element in the optimization process. MACO algorithm was applied to topology optimizations of both linear and geometrically nonlinear compliant mechanisms using three kinds of objective functions, and optimized topologies were compared each other. From the comparisons, it was concluded that MACO algorithm can effectively be applied to topology optimizations of linear and geometrically nonlinear compliant mechanisms, and the ratio of Mutual potential energy (MPE) to Strain energy (SE) type of objective function is the best for topology optimal design of compliant mechanisms.

Topological insulating phases of non-Abelian anyonic chains

Energy Technology Data Exchange (ETDEWEB)

DeGottardi, Wade

2014-08-01

Boundary conformal field theory is brought to bear on the study of topological insulating phases of non- Abelian anyonic chains. These phases display protected anyonic end modes. We consider spin-1/2 su(2)t chains at any level k, focusing on the most prominent examples: the case k = 2 describes Ising anyons (equivalent to Majorana fermions) and k = 3 corresponds to Fibonacci anyons. The method we develop is quite general and rests on a deep connection between boundary conformal field theory and topological symmetry. This method tightly constrains the nature of the topological insulating phases of these chains for general k. Emergent anyons which arise at domain walls are shown to have the same braiding properties as the physical quasiparticles. This suggests a "solid-stat.e" topological quantum computation scheme in which emergent anyons are braided by tuning the couplings of non-Abelian quasiparticles in a fixed network.

Comparing topological charge definitions using topology fixing actions

International Nuclear Information System (INIS)

Bruckmann, Falk; Gruber, Florian; Jansen, Karl; Marinkovic, Marina; Urbach, Carsten; Wagner, Marc

2009-05-01

We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge - the field theoretic and the index definition - is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite volume effects arising in the static potential and related quantities due to topology fixing. (orig.)

Grain topology in Ti-6Al-4V welds-Monte Carlo simulation and experiments

International Nuclear Information System (INIS)

Mishra, S; DebRoy, T

2004-01-01

The importance of topological features of grains in the evolution of grain structure is well recognized in isothermal systems. However, during fusion welding, strong spatial gradients of temperature exist in the heat-affected zone (HAZ), and this region undergoes rapid heating and cooling. The effects of spatial and temporal variations of temperature on the topological class distribution, relationship between size and topology of grains and the interdependence between grain topology and its neighbours are not known. Topological features of grains in the HAZ of Ti-6Al-4V alloy welds were measured for various heat inputs in the range 0.55-4.33 MJ m -1 . The topological class distributions were also calculated using a three-dimensional Monte Carlo model utilizing thermal cycles computed from a well tested numerical heat transfer and fluid flow model. The computed results showed that the topological class distributions were unaffected by the spatial and temporal variations of temperature. Experimental investigations of a few sections confirmed the simulation results. The average grain size for each edge class varied linearly with the edge class number. The local topological environment, i.e. the average number of sides of neighbours, n n , varied linearly with the inverse of the number of sides of grains, 1/n r , at a given location in the HAZ. Locations with the same topological environment showed the same grain size, indicating the significant influence of grain topology on grain growth in the HAZ

Topological Superconductivity on the Surface of Fe-Based Superconductors.

Science.gov (United States)

Xu, Gang; Lian, Biao; Tang, Peizhe; Qi, Xiao-Liang; Zhang, Shou-Cheng

2016-07-22

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

Topology for Statistical Modeling of Petascale Data

Energy Technology Data Exchange (ETDEWEB)

Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Bremer, P. -T. [Univ. of Utah, Salt Lake City, UT (United States)

2013-10-31

Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.

On deformations and quantization in topological string theory

International Nuclear Information System (INIS)

Kay, Michael

2014-01-01

The study of moduli spaces of N=(2,2) superconformal field theories and more generally of N=(2,2) supersymmetric quantum field theories, has been a longstanding, multifaceted area of research. In this thesis we focus on certain selected general aspects of this study and develop general techniques within the framework of topological string theory. This work is naturally divided into two parts. The first is concerned with aspects of closed topological string theory, and culminates with a theory, where the geometrical structure of the topological anti-topological moduli spaces of N=(2,2) superconformal field theories with central charge c=9 is rediscovered in the light of quantization, within a general framework. The second part is concerned with aspects of the study of the open and closed moduli space of topological conformal field theories at genus zero. In particular, it contains an exposition of a paper, where general results on the classification and computation of bulk-induced deformations of open topological conformal field theories were obtained from a coherent algebraic approach, drawing from the defining L ∞ and A ∞ structures involved. In part, the latter investigation is restricted to arbitrary affine B-twisted Landau Ginzburg models. Subsequently, further original work is presented that completes the topological string field theory structure of B-twisted Landau Ginzburg models.

Topology-optimized dual-polarization Dirac cones

Science.gov (United States)

Lin, Zin; Christakis, Lysander; Li, Yang; Mazur, Eric; Rodriguez, Alejandro W.; Lončar, Marko

2018-02-01

We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization Dirac cones. We present photonic crystals of different symmetry types, such as fourfold and sixfold rotational symmetries, with Dirac cones at different points within the Brillouin zone. The demonstrated and related optimization techniques open avenues to band-structure engineering and manipulating the propagation of light in periodic media, with possible applications to exotic optical phenomena such as effective zero-index media and topological photonics.

Entanglement from topology in Chern-Simons theory

Science.gov (United States)

Salton, Grant; Swingle, Brian; Walter, Michael

2017-05-01

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.

Open string topological amplitudes and gaugino masses

International Nuclear Information System (INIS)

Antoniadis, I.; Narain, K.S.; Taylor, T.R.

2005-09-01

We discuss the moduli-dependent couplings of the higher derivative F-terms (TrW 2 ) h-1 , where W is the gauge N =1 chiral superfield. They are determined by the genus zero topological partition function F (0,h) , on a world-sheet with h boundaries. By string duality, these terms are also related to heterotic topological amplitudes studied in the past, with the topological twist applied only in the left-moving supersymmetric sector of the internal N =(2,0) superconformal field theory. The holomorphic anomaly of these couplings relates them to terms of the form Π n (TrW 2 ) h-2 , where Π's represent chiral projections of non-holomorphic functions of chiral superfields. An important property of these couplings is that they violate R-symmetry for h ≥ 3. As a result, once supersymmetry is broken by D-term expectation values, (TrW 2 ) 2 generates gaugino masses that can be hierarchically smaller than the scalar masses, behaving as m 1/2 ∼ m 0 4 in string units. Similarly, ΠTrW 2 generates Dirac masses for non-chiral brane fermions, of the same order of magnitude. This mechanism can be used for instance to obtain fermion masses at the TeV scale for scalar masses as high as m 0 ∼ O (10 13 ) GeV. We present explicit examples in toroidal string compactifications with intersecting D-branes. (author)

Service task partition and distribution in star topology computer grid subject to data security constraints

Energy Technology Data Exchange (ETDEWEB)

Xiang Yanping [Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China (China); Levitin, Gregory, E-mail: levitin@iec.co.il [Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China (China); Israel electric corporation, P. O. Box 10, Haifa 31000 (Israel)

2011-11-15

The paper considers grid computing systems in which the resource management systems (RMS) can divide service tasks into execution blocks (EBs) and send these blocks to different resources. In order to provide a desired level of service reliability the RMS can assign the same blocks to several independent resources for parallel execution. The data security is a crucial issue in distributed computing that affects the execution policy. By the optimal service task partition into the EBs and their distribution among resources, one can achieve the greatest possible service reliability and/or expected performance subject to data security constraints. The paper suggests an algorithm for solving this optimization problem. The algorithm is based on the universal generating function technique and on the evolutionary optimization approach. Illustrative examples are presented. - Highlights: > Grid service with star topology is considered. > An algorithm for evaluating service reliability and data security is presented. > A tradeoff between the service reliability and data security is analyzed. > A procedure for optimal service task partition and distribution is suggested.

Service task partition and distribution in star topology computer grid subject to data security constraints

International Nuclear Information System (INIS)

Xiang Yanping; Levitin, Gregory

2011-01-01

The paper considers grid computing systems in which the resource management systems (RMS) can divide service tasks into execution blocks (EBs) and send these blocks to different resources. In order to provide a desired level of service reliability the RMS can assign the same blocks to several independent resources for parallel execution. The data security is a crucial issue in distributed computing that affects the execution policy. By the optimal service task partition into the EBs and their distribution among resources, one can achieve the greatest possible service reliability and/or expected performance subject to data security constraints. The paper suggests an algorithm for solving this optimization problem. The algorithm is based on the universal generating function technique and on the evolutionary optimization approach. Illustrative examples are presented. - Highlights: → Grid service with star topology is considered. → An algorithm for evaluating service reliability and data security is presented. → A tradeoff between the service reliability and data security is analyzed. → A procedure for optimal service task partition and distribution is suggested.

Space-Time Foam in 2D and the Sum Over Topologies

International Nuclear Information System (INIS)

Loll, R.; Westra, W.

2003-01-01

It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravitational path integral. Not even in dimension 2, where a non-perturbative quantum gravity theory can be constructed explicitly from a (regularized) path integral, has this problem found a satisfactory solution. In the present work, we extend a previous 2d Lorentzian path integral, regulated in terms of Lorentzian random triangulations, to include space-times with an arbitrary number of handles. We show that after the imposition of physically motivated causality constraints, the combined sum over geometries and topologies is well-defined and possesses a continuum limit which yields a concrete model of space-time foam in two dimensions. (author)

The Real Topological String on a local Calabi-Yau

CERN Document Server

Krefl, Daniel

2009-01-01

We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by the anti-holomorphic involution. This leads to a computation of open and unoriented Gromov-Witten invariants that can be applied to any toric Calabi-Yau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. We obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results derive in the B-model from the extended holomorphic anomaly equation, together with appropriate boundary conditions. The expansion at the conifold exhibits a gap structure that belongs to a so far unidentified universality class.

Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

Directory of Open Access Journals (Sweden)

Apu Kumar Saha

2015-06-01

Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.

Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group

International Nuclear Information System (INIS)

Katzgraber, Helmut G.; Bombin, H.; Andrist, Ruben S.; Martin-Delgado, M. A.

2010-01-01

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.

Real-space mapping of topological invariants using artificial neural networks

Science.gov (United States)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Topology for Statistical Modeling of Petascale Data

Energy Technology Data Exchange (ETDEWEB)

Bennett, Janine Camille [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pebay, Philippe Pierre [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Rojas, Maurice [Texas A & M Univ., College Station, TX (United States)

2014-07-01

This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled "Topology for Statistical Modeling of Petascale Data", funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program.

Explicit Solutions for One-Dimensional Mean-Field Games

KAUST Repository

Prazeres, Mariana

2017-04-05

In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.

On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

International Nuclear Information System (INIS)

Carvalho-Santos, V.L.; Apolonio, F.A.; Oliveira-Neto, N.M.

2013-01-01

We study the Heisenberg model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and π solitons are predicted. The second one is given by the XY model, leading to a vortex turning around the surface. Helical states are also considered, however, topological arguments cannot be used to ensure its stability. The energy and the anisotropy parameter which stabilizes the vortex state are explicitly calculated for two surfaces: catenoid and hyperboloid. The results show that the anisotropy and the vortex energy depends on the underlying geometry. -- Highlights: •Applying the anisotropic Heisenberg model on curved surfaces. •Appearance of topological solitons on curved surfaces with cylindrical symmetry. •Calculus of the vortex energy, which depends on curvature. •Discussion on features of non-topological helical-like states. •Vortex stability ensured by the anisotropy parameter value

Topological insulators and C*-algebras: Theory and numerical practice

International Nuclear Information System (INIS)

Hastings, Matthew B.; Loring, Terry A.

2011-01-01

Research highlights: → We classify topological insulators using C* algebras. → We present new K-theory invariants. → We develop efficient numerical algorithms based on this technique. → We observe unexpected quantum phase transitions using our algorithm. - Abstract: We apply ideas from C*-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12 3 , averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an 'order parameter' for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C*-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.

Six networks on a universal neuromorphic computing substrate

Directory of Open Access Journals (Sweden)

Thomas ePfeil

2013-02-01

Full Text Available In this study, we present a highly configurable neuromorphic computing substrate and use it for emulating several types of neural networks. At the heart of this system lies a mixed-signal chip, with analog implementations of neurons and synapses and digital transmission of action potentials. Major advantages of this emulation device, which has been explicitly designed as a universal neural network emulator, are its inherent parallelism and high acceleration factor compared to conventional computers. Its configurability allows the realization of almost arbitrary network topologies and the use of widely varied neuronal and synaptic parameters. Fixed-pattern noise inherent to analog circuitry is reduced by calibration routines. An integrated development environment allows neuroscientists to operate the device without any prior knowledge of neuromorphic circuit design. As a showcase for the capabilities of the system, we describe the successful emulation of six different neural networks which cover a broad spectrum of both structure and functionality.

Six networks on a universal neuromorphic computing substrate.

Science.gov (United States)

Pfeil, Thomas; Grübl, Andreas; Jeltsch, Sebastian; Müller, Eric; Müller, Paul; Petrovici, Mihai A; Schmuker, Michael; Brüderle, Daniel; Schemmel, Johannes; Meier, Karlheinz

2013-01-01

In this study, we present a highly configurable neuromorphic computing substrate and use it for emulating several types of neural networks. At the heart of this system lies a mixed-signal chip, with analog implementations of neurons and synapses and digital transmission of action potentials. Major advantages of this emulation device, which has been explicitly designed as a universal neural network emulator, are its inherent parallelism and high acceleration factor compared to conventional computers. Its configurability allows the realization of almost arbitrary network topologies and the use of widely varied neuronal and synaptic parameters. Fixed-pattern noise inherent to analog circuitry is reduced by calibration routines. An integrated development environment allows neuroscientists to operate the device without any prior knowledge of neuromorphic circuit design. As a showcase for the capabilities of the system, we describe the successful emulation of six different neural networks which cover a broad spectrum of both structure and functionality.

Parallel implementations of 2D explicit Euler solvers

International Nuclear Information System (INIS)

Giraud, L.; Manzini, G.

1996-01-01

In this work we present a subdomain partitioning strategy applied to an explicit high-resolution Euler solver. We describe the design of a portable parallel multi-domain code suitable for parallel environments. We present several implementations on a representative range of MlMD computers that include shared memory multiprocessors, distributed virtual shared memory computers, as well as networks of workstations. Computational results are given to illustrate the efficiency, the scalability, and the limitations of the different approaches. We discuss also the effect of the communication protocol on the optimal domain partitioning strategy for the distributed memory computers

Geodesic paths and topological charges in quantum systems

Science.gov (United States)

Grangeiro Souza Barbosa Lima, Tiago Aecio

This dissertation focuses on one question: how should one drive an experimentally prepared state of a generic quantum system into a different target-state, simultaneously minimizing energy dissipation and maximizing the fidelity between the target and evolved-states? We develop optimal adiabatic driving protocols for general quantum systems, and show that these are geodesic paths. Geometric ideas have always played a fundamental role in the understanding and unification of physical phenomena, and the recent discovery of topological insulators has drawn great interest to topology from the field of condensed matter physics. Here, we discuss the quantum geometric tensor, a mathematical object that encodes geometrical and topological properties of a quantum system. It is related to the fidelity susceptibility (an important quantity regarding quantum phase transitions) and to the Berry curvature, which enables topological characterization through Berry phases. A refined understanding of the interplay between geometry and topology in quantum mechanics is of direct relevance to several emergent technologies, such as quantum computers, quantum cryptography, and quantum sensors. As a demonstration of how powerful geometric and topological ideas can become when combined, we present the results of an experiment that we recently proposed. This experimental work was done at the Google Quantum Lab, where researchers were able to visualize the topological nature of a two-qubit system in sharp detail, a startling contrast with earlier methods. To achieve this feat, the optimal protocols described in this dissertation were used, allowing for a great improvement on the experimental apparatus, without the need for technical engineering advances. Expanding the existing literature on the quantum geometric tensor using notions from differential geometry and topology, we build on the subject nowadays known as quantum geometry. We discuss how slowly changing a parameter of a quantum

A heuristic approach to optimization of structural topology including self-weight

Science.gov (United States)

Tajs-Zielińska, Katarzyna; Bochenek, Bogdan

2018-01-01

Topology optimization of structures under a design-dependent self-weight load is investigated in this paper. The problem deserves attention because of its significant importance in the engineering practice, especially nowadays as topology optimization is more often applied when designing large engineering structures, for example, bridges or carrying systems of tall buildings. It is worth noting that well-known approaches of topology optimization which have been successfully applied to structures under fixed loads cannot be directly adapted to the case of design-dependent loads, so that topology generation can be a challenge also for numerical algorithms. The paper presents the application of a simple but efficient non-gradient method to topology optimization of elastic structures under self-weight loading. The algorithm is based on the Cellular Automata concept, the application of which can produce effective solutions with low computational cost.

Topological magnetoelectric pump in three dimensions

Science.gov (United States)

Fukui, Takahiro; Fujiwara, Takanori

2017-11-01

We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) current density for a lattice fermion model, a variant of the Wilson-Dirac model. The model we introduce is defined on a lattice in space but in continuous time, which is suited for the study of the topological pump. For such a model, we derive the conserved U(1) current density and calculate it directly for the (1 +1 )-dimensional system as well as (3 +1 )-dimensional system in the limit of the small lattice constant. We find that the current includes a nontrivial lattice effect characterized by the Chern number, and therefore the pumped particle number is quantized by the topological reason. Finally, we study the topological temporal pump in 3 +1 dimensions by numerical calculations. We discuss the relationship between the second Chern number and the first Chern number, the bulk-edge correspondence, and the generalized Streda formula which enables us to compute the second Chern number using the spectral asymmetry.

Exploratory Topology Modelling of Form-Active Hybrid Structures

DEFF Research Database (Denmark)

Holden Deleuran, Anders; Pauly, Mark; Tamke, Martin

2016-01-01

The development of novel form-active hybrid structures (FAHS) is impeded by a lack of modelling tools that allow for exploratory topology modelling of shaped assemblies. We present a flexible and real-time computational design modelling pipeline developed for the exploratory modelling of FAHS...... that enables designers and engineers to iteratively construct and manipulate form-active hybrid assembly topology on the fly. The pipeline implements Kangaroo2's projection-based methods for modelling hybrid structures consisting of slender beams and cable networks. A selection of design modelling sketches...

Advanced Topology Optimization Methods for Conceptual Architectural Design

DEFF Research Database (Denmark)

Aage, Niels; Amir, Oded; Clausen, Anders

2015-01-01

This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...

Advanced Topology Optimization Methods for Conceptual Architectural Design

DEFF Research Database (Denmark)

Aage, Niels; Amir, Oded; Clausen, Anders

2014-01-01

This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...

Depletion benchmarks calculation of random media using explicit modeling approach of RMC

International Nuclear Information System (INIS)

Liu, Shichang; She, Ding; Liang, Jin-gang; Wang, Kan

2016-01-01

Highlights: • Explicit modeling of RMC is applied to depletion benchmark for HTGR fuel element. • Explicit modeling can provide detailed burnup distribution and burnup heterogeneity. • The results would serve as a supplement for the HTGR fuel depletion benchmark. • The method of adjacent burnup regions combination is proposed for full-core problems. • The combination method can reduce memory footprint, keeping the computing accuracy. - Abstract: Monte Carlo method plays an important role in accurate simulation of random media, owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. Three stochastic geometry modeling methods including Random Lattice Method, Chord Length Sampling and explicit modeling approach with mesh acceleration technique, have been implemented in RMC to simulate the particle transport in the dispersed fuels, in which the explicit modeling method is regarded as the best choice. In this paper, the explicit modeling method is applied to the depletion benchmark for HTGR fuel element, and the method of combination of adjacent burnup regions has been proposed and investigated. The results show that the explicit modeling can provide detailed burnup distribution of individual TRISO particles, and this work would serve as a supplement for the HTGR fuel depletion benchmark calculations. The combination of adjacent burnup regions can effectively reduce the memory footprint while keeping the computational accuracy.

Generalized Modular Transformations in (3+1D Topologically Ordered Phases and Triple Linking Invariant of Loop Braiding

Directory of Open Access Journals (Sweden)

Shenghan Jiang

2014-09-01

Full Text Available In topologically ordered quantum states of matter in (2+1D (spacetime dimensions, the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property that is directly related to global transformations of the ground-state wave functions on a torus (the modular transformations. On the other hand, there are theoretical descriptions of various topologically ordered states in (3+1D, which exhibit both pointlike and looplike excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of looplike excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a nontrivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work, we consider realizations of topological order in (3+1D using cohomological gauge theory in which the loops have Abelian statistics and explicitly demonstrate our results on examples with Z_{2}×Z_{2} topological order.

Topological Sound and Flocking on Curved Surfaces

Science.gov (United States)

Shankar, Suraj; Bowick, Mark J.; Marchetti, M. Cristina

2017-07-01

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature, orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state because of the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow, the system additionally supports long-wavelength propagating sound modes that get gapped by the curvature of the underlying substrate. We analytically compute the steady-state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry-protected topological modes that get localized to special geodesics on the surface (the equator or the neck, respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.

GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations.

Science.gov (United States)

Strbac, V; Pierce, D M; Vander Sloten, J; Famaey, N

2017-12-01

Finite element (FE) simulations are increasingly valuable in assessing and improving the performance of biomedical devices and procedures. Due to high computational demands such simulations may become difficult or even infeasible, especially when considering nearly incompressible and anisotropic material models prevalent in analyses of soft tissues. Implementations of GPGPU-based explicit FEs predominantly cover isotropic materials, e.g. the neo-Hookean model. To elucidate the computational expense of anisotropic materials, we implement the Gasser-Ogden-Holzapfel dispersed, fiber-reinforced model and compare solution times against the neo-Hookean model. Implementations of GPGPU-based explicit FEs conventionally rely on single-point (under) integration. To elucidate the expense of full and selective-reduced integration (more reliable) we implement both and compare corresponding solution times against those generated using underintegration. To better understand the advancement of hardware, we compare results generated using representative Nvidia GPGPUs from three recent generations: Fermi (C2075), Kepler (K20c), and Maxwell (GTX980). We explore scaling by solving the same boundary value problem (an extension-inflation test on a segment of human aorta) with progressively larger FE meshes. Our results demonstrate substantial improvements in simulation speeds relative to two benchmark FE codes (up to 300[Formula: see text] while maintaining accuracy), and thus open many avenues to novel applications in biomechanics and medicine.

Topological Methods for Visualization

Energy Technology Data Exchange (ETDEWEB)

Berres, Anne Sabine [Los Alamos National Lab. (LANL), Los Alamos, NM (United Stat

2016-04-07

This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

Introduction to topology

CERN Document Server

Gamelin, Theodore W

1999-01-01

A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations. Index. 51 illustrations.

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed

2012-11-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana

2012-01-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Dual-scale topology optoelectronic processor.

Science.gov (United States)

Marsden, G C; Krishnamoorthy, A V; Esener, S C; Lee, S H

1991-12-15

The dual-scale topology optoelectronic processor (D-STOP) is a parallel optoelectronic architecture for matrix algebraic processing. The architecture can be used for matrix-vector multiplication and two types of vector outer product. The computations are performed electronically, which allows multiplication and summation concepts in linear algebra to be generalized to various nonlinear or symbolic operations. This generalization permits the application of D-STOP to many computational problems. The architecture uses a minimum number of optical transmitters, which thereby reduces fabrication requirements while maintaining area-efficient electronics. The necessary optical interconnections are space invariant, minimizing space-bandwidth requirements.

Design as Topology

DEFF Research Database (Denmark)

Ekman, Ulrik

2015-01-01

that increasingly develop mixed reality environments with context-aware out-of-the-box computing as well as the soci-ocultural and experiental horizon of a virtually and physically mobile citizenry. Design here must meet an ongoing and exceedingly complex interactivity among environmental, technical, social...... and personal multiplicities of urban nodes on the move. This chapter focuses on the design of a busy traffic intersection in the South Korean u-city Songdo. Hence, the discussion whether and how Songdo may be approached via design as topology primarily considers the situation, event, and experience in which...

Thermodynamics of the topological Kondo model

Directory of Open Access Journals (Sweden)

Francesco Buccheri

2015-07-01

Full Text Available Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.

Thermodynamics of the topological Kondo model

Energy Technology Data Exchange (ETDEWEB)

Buccheri, Francesco, E-mail: buccheri@iip.ufrn.br [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); Babujian, Hrachya [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); Yerevan Physics Institute, Alikhanian Brothers 2, Yerevan, 375036 (Armenia); Korepin, Vladimir E. [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); C. N. Yang Institute for Theoretical Physics, Stony Brook University, NY 11794 (United States); Sodano, Pasquale [International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal, RN (Brazil); Departemento de Fisíca Teorica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Trombettoni, Andrea [CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste (Italy); SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste (Italy)

2015-07-15

Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.

Inference of Ancestral Recombination Graphs through Topological Data Analysis

Science.gov (United States)

Cámara, Pablo G.; Levine, Arnold J.; Rabadán, Raúl

2016-01-01

The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constitute examples of pervasive biological phenomena that cannot be captured by tree-like representations. Starting from hundreds of genomes, we are interested in the reconstruction of potential evolutionary histories leading to the observed data. Ancestral recombination graphs represent potential histories that explicitly accommodate recombination and mutation events across orthologous genomes. However, they are computationally costly to reconstruct, usually being infeasible for more than few tens of genomes. Recently, Topological Data Analysis (TDA) methods have been proposed as robust and scalable methods that can capture the genetic scale and frequency of recombination. We build upon previous TDA developments for detecting and quantifying recombination, and present a novel framework that can be applied to hundreds of genomes and can be interpreted in terms of minimal histories of mutation and recombination events, quantifying the scales and identifying the genomic locations of recombinations. We implement this framework in a software package, called TARGet, and apply it to several examples, including small migration between different populations, human recombination, and horizontal evolution in finches inhabiting the Galápagos Islands. PMID:27532298

Moyal Deformations of Gravity via SU ( N ) Gauge Theories, Branes and Topological Chern-Simons Matrix Models

CERN Document Server

Castro \\C

2003-01-01

Moyal noncommutative star-product deformations of higher dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(\\infty) gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional "knots" have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W_\\infty symmetries which are very relevant in the study of W_\\infty Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix mod...

Lattice topological field theory on nonorientable surfaces

International Nuclear Information System (INIS)

Karimipour, V.; Mostafazadeh, A.

1997-01-01

The lattice definition of the two-dimensional topological quantum field theory [Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that there is a one-to-one correspondence between real associative *-algebras and the topological state sum invariants defined on such surfaces. The partition and n-point functions on all two-dimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitrary *-algebras in general, and for the group ring A=R[G] of discrete groups G, in particular. copyright 1997 American Institute of Physics

p-topological Cauchy completions

Directory of Open Access Journals (Sweden)

J. Wig

1999-01-01

Full Text Available The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular, p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and only if it is “cushioned,” meaning that each equivalence class of nonconvergent Cauchy filters contains a smallest filter. For a Cauchy space allowing a p-topological completion, it is shown that a certain class of Reed completions preserve the p-topological property, including the Wyler and Kowalsky completions, which are, respectively, the finest and the coarsest p-topological completions. However, not all p-topological completions are Reed completions. Several extension theorems for p-topological completions are obtained. The most interesting of these states that any Cauchy-continuous map between Cauchy spaces allowing p-topological and p′-topological completions, respectively, can always be extended to a θ-continuous map between any p-topological completion of the first space and any p′-topological completion of the second.

Emerging Trends in Topological Insulators and Topological ...

Indian Academy of Sciences (India)

/fulltext/reso/022/08/0787-0800. Keywords. Superconductor, quantum Hall effect, topological insulator, Majorana fermions. Abstract. Topological insulators are new class of materials which arecharacterized by a bulk band gap like ordinary ...

Open String Diagrams I: Topological Type

OpenAIRE

Nag, Subhashis; Sankaran, Parameswaran

1992-01-01

An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the non-orientable cases. Algorithms are found to mechanically compute the topological characteristics of the resulting surface from the structure of the signed oriented graph. Whitney's permutation-theoretic coding of graphs is utilized.

Running parallel applications with topology-aware grid middleware

NARCIS (Netherlands)

Bar, P.; Coti, C.; Groen, D.; Herault, T.; Kravtsov, V.; Schuster, A; Swain, M.

2009-01-01

The concept of topology-aware grid applications is derived from parallelized computational models of complex systems that are executed on heterogeneous resources, either because they require specialized hardware for certain calculations, or because their parallelization is flexible enough to exploit

Topology

CERN Document Server

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.

Beginning topology

CERN Document Server

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

Topological Gyroscopic Metamaterials

Science.gov (United States)

Nash, Lisa Michelle

Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.

Topological Sound and Flocking on Curved Surfaces

Directory of Open Access Journals (Sweden)

Suraj Shankar

2017-09-01

Full Text Available Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature, orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state because of the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow, the system additionally supports long-wavelength propagating sound modes that get gapped by the curvature of the underlying substrate. We analytically compute the steady-state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry-protected topological modes that get localized to special geodesics on the surface (the equator or the neck, respectively. These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.

Implicit and explicit memory for spatial information in Alzheimer's disease.

Science.gov (United States)

Kessels, R P C; Feijen, J; Postma, A

2005-01-01

There is abundant evidence that memory impairment in dementia in patients with Alzheimer's disease (AD) is related to explicit, conscious forms of memory, whereas implicit, unconscious forms of memory function remain relatively intact or are less severely affected. Only a few studies have been performed on spatial memory function in AD, showing that AD patients' explicit spatial memory is impaired, possibly related to hippocampal dysfunction. However, studies on implicit spatial memory in AD are lacking. The current study set out to investigate implicit and explicit spatial memory in AD patients (n=18) using an ecologically valid computer task, in which participants had to remember the locations of various objects in common rooms. The contribution of implicit and explicit memory functions was estimated by means of the process dissociation procedure. The results show that explicit spatial memory is impaired in AD patients compared with a control group (n=21). However, no group difference was found on implicit spatial function. This indicates that spared implicit memory in AD extends to the spatial domain, while the explicit spatial memory function deteriorates. Clinically, this finding might be relevant, in that an intact implicit memory function might be helpful in overcoming problems in explicit processing. Copyright (c) 2005 S. Karger AG, Basel.

Topological design of compliant smart structures with embedded movable actuators

International Nuclear Information System (INIS)

Wang, Yiqiang; Zhang, Xiaopeng; Kang, Zhan; Luo, Zhen

2014-01-01

In the optimal configuration design of piezoelectric smart structures, it is favorable to use actuation elements with certain predefined geometries from the viewpoint of manufacturability of fragile piezoelectric ceramics in practical applications. However, preserving the exact shape of these embedded actuators and tracking their dynamic motions presents a more challenging research task than merely allowing them to take arbitrary shapes. This paper proposes an integrated topology optimization method for the systematic design of compliant smart structures with embedded movable PZT (lead zirconate titanate) actuators. Compared with most existing studies, which either optimize positions/sizes of the actuators in a given host structure or design the host structure with pre-determined actuator locations, the proposed method simultaneously optimizes the positions of the movable PZT actuators and the topology of the host structure, typically a compliant mechanism for amplifying the small strain stroke. A combined topological description model is employed in the optimization, where the level set model is used to track the movements of the PZT actuators and the independent point-wise density interpolation (iPDI) approach is utilized to search for the optimal topology of the host structure. Furthermore, we define an integral-type constraint function to prevent overlaps between the PZT actuators and between the actuators and the external boundaries of the design domain. Such a constraint provides a unified and explicit mathematical statement of the non-overlap condition for any number of arbitrarily shaped embedded actuators. Several numerical examples are used to demonstrate the effectiveness of the proposed optimization method. (paper)

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

Science.gov (United States)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

Network topology analysis.

Energy Technology Data Exchange (ETDEWEB)

Kalb, Jeffrey L.; Lee, David S.

2008-01-01

Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.

Congestion management through topological corrections: A case study of Central Western Europe

International Nuclear Information System (INIS)

Han, Jinil; Papavasiliou, Anthony

2015-01-01

The integration of an increasing amount of renewable generation within Europe is posing operational challenges that require various balancing actions. System operators therefore need to rely increasingly on the active control of the transmission network. Transmission topology control is a fast and economical option to add flexibility to the transmission system. We model the current methodology for controlling congestion in the Central Western European (CWE) market and quantify the benefits of topology control. We also compare the results with a nodal pricing model. Our computational results suggest that topology control can significantly reduce congestion management costs under the current market coupling regime whereas the benefits of topology control are limited under nodal pricing. Topology control emerges as an attractive and implementable means of managing congestion as it provides a significant percentage of the cost savings that would be achieved by overhauling the existing European market design and shifting to a nodal pricing regime. - Highlights: • We present the congestion management model in the CWE region. • The benefits of topology control in the CWE region are quantified. • Topology control significantly reduce congestion under the current market coupling. • The benefits of topology control are limited under the nodal pricing regime. • Network topology control is a promising option for mitigating congestion in Europe.

Explicit integration of extremely stiff reaction networks: partial equilibrium methods

International Nuclear Information System (INIS)

Guidry, M W; Hix, W R; Billings, J J

2013-01-01

In two preceding papers (Guidry et al 2013 Comput. Sci. Disc. 6 015001 and Guidry and Harris 2013 Comput. Sci. Disc. 6 015002), we have shown that when reaction networks are well removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically stabilized integration schemes that rival standard implicit methods in accuracy and speed for extremely stiff systems. However, we also showed that these explicit methods remain accurate but are no longer competitive in speed as the network approaches equilibrium. In this paper, we analyze this failure and show that it is associated with the presence of fast equilibration timescales that neither asymptotic nor quasi-steady-state approximations are able to remove efficiently from the numerical integration. Based on this understanding, we develop a partial equilibrium method to deal effectively with the approach to equilibrium and show that explicit asymptotic methods, combined with the new partial equilibrium methods, give an integration scheme that can plausibly deal with the stiffest networks, even in the approach to equilibrium, with accuracy and speed competitive with that of implicit methods. Thus we demonstrate that such explicit methods may offer alternatives to implicit integration of even extremely stiff systems and that these methods may permit integration of much larger networks than have been possible before in a number of fields. (paper)

Topological quantum computing with a very noisy network and local error rates approaching one percent.

Science.gov (United States)

Nickerson, Naomi H; Li, Ying; Benjamin, Simon C

2013-01-01

A scalable quantum computer could be built by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. A solution is for cells to repeatedly communicate with each other and so purify any imperfections; however prior studies suggest that the cells themselves must then have prohibitively low internal error rates. Here we describe a method by which even error-prone cells can perform purification: groups of cells generate shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (≥10% error rate) we find that our protocol can succeed provided that intra-cell error rates for initialisation, state manipulation and measurement are below 0.82%. This level of fidelity is already achievable in several laboratory systems.

Topological superconductivity in the extended Kitaev-Heisenberg model

Science.gov (United States)

Schmidt, Johann; Scherer, Daniel D.; Black-Schaffer, Annica M.

2018-01-01

We study superconducting pairing in the doped Kitaev-Heisenberg model by taking into account the recently proposed symmetric off-diagonal exchange Γ . By performing a mean-field analysis, we classify all possible superconducting phases in terms of symmetry, explicitly taking into account effects of spin-orbit coupling. Solving the resulting gap equations self-consistently, we map out a phase diagram that involves several topologically nontrivial states. For Γ breaking chiral phase with Chern number ±1 and a time-reversal symmetric nematic phase that breaks the rotational symmetry of the lattice. On the other hand, for Γ ≥0 we find a time-reversal symmetric phase that preserves all the lattice symmetries, thus yielding clearly distinguishable experimental signatures for all superconducting phases. Both of the time-reversal symmetric phases display a transition to a Z2 nontrivial phase at high doping levels. Finally, we also include a symmetry-allowed spin-orbit coupling kinetic energy and show that it destroys a tentative symmetry-protected topological order at lower doping levels. However, it can be used to tune the time-reversal symmetric phases into a Z2 nontrivial phase even at lower doping.

Chiral topological phases from artificial neural networks

Science.gov (United States)

Kaubruegger, Raphael; Pastori, Lorenzo; Budich, Jan Carl

2018-05-01

Motivated by recent progress in applying techniques from the field of artificial neural networks (ANNs) to quantum many-body physics, we investigate to what extent the flexibility of ANNs can be used to efficiently study systems that host chiral topological phases such as fractional quantum Hall (FQH) phases. With benchmark examples, we demonstrate that training ANNs of restricted Boltzmann machine type in the framework of variational Monte Carlo can numerically solve FQH problems to good approximation. Furthermore, we show by explicit construction how n -body correlations can be kept at an exact level with ANN wave functions exhibiting polynomial scaling with power n in system size. Using this construction, we analytically represent the paradigmatic Laughlin wave function as an ANN state.

A topological approach to migration and visualization of time-varying volume data

International Nuclear Information System (INIS)

Fujishiro, Issei; Otsuka, Rieko; Hamaoka, Aya; Takeshima, Yuriko; Takahashi, Shigeo

2004-01-01

Rapid advance in high performance computing and measurement technologies has recently made it possible to produce a stupendous amount of time-varying volume datasets in various disciplines. However, there exist a few known visual exploration tools which allow us to investigate the core of their complex behavior effectively. In this article, our previous approach to topological volume skeletonization is extended to capture the topological skeleton of a 4D volumetric field in terms of critical timing. A cyclic information drilldown scheme, termed T-map, is presented, where a wide choice of information visualization techniques are deployed so that the users are allowed to repeatedly squeeze partial spatiotemporal domains of interest until the size gets fitted into an available computing storage space, prior to topologically-accentuated visualization of the pinpointed volumetric domains. A case study with datasets from atomic collision research is performed to illustrate the feasibility of the present method. (author)

Fact or Fuzzy? On the Topology of Space Perception in Digital Architeture

DEFF Research Database (Denmark)

Markussen, Thomas

2008-01-01

these architectural ideas. It should not go unnoticed, for instance, that neurobiologist David Marr’s computational theory of visual cognition (Marr, 1982) strongly indicates the existence of some underlying principles of space perception comparable to the topological surface qualities celebrated by the digital...... in particular to how it is laid out in Spuybroek’s conception of ‘motorized geometry’. Next, I introduce and apply Marr’s computational theory in my inquiries into some seminal projects by NOX and UN Studio in order to increase knowledge of the topology of space perception in digital architecture. By so doing I...... theory, Greg Lynn has claimed that through topological design a new and more profound alliance has been instigated between space, geometry and body (Lynn, 1998). In the same vein Lars Spuybroek has introduced the concept of “motorized geometry” in order to explain how interactive buildings is able...

Age effects on explicit and implicit memory

Directory of Open Access Journals (Sweden)

Emma eWard

2013-09-01

Full Text Available It is well documented that explicit memory (e.g., recognition declines with age. In contrast, many argue that implicit memory (e.g., priming is preserved in healthy aging. For example, priming on tasks such as perceptual identification is often not statistically different in groups of young and older adults. Such observations are commonly taken as evidence for distinct explicit and implicit learning/memory systems. In this article we discuss several lines of evidence that challenge this view. We describe how patterns of differential age-related decline may arise from differences in the ways in which the two forms of memory are commonly measured, and review recent research suggesting that under improved measurement methods, implicit memory is not age-invariant. Formal computational models are of considerable utility in revealing the nature of underlying systems. We report the results of applying single and multiple-systems models to data on age effects in implicit and explicit memory. Model comparison clearly favours the single-system view. Implications for the memory systems debate are discussed.

Age effects on explicit and implicit memory.

Science.gov (United States)

Ward, Emma V; Berry, Christopher J; Shanks, David R

2013-01-01

It is well-documented that explicit memory (e.g., recognition) declines with age. In contrast, many argue that implicit memory (e.g., priming) is preserved in healthy aging. For example, priming on tasks such as perceptual identification is often not statistically different in groups of young and older adults. Such observations are commonly taken as evidence for distinct explicit and implicit learning/memory systems. In this article we discuss several lines of evidence that challenge this view. We describe how patterns of differential age-related decline may arise from differences in the ways in which the two forms of memory are commonly measured, and review recent research suggesting that under improved measurement methods, implicit memory is not age-invariant. Formal computational models are of considerable utility in revealing the nature of underlying systems. We report the results of applying single and multiple-systems models to data on age effects in implicit and explicit memory. Model comparison clearly favors the single-system view. Implications for the memory systems debate are discussed.

Topological effects on the mechanical properties of polymer knots

Science.gov (United States)

Zhao, Yani; Ferrari, Franco

2017-11-01

The mechanical properties of knotted polymer rings under stretching in a bad or good solvent are investigated by applying a force F to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer conformations is performed on a simple cubic lattice using the Wang-Landau algorithm. The specific energy, specific heat capacity, gyration radius and the force-elongation curves are computed for several knot topologies with lengths up to 120 lattice units. The common features of the mechanical and thermal behavior of stretched short polymer rings forming knots of a given topological type are analyzed as well as the differences arising due to topology and size effects. It is found that these systems admit three different phases depending on the values of the tensile force F and the temperature T. The transitions from one phase to the other are well characterized by the peaks of the specific heat capacity and by the data of the gyration radius and specific energy. At very low temperatures the force-elongation curves show that the stretching of a knot is a stepwise process, which becomes smooth at higher temperatures. Criteria for distinguishing topological and size effects are provided. It turns out from our study that the behavior of short polymer rings is strongly influenced by topological effects. In particular, the swelling and the swelling rate of knots are severely limited by the topological constraints. Several other properties that are affected by topology, like the decay of the specific energy at high tensile forces, are discussed. The fading out of the influences of topological origin with increasing knot lengths has been verified. Some anomalies detected in the plots of the specific heat capacity of very short and complex knots have been explained by the limitations in the number of accessible energy states due to the topological constraints.

On topological modifications of Newton's law

International Nuclear Information System (INIS)

Floratos, E.G.; Leontaris, G.K.

2012-01-01

Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R 2 × S 1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newton's gravitational potential and we find that for distances smaller than the S 1 radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newton's force from 1/r 2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level

On Topological Indices of Certain Dendrimer Structures

Science.gov (United States)

Aslam, Adnan; Bashir, Yasir; Ahmad, Safyan; Gao, Wei

2017-05-01

A topological index can be considered as transformation of chemical structure in to real number. In QSAR/QSPR study, physicochemical properties and topological indices such as Randić, Zagreb, atom-bond connectivity ABC, and geometric-arithmetic GA index are used to predict the bioactivity of chemical compounds. Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper we determine generalised Randić, general Zagreb, general sum-connectivity indices of poly(propyl) ether imine, porphyrin, and zinc-Porphyrin dendrimers. We also compute ABC and GA indices of these families of dendrimers.

Topology with applications topological spaces via near and far

CERN Document Server

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...

Protected gates for topological quantum field theories

International Nuclear Information System (INIS)

Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit

2016-01-01

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group

The large N limit of the topological susceptibility of Yang-Mills gauge theory

Energy Technology Data Exchange (ETDEWEB)

Ce, Marco [Scuola Normale Superiore, Pisa (Italy); INFN, Pisa (Italy); Garcia Vera, Miguel [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Giusti, Leonardo [Milano Bicocca Univ., Milano (Italy); INFN, Milano Bicocca (Italy); Schaefer, Stefan [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2016-10-27

We present a precise computation of the topological susceptibility χ{sub YM} of SU(N) Yang-Mills theory in the large N limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with N=3,4,5,6 and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger N compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity t{sub 0}{sup 2}χ{sub YM} to the continuum and large N limits with confidence. The accuracy of the final result represents a new quality in the verification of large N scaling.

Global regularizing flows with topology preservation for active contours and polygons.

Science.gov (United States)

Sundaramoorthi, Ganesh; Yezzi, Anthony

2007-03-01

Active contour and active polygon models have been used widely for image segmentation. In some applications, the topology of the object(s) to be detected from an image is known a priori, despite a complex unknown geometry, and it is important that the active contour or polygon maintain the desired topology. In this work, we construct a novel geometric flow that can be added to image-based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon. We emphasize that, unlike other methods for topology preservation, the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change. The flow also serves as a global regularity term for the evolving contour, and has smoothness properties similar to curvature flow. These properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes. The proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles. The evolution of a single point on the contour depends on all other points of the contour, which is different from traditional curve evolutions in the computer vision literature.

A Topological Framework for Interactive Queries on 3D Models in the Web

Science.gov (United States)

Figueiredo, Mauro; Rodrigues, José I.; Silvestre, Ivo; Veiga-Pires, Cristina

2014-01-01

Several technologies exist to create 3D content for the web. With X3D, WebGL, and X3DOM, it is possible to visualize and interact with 3D models in a web browser. Frequently, three-dimensional objects are stored using the X3D file format for the web. However, there is no explicit topological information, which makes it difficult to design fast algorithms for applications that require adjacency and incidence data. This paper presents a new open source toolkit TopTri (Topological model for Triangle meshes) for Web3D servers that builds the topological model for triangular meshes of manifold or nonmanifold models. Web3D client applications using this toolkit make queries to the web server to get adjacent and incidence information of vertices, edges, and faces. This paper shows the application of the topological information to get minimal local points and iso-lines in a 3D mesh in a web browser. As an application, we present also the interactive identification of stalactites in a cave chamber in a 3D web browser. Several tests show that even for large triangular meshes with millions of triangles, the adjacency and incidence information is returned in real time making the presented toolkit appropriate for interactive Web3D applications. PMID:24977236

A Topological Framework for Interactive Queries on 3D Models in the Web

Directory of Open Access Journals (Sweden)

Mauro Figueiredo

2014-01-01

Full Text Available Several technologies exist to create 3D content for the web. With X3D, WebGL, and X3DOM, it is possible to visualize and interact with 3D models in a web browser. Frequently, three-dimensional objects are stored using the X3D file format for the web. However, there is no explicit topological information, which makes it difficult to design fast algorithms for applications that require adjacency and incidence data. This paper presents a new open source toolkit TopTri (Topological model for Triangle meshes for Web3D servers that builds the topological model for triangular meshes of manifold or nonmanifold models. Web3D client applications using this toolkit make queries to the web server to get adjacent and incidence information of vertices, edges, and faces. This paper shows the application of the topological information to get minimal local points and iso-lines in a 3D mesh in a web browser. As an application, we present also the interactive identification of stalactites in a cave chamber in a 3D web browser. Several tests show that even for large triangular meshes with millions of triangles, the adjacency and incidence information is returned in real time making the presented toolkit appropriate for interactive Web3D applications.

Topological BF field theory description of topological insulators

International Nuclear Information System (INIS)

Cho, Gil Young; Moore, Joel E.

2011-01-01

Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems

Science.gov (United States)

Setiawan, F.; Sengupta, K.; Spielman, I. B.; Sau, Jay D.

2015-11-01

We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov-de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.

Explicit knowledge programming for computer games

NARCIS (Netherlands)

Witzel, A.; Zvesper, J.A.; Kennerly, E.; Darken, C.; Mateas, M.

2008-01-01

The main aim of this paper is to raise awareness of higher-order knowledge (knowledge about someone else's knowledge) as an issue for computer game AI. We argue that a number of existing game genres, especially those involving social interaction, are natural fields of application for an approach we

Lagrangian statistics and flow topology in forced two-dimensional turbulence.

Science.gov (United States)

Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K

2011-03-01

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

An explicit multi-time-stepping algorithm for aerodynamic flows

NARCIS (Netherlands)

Niemann-Tuitman, B.E.; Veldman, A.E.P.

1997-01-01

An explicit multi-time-stepping algorithm with applications to aerodynamic flows is presented. In the algorithm, in different parts of the computational domain different time steps are taken, and the flow is synchronized at the so-called synchronization levels. The algorithm is validated for

Scaling-up spatially-explicit ecological models using graphics processors

NARCIS (Netherlands)

Koppel, Johan van de; Gupta, Rohit; Vuik, Cornelis

2011-01-01

How the properties of ecosystems relate to spatial scale is a prominent topic in current ecosystem research. Despite this, spatially explicit models typically include only a limited range of spatial scales, mostly because of computing limitations. Here, we describe the use of graphics processors to

Topological Aspects of Information Retrieval.

Science.gov (United States)

Egghe, Leo; Rousseau, Ronald

1998-01-01

Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)

Localization and traces in open-closed topological Landau-Ginzburg models

International Nuclear Information System (INIS)

Herbst, Manfred; Lazaroiu, Calin-Iuliu

2005-01-01

We reconsider the issue of localization in open-closed B-twisted Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful analysis of zero-mode reduction, we show that the closed model allows for a one-parameter family of localization pictures, which generalize the standard residue representation. The parameter λ which indexes these pictures measures the area of worldsheets with S 2 topology, with the residue representation obtained in the limit of small area. In the boundary sector, we find a double family of such pictures, depending on parameters λ and μ which measure the area and boundary length of worldsheets with disk topology. We show that setting μ = 0 and varying λ interpolates between the localization picture of the B-model with a noncompact target space and a certain residue representation proposed recently. This gives a complete derivation of the boundary residue formula, starting from the explicit construction of the boundary coupling. We also show that the various localization pictures are related by a semigroup of homotopy equivalences

Investigating the Cosmic Web with Topological Data Analysis

Science.gov (United States)

Cisewski-Kehe, Jessi; Wu, Mike; Fasy, Brittany; Hellwing, Wojciech; Lovell, Mark; Rinaldo, Alessandro; Wasserman, Larry

2018-01-01

Data exhibiting complicated spatial structures are common in many areas of science (e.g. cosmology, biology), but can be difficult to analyze. Persistent homology is a popular approach within the area of Topological Data Analysis that offers a new way to represent, visualize, and interpret complex data by extracting topological features, which can be used to infer properties of the underlying structures. In particular, TDA may be useful for analyzing the large-scale structure (LSS) of the Universe, which is an intricate and spatially complex web of matter. In order to understand the physics of the Universe, theoretical and computational cosmologists develop large-scale simulations that allow for visualizing and analyzing the LSS under varying physical assumptions. Each point in the 3D data set represents a galaxy or a cluster of galaxies, and topological summaries ("persistent diagrams") can be obtained summarizing the different ordered holes in the data (e.g. connected components, loops, voids).The topological summaries are interesting and informative descriptors of the Universe on their own, but hypothesis tests using the topological summaries would provide a way to make more rigorous comparisons of LSS under different theoretical models. For example, the received cosmological model has cold dark matter (CDM); however, while the case is strong for CDM, there are some observational inconsistencies with this theory. Another possibility is warm dark matter (WDM). It is of interest to see if a CDM Universe and WDM Universe produce LSS that is topologically distinct.We present several possible test statistics for two-sample hypothesis tests using the topological summaries, carryout a simulation study to investigate the suitableness of the proposed test statistics using simulated data from a variation of the Voronoi foam model, and finally we apply the proposed inference framework to WDM vs. CDM cosmological simulation data.

Reduced order modeling in topology optimization of vibroacoustic problems

DEFF Research Database (Denmark)

Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas

2017-01-01

complex 3D parts. The optimization process can therefore become highly time consuming due to the need to solve a large system of equations at each iteration. Projection-based parametric Model Order Reduction (pMOR) methods have successfully been applied for reducing the computational cost of material......There is an interest in introducing topology optimization techniques in the design process of structural-acoustic systems. In topology optimization, the design space must be finely meshed in order to obtain an accurate design, which results in large numbers of degrees of freedom when designing...... or size optimization in large vibroacoustic models; however, new challenges are encountered when dealing with topology optimization. Since a design parameter per element is considered, the total number of design variables becomes very large; this poses a challenge to most existing pMOR techniques, which...

The Topological Analysis of Urban Transit System as a Small-World Network

OpenAIRE

Zhaosheng Yang; Huxing Zhou; Peng Gao; Hong Chen; Nan Zhang

2011-01-01

This paper proposes a topological analysis of urban transit system based on a functional representation network constructed from the urban transit system in Beijing. The representation gives a functional view on nodes named a transit line. Statistical measures are computed and introduced in complex network analysis. It shows that the urban transit system forms small-world networks and exhibits properties different from random networks and regular networks. Furthermore, the topological propert...

Calculation of the two-electron Darwin term using explicitly correlated wave functions

International Nuclear Information System (INIS)

Middendorf, Nils; Höfener, Sebastian; Klopper, Wim; Helgaker, Trygve

2012-01-01

Graphical abstract: The two-electron Darwin term is computed analytically at the MP2-F12 level of theory using density fitted integrals. Highlights: ► Two-electron Darwin term computed analytically at the MP2-F12 level. ► Darwin two-electron integrals computed using density fitting techniques. ► Two-electron Darwin term dominated by singlet pair contributions. ► Much improved basis set convergence is achieved with F12 methods. ► Interference correction works well for the two-electron Darwin term. - Abstract: This article is concerned with the calculation of the two-electron Darwin term (D2). At the level of explicitly correlated second-order perturbation theory (MP2-F12), the D2 term is obtained as an analytic energy derivative; at the level of explicitly correlated coupled-cluster theory, it is obtained from finite differences. To avoid the calculation of four-center integrals, a density-fitting approximation is applied to the D2 two-electron integrals without loss of accuracy, even though the absolute value of the D2 term is typically about 0.1 mE h . Explicitly correlated methods provide a qualitatively correct description of the short-range region around the Coulomb hole, even for small orbital basis sets. Therefore, explicitly correlated wave functions remedy the otherwise extremely slow convergence of the D2 contribution with respect to the basis-set size, yielding more accurate results than those obtained by two-point basis-set extrapolation. Moreover, we show that the interference correction of Petersson’s complete-basis-set model chemistry can be used to compute a D2 basis-set correction at the MP2-F12 level to improve standard coupled-cluster singles-and-doubles results.

The topology of architecture

DEFF Research Database (Denmark)

Marcussen, Lars

2003-01-01

Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum.......Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum....

Cosmic Topology

Science.gov (United States)

Luminet, Jean-Pierre

2015-08-01

Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

Directory of Open Access Journals (Sweden)

Zhong Wang

2014-01-01

Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

Elements of topology

CERN Document Server

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

Using maximum topology matching to explore differences in species distribution models

Science.gov (United States)

Poco, Jorge; Doraiswamy, Harish; Talbert, Marian; Morisette, Jeffrey; Silva, Claudio

2015-01-01

Species distribution models (SDM) are used to help understand what drives the distribution of various plant and animal species. These models are typically high dimensional scalar functions, where the dimensions of the domain correspond to predictor variables of the model algorithm. Understanding and exploring the differences between models help ecologists understand areas where their data or understanding of the system is incomplete and will help guide further investigation in these regions. These differences can also indicate an important source of model to model uncertainty. However, it is cumbersome and often impractical to perform this analysis using existing tools, which allows for manual exploration of the models usually as 1-dimensional curves. In this paper, we propose a topology-based framework to help ecologists explore the differences in various SDMs directly in the high dimensional domain. In order to accomplish this, we introduce the concept of maximum topology matching that computes a locality-aware correspondence between similar extrema of two scalar functions. The matching is then used to compute the similarity between two functions. We also design a visualization interface that allows ecologists to explore SDMs using their topological features and to study the differences between pairs of models found using maximum topological matching. We demonstrate the utility of the proposed framework through several use cases using different data sets and report the feedback obtained from ecologists.

Topology optimization and lattice Boltzmann methods

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund

This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...

A topological derivative method for topology optimization

DEFF Research Database (Denmark)

Norato, J.; Bendsøe, Martin P.; Haber, RB

2007-01-01

resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void......We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric...... regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures....

Topological cross section in the perturbative Reggeon calculus

International Nuclear Information System (INIS)

Pajares, C.; Pascual, R.

1977-01-01

The topological cross section sigma/sub n/ and the multiplicities are computed in perturbative Reggeon calculus with a pomeron with α (0) > 1. It is found that the data from p-p scattering can be explain with the same set of parameters obtained from fits to other exclusive and inclusive data

Graph topology and gap topology for unstable systems

NARCIS (Netherlands)

Zhu, S.Q.

1989-01-01

A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the

Computational scheme for pH-dependent binding free energy calculation with explicit solvent.

Science.gov (United States)

Lee, Juyong; Miller, Benjamin T; Brooks, Bernard R

2016-01-01

We present a computational scheme to compute the pH-dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant-pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi-grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host-guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH-dependent binding free energy profiles of the benchmark system are obtained with three different long-range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH-dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol(-1) . We also discuss the characteristics of three long-range interaction calculation methods for constant-pH simulations. © 2015 The Protein Society.

Boundary fidelity and entanglement in the symmetry protected topological phase of the SSH model

International Nuclear Information System (INIS)

Sirker, J; Maiti, M; Konstantinidis, N P; Sedlmayr, N

2014-01-01

We present a detailed study of the fidelity, the entanglement entropy and the entanglement spectrum, for a dimerized chain of spinless fermions—a simplified Su–Schrieffer–Heeger (SSH) model—with open boundary conditions which is a well-known example for a model supporting a symmetry protected topological (SPT) phase. In the non-interacting case the Hamiltonian matrix is tridiagonal and the eigenvalues and vectors can be given explicitly as a function of a single parameter which is known analytically for odd chain lengths and can be determined numerically in the even length case. From a scaling analysis of these data for essentially semi-infinite chains we obtain the fidelity susceptibility and show that it contains a boundary contribution which is different in the topologically ordered than in the topologically trivial phase. For the entanglement spectrum and entropy we confirm predictions from massive field theory for a block in the middle of an infinite chain but also consider blocks containing the edge of the chain. For the latter case we show that in the SPT phase additional entanglement—as compared to the trivial phase—is present which is localized at the boundary. Finally, we extend our study to the dimerized chain with a nearest-neighbour interaction using exact diagonalization, Arnoldi and density-matrix renormalization group methods and show that a phase transition into a topologically trivial charge-density wave phase occurs. (paper)

Topologically Guided, Automated Construction of Metal–Organic Frameworks and Their Evaluation for Energy-Related Applications

Energy Technology Data Exchange (ETDEWEB)

Colón, Yamil J. [Department; Institute for Molecular Engineering and Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States; Gómez-Gualdrón, Diego A. [Department; Department; Snurr, Randall Q. [Department

2017-09-28

Metal-organic frameworks (MOFs) are promising materials for a range of energy and environmental applications. Here we describe in detail a computational algorithm and code to generate MOFs based on edge-transitive topological nets for subsequent evaluation via molecular simulation. This algorithm has been previously used by us to construct and evaluate 13 512 MOFs of 41 different topologies for cryo-adsorbed hydrogen storage. Grand canonical Monte Carlo simulations are used here to evaluate the 13 512 structures for the storage of gaseous fuels such as hydrogen and methane and nondistillative separation of xenon/krypton mixtures at various operating conditions. MOF performance for both gaseous fuel storage and xenon/krypton separation is influenced by topology. Simulation data suggest that gaseous fuel storage performance is topology-dependent due to MOF properties such as void fraction and surface area combining differently in different topologies, whereas xenon/krypton separation performance is topology-dependent due to how topology constrains the pore size distribution.

Integrated topology and shape optimization in structural design

Science.gov (United States)

Bremicker, M.; Chirehdast, M.; Kikuchi, N.; Papalambros, P. Y.

1990-01-01

Structural optimization procedures usually start from a given design topology and vary its proportions or boundary shapes to achieve optimality under various constraints. Two different categories of structural optimization are distinguished in the literature, namely sizing and shape optimization. A major restriction in both cases is that the design topology is considered fixed and given. Questions concerning the general layout of a design (such as whether a truss or a solid structure should be used) as well as more detailed topology features (e.g., the number and connectivities of bars in a truss or the number of holes in a solid) have to be resolved by design experience before formulating the structural optimization model. Design quality of an optimized structure still depends strongly on engineering intuition. This article presents a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated in addition to selecting shape and size dimensions. A three-phase design process is discussed: an optimal initial topology is created by a homogenization method as a gray level image, which is then transformed to a realizable design using computer vision techniques; this design is then parameterized and treated in detail by sizing and shape optimization. A fully automated process is described for trusses. Optimization of two dimensional solid structures is also discussed. Several application-oriented examples illustrate the usefulness of the proposed methodology.

Topological and non-topological soliton solutions to some time

Indian Academy of Sciences (India)

Topological and non-topological soliton solutions to some time-fractional differential equations ... These equations have been widely applied in many branches of nonlinear ... Department of Engineering Sciences, Faculty of Technology and ...

QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computations.

Science.gov (United States)

Valdés-Martiní, José R; Marrero-Ponce, Yovani; García-Jacas, César R; Martinez-Mayorga, Karina; Barigye, Stephen J; Vaz d'Almeida, Yasser Silveira; Pham-The, Hai; Pérez-Giménez, Facundo; Morell, Carlos A

2017-06-07

In previous reports, Marrero-Ponce et al. proposed algebraic formalisms for characterizing topological (2D) and chiral (2.5D) molecular features through atom- and bond-based ToMoCoMD-CARDD (acronym for Topological Molecular Computational Design-Computer Aided Rational Drug Design) molecular descriptors. These MDs codify molecular information based on the bilinear, quadratic and linear algebraic forms and the graph-theoretical electronic-density and edge-adjacency matrices in order to consider atom- and bond-based relations, respectively. These MDs have been successfully applied in the screening of chemical compounds of different therapeutic applications ranging from antimalarials, antibacterials, tyrosinase inhibitors and so on. To compute these MDs, a computational program with the same name was initially developed. However, this in house software barely offered the functionalities required in contemporary molecular modeling tasks, in addition to the inherent limitations that made its usability impractical. Therefore, the present manuscript introduces the QuBiLS-MAS (acronym for Quadratic, Bilinear and N-Linear mapS based on graph-theoretic electronic-density Matrices and Atomic weightingS) software designed to compute topological (0-2.5D) molecular descriptors based on bilinear, quadratic and linear algebraic forms for atom- and bond-based relations. The QuBiLS-MAS module was designed as standalone software, in which extensions and generalizations of the former ToMoCoMD-CARDD 2D-algebraic indices are implemented, considering the following aspects: (a) two new matrix normalization approaches based on double-stochastic and mutual probability formalisms; (b) topological constraints (cut-offs) to take into account particular inter-atomic relations; (c) six additional atomic properties to be used as weighting schemes in the calculation of the molecular vectors; (d) four new local-fragments to consider molecular regions of interest; (e) number of lone-pair electrons in

Abe homotopy classification of topological excitations under the topological influence of vortices

International Nuclear Information System (INIS)

Kobayashi, Shingo; Kobayashi, Michikazu; Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito

2012-01-01

Topological excitations are usually classified by the nth homotopy group π n . However, for topological excitations that coexist with vortices, there are cases in which an element of π n cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of π n corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π 1 on π n . In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κ n . The nth Abe homotopy group κ n is defined as a semi-direct product of π 1 and π n . In this framework, the action of π 1 on π n is understood as originating from noncommutativity between π 1 and π n . We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is S n /K, where S n is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).

$L$-Topological Spaces

Directory of Open Access Journals (Sweden)

Ali Bajravani

2018-04-01

Full Text Available ‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively.

Topological T-duality for torus bundles with monodromy

Science.gov (United States)

Baraglia, David

2015-05-01

We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficient conditions for existence of a T-dual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids persist in this general setting. We also give an example where twisted K-theory groups can be computed by iterating T-duality.

String-net condensation: A physical mechanism for topological phases

International Nuclear Information System (INIS)

Levin, Michael A.; Wen Xiaogang

2005-01-01

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases--namely topological phases. These phases occur when extended objects, called ''string-nets,'' become highly fluctuating and condense. We construct a large class of exactly soluble 2D spin Hamiltonians whose ground states are string-net condensed. Each ground state corresponds to a different parity invariant topological phase. The models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians--a spin-1/2 system on the honeycomb lattice--is a simple theoretical realization of a universal fault tolerant quantum computer. The higher dimensional case also yields an interesting result: we find that 3D string-net condensation naturally gives rise to both emergent gauge bosons and emergent fermions. Thus, string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions

Topological superconductors: a review.

Science.gov (United States)

Sato, Masatoshi; Ando, Yoichi

2017-07-01

This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

Topological entropy of continuous functions on topological spaces

International Nuclear Information System (INIS)

Liu Lei; Wang Yangeng; Wei Guo

2009-01-01

Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems

Efficient use of iterative solvers in nested topology optimization

DEFF Research Database (Denmark)

Amir, Oded; Stolpe, Mathias; Sigmund, Ole

2010-01-01

In the nested approach to structural optimization, most of the computational effort is invested in the solution of the analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the analysis problem, generated by a Krylov....... The approximation is computationally shown to be sufficiently accurate for the purpose of optimization though the nested equation system is not necessarily solved accurately. The approach is tested on several large-scale topology optimization problems, including minimum compliance problems and compliant mechanism...

Foundations of computer vision computational geometry, visual image structures and object shape detection

CERN Document Server

Peters, James F

2017-01-01

This book introduces the fundamentals of computer vision (CV), with a focus on extracting useful information from digital images and videos. Including a wealth of methods used in detecting and classifying image objects and their shapes, it is the first book to apply a trio of tools (computational geometry, topology and algorithms) in solving CV problems, shape tracking in image object recognition and detecting the repetition of shapes in single images and video frames. Computational geometry provides a visualization of topological structures such as neighborhoods of points embedded in images, while image topology supplies us with structures useful in the analysis and classification of image regions. Algorithms provide a practical, step-by-step means of viewing image structures. The implementations of CV methods in Matlab and Mathematica, classification of chapter problems with the symbols (easily solved) and (challenging) and its extensive glossary of key words, examples and connections with the fabric of C...

Charge-spin Transport in Surface-disordered Three-dimensional Topological Insulators

Science.gov (United States)

Peng, Xingyue

As one of the most promising candidates for the building block of the novel spintronic circuit, the topological insulator (TI) has attracted world-wide interest of study. Robust topological order protected by time-reversal symmetry (TRS) makes charge transport and spin generation in TIs significantly different from traditional three-dimensional (3D) or two-dimensional (2D) electronic systems. However, to date, charge transport and spin generation in 3D TIs are still primarily modeled as single-surface phenomena, happening independently on top and bottom surfaces. In this dissertation, I will demonstrate via both experimental findings and theoretical modeling that this "single surface'' theory neither correctly describes a realistic 3D TI-based device nor reveals the amazingly distinct physical picture of spin transport dynamics in 3D TIs. Instead, I present a new viewpoint of the spin transport dynamics where the role of the insulating yet topologically non-trivial bulk of a 3D TI becomes explicit. Within this new theory, many mysterious transport and magneto-transport anomalies can be naturally explained. The 3D TI system turns out to be more similar to its low dimensional sibling--2D TI rather than some other systems sharing the Dirac dispersion, such as graphene. This work not only provides valuable fundamental physical insights on charge-spin transport in 3D TIs, but also offers important guidance to the design of 3D TI-based spintronic devices.

Toric topology

CERN Document Server

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

Topological insulators

CERN Document Server

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

Guaranteed cost control of mobile sensor networks with Markov switching topologies.

Science.gov (United States)

Zhao, Yuan; Guo, Ge; Ding, Lei

2015-09-01

This paper investigates the consensus seeking problem of mobile sensor networks (MSNs) with random switching topologies. The network communication topologies are composed of a set of directed graphs (or digraph) with a spanning tree. The switching of topologies is governed by a Markov chain. The consensus seeking problem is addressed by introducing a global topology-aware linear quadratic (LQ) cost as the performance measure. By state transformation, the consensus problem is transformed to the stabilization of a Markovian jump system with guaranteed cost. A sufficient condition for global mean-square consensus is derived in the context of stochastic stability analysis of Markovian jump systems. A computational algorithm is given to synchronously calculate both the sub-optimal consensus controller gains and the sub-minimum upper bound of the cost. The effectiveness of the proposed design method is illustrated by three numerical examples. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

AGIS: Evolution of Distributed Computing Information system for ATLAS

CERN Document Server

Anisenkov, Alexey; The ATLAS collaboration; Alandes Pradillo, Maria; Karavakis, Edward

2015-01-01

The variety of the ATLAS Computing Infrastructure requires a central information system to define the topology of computing resources and to store the different parameters and configuration data which are needed by the various ATLAS software components. The ATLAS Grid Information System is the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and services.

(Non-)Abelian Kramers-Wannier duality and topological field theory

CERN Document Server

Severa, Pavol

2002-01-01

We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for higher-dimensional cases. In this form they lead to simple TFTs with boundary coloured in two colours. The statistical models live on the boundary of these TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie T-duality) suggest a non-abelian generalization in the 2dcase, with abelian groups replaced by quantum groups. Amazingly, the TFT formulation solves the problem without computation: quantum groups appear in pictures, independently of the classical motivation. Connection with Chern-Simons theory appears at the symplectic level, and also in the pictures of the Drinfeld double: Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the double, are included in these TFTs. All this suggests nice phenomena in higher dimensions.

Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks

International Nuclear Information System (INIS)

Hasan, M Zahid; Xu, Su-Yang; Bian, Guang

2015-01-01

Unlike string theory, topological physics in lower dimensional condensed matter systems is an experimental reality since the bulk-boundary correspondence can be probed experimentally in lower dimensions. In addition, recent experimental discoveries of non-quantum-Hall-like topological insulators, topological superconductors, Weyl semimetals and other topological states of matter also signal a clear departure from the quantum-Hall-effect-like transport paradigm that has dominated the field since the 1980s. It is these new forms of matter that enabled realizations of topological-Dirac, Weyl cones, helical-Cooper-pairs, Fermi-arc-quasiparticles and other emergent phenomena in fine-tuned photoemission (ARPES) experiments since ARPES experiments directly allow the study of bulk-boundary (topological) correspondence. In this proceeding we provide a brief overview of the key experiments and discuss our perspectives regarding the new research frontiers enabled by these experiments. Taken collectively, we argue in favor of the emergence of ‘topological-condensed-matter-physics’ in laboratory experiments for which a variety of theoretical concepts over the last 80 years paved the way. (review)

Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

Directory of Open Access Journals (Sweden)

Hongling Ye

2015-01-01

Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems.

Science.gov (United States)

Li, Ying

2016-09-16

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.

Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection

Science.gov (United States)

Chamon, Claudio

2005-01-01

This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1)have no quenched disorder, (2)have solely local interactions, (3)have an exactly solvable spectrum, (4)have topologically ordered ground states, and (5)have slow dynamical relaxation rates akin to those of strong structural glasses.

From topology to geometry

International Nuclear Information System (INIS)

Eberhart, M.

1996-01-01

A systematic study of the charge density topologies corresponding to a number of transition metal aluminides with the B2 structure indicates that unstable crystal structures are sometimes associated with uncharacteristic topologies. This observation invites the speculation that the distance to a topological instability might relate to a metals phase behavior. Following this speculation, a metric is imposed on the topological theory of Bader, producing a geometrical theory, where it is now possible to assign a distance from a calculated charge density topology to a topological instability. For the cubic transition metals, these distances are shown to correlate with single crystal elastic constants, where the metals that are furthest from an instability are observed to be the stiffest. (author). 16 refs., 1 tab., 9 figs

A Reconfigurable Mesh-Ring Topology for Bluetooth Sensor Networks

Directory of Open Access Journals (Sweden)

Ben-Yi Wang

2018-05-01

Full Text Available In this paper, a Reconfigurable Mesh-Ring (RMR algorithm is proposed for Bluetooth sensor networks. The algorithm is designed in three stages to determine the optimal configuration of the mesh-ring network. Firstly, a designated root advertises and discovers its neighboring nodes. Secondly, a scatternet criterion is built to compute the minimum number of piconets and distributes the connection information for piconet and scatternet. Finally, a peak-search method is designed to determine the optimal mesh-ring configuration for various sizes of networks. To maximize the network capacity, the research problem is formulated by determining the best connectivity of available mesh links. During the formation and maintenance phases, three possible configurations (including piconet, scatternet, and hybrid are examined to determine the optimal placement of mesh links. The peak-search method is a systematic approach, and is implemented by three functional blocks: the topology formation block generates the mesh-ring topology, the routing efficiency block computes the routing performance, and the optimum decision block introduces a decision-making criterion to determine the optimum number of mesh links. Simulation results demonstrate that the optimal mesh-ring configuration can be determined and that the scatternet case achieves better overall performance than the other two configurations. The RMR topology also outperforms the conventional ring-based and cluster-based mesh methods in terms of throughput performance for Bluetooth configurable networks.

Topological Acoustics

Science.gov (United States)

Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile

2015-03-01

The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.

General Topology of the Universe

OpenAIRE

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.

Topological classification and enumeration of RNA structures by genus

DEFF Research Database (Denmark)

Andersen, Joergen Ellegard; Penner, Robert C.; Reidys, Christian

2013-01-01

To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer-Zagier, we compute the generating function for the number of those structures of fixed genus and minimum...

Topological superfluids with finite-momentum pairing and Majorana fermions.

Science.gov (United States)

Qu, Chunlei; Zheng, Zhen; Gong, Ming; Xu, Yong; Mao, Li; Zou, Xubo; Guo, Guangcan; Zhang, Chuanwei

2013-01-01

Majorana fermions (MFs), quantum particles that are their own antiparticles, are not only of fundamental importance in elementary particle physics and dark matter, but also building blocks for fault-tolerant quantum computation. Recently MFs have been intensively studied in solid state and cold atomic systems. These studies are generally based on superconducting pairing with zero total momentum. On the other hand, finite total momentum Cooper pairings, known as Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) states, were widely studied in many branches of physics. However, whether FF and LO superconductors can support MFs has not been explored. Here we show that MFs can exist in certain types of gapped FF states, yielding a new quantum matter: topological FF superfluids/superconductors. We demonstrate the existence of such topological FF superfluids and the associated MFs using spin-orbit-coupled degenerate Fermi gases and derive their parameter regions. The implementation of topological FF superconductors in semiconductor/superconductor heterostructures is also discussed.

Frequency response as a surrogate eigenvalue problem in topology optimization

DEFF Research Database (Denmark)

Andreassen, Erik; Ferrari, Federico; Sigmund, Ole

2018-01-01

This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...

Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

Energy Technology Data Exchange (ETDEWEB)

Solbrig, Stefan

2008-07-01

In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

International Nuclear Information System (INIS)

Solbrig, Stefan

2008-01-01

In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

Ordered groups and topology

CERN Document Server

Clay, Adam

2016-01-01

This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

Topological valley-chiral edge states of Lamb waves in elastic thin plates

Science.gov (United States)

Wang, Jian; Mei, Jun

2018-05-01

We investigate the nontrivial topology of the band structure of Lamb waves in a thin phononic crystal plate. When inversion symmetry is broken, a valley pseudospin degree of freedom is formed around K and K‧ valleys for the A0 Lamb mode, which is decoupled from the S0 and SH0 modes in the low-frequency regime. Chiral edge states are explicitly demonstrated, which are immune to defects and exhibit unidirectional transport behaviors when intervalley scattering is weak. The quantum valley Hall effect is thus simulated in a simple way in the context of Lamb waves.

Surfaces of Minimal Paths from Topological Structures and Applications to 3D Object Segmentation

KAUST Repository

Algarni, Marei

2017-10-24

Extracting surfaces, representing boundaries of objects of interest, from volumetric images, has important applications in various scientific domains, from medicine to geology. In this thesis, I introduce novel mathematical, computational, and algorithmic machinery for extraction of sheet-like surfaces (with boundary), whose boundary is unknown a-priori, a particularly important case in applications that has no convenient methods. This case of a surface with boundaries has applications in extracting faults (among other geological structures) from seismic images in geological applications. Another application domain is in the extraction of structures in the lung from computed tomography (CT) images. Although many methods have been developed in computer vision for extraction of surfaces, including level sets, convex optimization approaches, and graph cut methods, none of these methods appear to be applicable to the case of surfaces with boundary. The novel methods for surface extraction, derived in this thesis, are built on the theory of Minimal Paths, which has been used primarily to extract curves in noisy or corrupted images and have had wide applicability in 2D computer vision. This thesis extends such methods to surfaces, and it is based on novel observations that surfaces can be determined by extracting topological structures from the solution of the eikonal partial differential equation (PDE), which is the basis of Minimal Path theory. Although topological structures are known to be difficult to extract from images, which are both noisy and discrete, this thesis builds robust methods based on Morse theory and computational topology to address such issues. The algorithms have run-time complexity O(NlogN), less complex than existing approaches. The thesis details the algorithms, theory, and shows an extensive experimental evaluation on seismic images and medical images. Experiments show out-performance in accuracy, computational speed, and user convenience

A New Chaotic System with Positive Topological Entropy

Directory of Open Access Journals (Sweden)

Zhonglin Wang

2015-08-01

Full Text Available This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are analyzed via Lyapunov exponent spectrum, bifurcation diagrams, phase portraits and the Poincaré map. The compound structures of this new system are also analyzed. By means of topological horseshoe theory and numerical computation, the Poincaré map defined for the system is proved to be semi-conjugate to 3-shift map, and thus the system has positive topological entropy.

Quantum A∞-structures for open-closed topological strings

International Nuclear Information System (INIS)

Herbst, M.

2006-02-01

We study factorizations of topological string amplitudes on higher genus Riemann surfaces with multiple boundary components and find quantum A ∞ -relations, which are the higher genus analog of the (classical) A ∞ -relations on the disk. For topological strings with c=3 the quantum A ∞ -relations are trivially satisfied on a single D-brane, whereas in a multiple D-brane configuration they may be used to compute open higher genus amplitudes recursively from disk amplitudes. This can be helpful in open Gromov-Witten theory in order to determine open string higher genus instanton corrections. Finally, we find that the quantum A ∞ -structure cannot quite be recast into a quantum master equation on the open string moduli space. (orig.)

A second-order iterative implicit-explicit hybrid scheme for hyperbolic systems of conservation laws

International Nuclear Information System (INIS)

Dai, Wenlong; Woodward, P.R.

1996-01-01

An iterative implicit-explicit hybrid scheme is proposed for hyperbolic systems of conservation laws. Each wave in a system may be implicitly, or explicitly, or partially implicitly and partially explicitly treated depending on its associated Courant number in each numerical cell, and the scheme is able to smoothly switch between implicit and explicit calculations. The scheme is of Godunov-type in both explicit and implicit regimes, is in a strict conservation form, and is accurate to second-order in both space and time for all Courant numbers. The computer code for the scheme is easy to vectorize. Multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step. The feature of the scheme is shown through numerical examples. 38 refs., 12 figs

Extrapolated stabilized explicit Runge-Kutta methods

Science.gov (United States)

Martín-Vaquero, J.; Kleefeld, B.

2016-12-01

Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve multi-dimensional nonlinear partial differential equations (PDEs). In such methods it is necessary to evaluate the function nt times per step, but the stability region is O (nt2). Hence, the computational cost is O (nt) times lower than for a traditional explicit algorithm. In that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used. Therefore, they are especially well-suited for the method of lines (MOL) discretizations of parabolic nonlinear multi-dimensional PDEs. In this work, first s-stages first-order methods with extended stability along the negative real axis are obtained. They have slightly shorter stability regions than other traditional first-order stabilized explicit Runge-Kutta algorithms (also called Runge-Kutta-Chebyshev codes). Later, they are used to derive nt-stages second- and fourth-order schemes using Richardson extrapolation. The stability regions of these fourth-order codes include the interval [ - 0.01nt2, 0 ] (nt being the number of total functions evaluations), which are shorter than stability regions of ROCK4 methods, for example. However, the new algorithms neither suffer from propagation of errors (as other Runge-Kutta-Chebyshev codes as ROCK4 or DUMKA) nor internal instabilities. Additionally, many other types of higher-order (and also lower-order) methods can be obtained easily in a similar way. These methods also allow adaptation of the length step with no extra cost. Hence, the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way, i.e., with minimal number of additional stages. We compare the new techniques with other well-known algorithms with good results in very stiff diffusion or reaction-diffusion multi-dimensional nonlinear equations.

Quasinormal modes, stability analysis and absorption cross section for 4-dimensional topological Lifshitz black hole

International Nuclear Information System (INIS)

Gonzalez, P.A.; Moncada, Felipe; Vasquez, Yerko

2012-01-01

We study scalar perturbations in the background of a topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, for a real scalar field mass. (orig.)

Quasinormal modes, stability analysis and absorption cross section for 4-dimensional topological Lifshitz black hole

Energy Technology Data Exchange (ETDEWEB)

Gonzalez, P.A. [Universidad Central de Chile, Escuela de Ingenieria Civil en Obras Civiles, Facultad de Ciencias Fisicas y Matematicas, Santiago (Chile); Universidad Diego Portales, Santiago (Chile); Moncada, Felipe; Vasquez, Yerko [Universidad de La Frontera, Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Temuco (Chile)

2012-12-15

We study scalar perturbations in the background of a topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, for a real scalar field mass. (orig.)

Fine topology and locally Minkowskian manifolds

Science.gov (United States)

Agrawal, Gunjan; Sinha, Soami Pyari

2018-05-01

Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.

Dual little strings and their partition functions

Science.gov (United States)

Bastian, Brice; Hohenegger, Stefan; Iqbal, Amer; Rey, Soo-Jong

2018-05-01

We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds XN ,M at a generic point in the Kähler moduli space. These manifolds engineer little string theories in five dimensions or lower and are dual to stacks of M5-branes probing a transverse orbifold singularity. Using the refined topological vertex formalism, we explicitly calculate a generic building block which allows us to compute the topological string partition function of XN ,M as a series expansion in different Kähler parameters. Using this result, we give further explicit proof for a duality found previously in the literature, which relates XN ,M˜XN',M' for N M =N'M' and gcd (N ,M )=gcd (N',M') .

Vacuum fluctuations and topological Casimir effect in Friedmann-Robertson-Walker cosmologies with compact dimensions

International Nuclear Information System (INIS)

Saharian, A.A.; Mkhitaryan, A.L.

2010-01-01

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way the renormalization is reduced to that for the model with trivial topology. In the limit when the comoving lengths of the compact dimensions are very short compared to the Hubble length, the topological parts coincide with those for a conformal coupling and they are related to the corresponding quantities in the flat spacetime by standard conformal transformation. This limit corresponds to the adiabatic approximation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values. In the monotonic regime and for non-conformally and non-minimally coupled fields the vacuum stresses are isotropic and the equation of state for the topological parts in the energy density and pressures is of barotropic type. For conformal and minimal couplings the leading terms in the corresponding asymptotic expansions vanish and the vacuum stresses, in general, are anisotropic, though the equation of state remains of barotropic type. In the oscillatory regime, the amplitude of the oscillations for the topological part in the expectation value of the field squared can be either decreasing or increasing with time, whereas for the energy-momentum tensor the oscillations are damping. The limits of validity of the adiabatic approximation are discussed. (orig.)

Acoustic frequency filter based on anisotropic topological phononic crystals

KAUST Repository

Chen, Zeguo

2017-11-02

We present a design of acoustic frequency filter based on a two-dimensional anisotropic phononic crystal. The anisotropic band structure exhibits either a directional or a combined (global + directional) bandgap at certain frequency regions, depending on the geometry. When the time-reversal symmetry is broken, it may introduce a topologically nontrivial bandgap. The induced nontrivial bandgap and the original directional bandgap result in various interesting wave propagation behaviors, such as frequency filter. We develop a tight-binding model to characterize the effective Hamiltonian of the system, from which the contribution of anisotropy is explicitly shown. Different from the isotropic cases, the Zeeman-type splitting is not linear and the anisotropic bandgap makes it possible to achieve anisotropic propagation characteristics along different directions and at different frequencies.

Acoustic frequency filter based on anisotropic topological phononic crystals

KAUST Repository

Chen, Zeguo; Zhao, Jiajun; Mei, Jun; Wu, Ying

2017-01-01

We present a design of acoustic frequency filter based on a two-dimensional anisotropic phononic crystal. The anisotropic band structure exhibits either a directional or a combined (global + directional) bandgap at certain frequency regions, depending on the geometry. When the time-reversal symmetry is broken, it may introduce a topologically nontrivial bandgap. The induced nontrivial bandgap and the original directional bandgap result in various interesting wave propagation behaviors, such as frequency filter. We develop a tight-binding model to characterize the effective Hamiltonian of the system, from which the contribution of anisotropy is explicitly shown. Different from the isotropic cases, the Zeeman-type splitting is not linear and the anisotropic bandgap makes it possible to achieve anisotropic propagation characteristics along different directions and at different frequencies.

Visualization of Morse connection graphs for topologically rich 2D vector fields.

Science.gov (United States)

Szymczak, Andrzej; Sipeki, Levente

2013-12-01

Recent advances in vector field topologymake it possible to compute its multi-scale graph representations for autonomous 2D vector fields in a robust and efficient manner. One of these representations is a Morse Connection Graph (MCG), a directed graph whose nodes correspond to Morse sets, generalizing stationary points and periodic trajectories, and arcs - to trajectories connecting them. While being useful for simple vector fields, the MCG can be hard to comprehend for topologically rich vector fields, containing a large number of features. This paper describes a visual representation of the MCG, inspired by previous work on graph visualization. Our approach aims to preserve the spatial relationships between the MCG arcs and nodes and highlight the coherent behavior of connecting trajectories. Using simulations of ocean flow, we show that it can provide useful information on the flow structure. This paper focuses specifically on MCGs computed for piecewise constant (PC) vector fields. In particular, we describe extensions of the PC framework that make it more flexible and better suited for analysis of data on complex shaped domains with a boundary. We also describe a topology simplification scheme that makes our MCG visualizations less ambiguous. Despite the focus on the PC framework, our approach could also be applied to graph representations or topological skeletons computed using different methods.

AGIS: Integration of new technologies used in ATLAS Distributed Computing

OpenAIRE

Anisenkov, Alexey; Di Girolamo, Alessandro; Alandes Pradillo, Maria

2017-01-01

The variety of the ATLAS Distributed Computing infrastructure requires a central information system to define the topology of computing resources and to store different parameters and configuration data which are needed by various ATLAS software components. The ATLAS Grid Information System (AGIS) is the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and s...

Topology control

NARCIS (Netherlands)

Buchin, K.; Buchin, M.; Wagner, D.; Wattenhofer, R.

2007-01-01

Information between two nodes in a network is sent based on the network topology, the structure of links connecting pairs of nodes of a network. The task of topology control is to choose a connecting subset from all possible links such that the overall network performance is good. For instance, a

Algebraic topology VIASM 2012–2015

CERN Document Server

Schwartz, Lionel

2017-01-01

Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G. Ginot, H.-W. Henn and G. Powell. They are all introductory texts and can be used by PhD students and experts in the field.   Among the three contributions, two concern stable homotopy of spheres: Henn focusses on the chromatic point of view, the Morava K(n)-localization and the cohomology of the Morava stabilizer groups. Powell’s chapter is concerned with the derived functors of the destabilization and iterated loop functors and provides a small complex to compute them. Indications are given for the odd prime case.   Providing an introduction to some aspects of string and brane topology, Ginot’s contribution focusses on Hochschild homology and its generalizations. It contains a number of new results and fills a gap in the literature. .

Leveraging Fog Computing for Scalable IoT Datacenter Using Spine-Leaf Network Topology

Directory of Open Access Journals (Sweden)

K. C. Okafor

2017-01-01

Full Text Available With the Internet of Everything (IoE paradigm that gathers almost every object online, huge traffic workload, bandwidth, security, and latency issues remain a concern for IoT users in today’s world. Besides, the scalability requirements found in the current IoT data processing (in the cloud can hardly be used for applications such as assisted living systems, Big Data analytic solutions, and smart embedded applications. This paper proposes an extended cloud IoT model that optimizes bandwidth while allowing edge devices (Internet-connected objects/devices to smartly process data without relying on a cloud network. Its integration with a massively scaled spine-leaf (SL network topology is highlighted. This is contrasted with a legacy multitier layered architecture housing network services and routing policies. The perspective offered in this paper explains how low-latency and bandwidth intensive applications can transfer data to the cloud (and then back to the edge application without impacting QoS performance. Consequently, a spine-leaf Fog computing network (SL-FCN is presented for reducing latency and network congestion issues in a highly distributed and multilayer virtualized IoT datacenter environment. This approach is cost-effective as it maximizes bandwidth while maintaining redundancy and resiliency against failures in mission critical applications.

L2TTMON Monitoring Program for L2 Topological Trigger in H1 Experiment - User's Guide

International Nuclear Information System (INIS)

Banas, E.; Ducorps, A.

1999-01-01

Monitoring software for the L2 Topological Trigger in H1 experiment consists of two parts working on two different computers. The hardware read-out and data processing is done on a fast FIC 8234 computer working with the OS9 real time operating system. The Macintosh Quadra is used as a Graphic User Interface for accessing the OS9 trigger monitoring software. The communication between both computers is based on the parallel connection between the Macintosh and the VME crate, where the FIC computer is placed. The special designed protocol (client-server) is used to communicate between both nodes. The general scheme of monitoring for the L2 Topological Trigger and detailed description of using of the monitoring software in both nodes are given in this guide. (author)

Amplitude-dependent topological edge states in nonlinear phononic lattices

Science.gov (United States)

Pal, Raj Kumar; Vila, Javier; Leamy, Michael; Ruzzene, Massimo

2018-03-01

This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.

Interplay between topology and disorder in a two-dimensional semi-Dirac material

Science.gov (United States)

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2018-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes—single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

Strain effects in topological insulators: Topological order and the emergence of switchable topological interface states in Sb2Te3/Bi2Te3 heterojunctions

Science.gov (United States)

Aramberri, H.; Muñoz, M. C.

2017-05-01

We investigate the effects of strain on the topological order of the Bi2Se3 family of topological insulators by ab initio first-principles methods. Strain can induce a topological phase transition and we present the phase diagram for the 3D topological insulators, Bi2Te3 , Sb2Te3 , Bi2Se3 , and Sb2Se3 , under combined uniaxial and biaxial strain. Their phase diagram is universal and shows metallic and insulating phases, both topologically trivial and nontrivial. In particular, uniaxial tension can drive the four compounds into a topologically trivial insulating phase. We propose a Sb2Te3/Bi2Te3 heterojunction in which a strain-induced topological interface state arises in the common gap of this normal insulator-topological insulator heterojunction. Unexpectedly, the interface state is confined in the topologically trivial subsystem and is physically protected from ambient impurities. It can be switched on or off by means of uniaxial strain and therefore Sb2Te3 /Bi2Te3 heterojunctions provide a topological system which hosts tunable robust helical interface states with promising spintronic applications.

Creating geometrically robust designs for highly sensitive problems using topology optimization: Acoustic cavity design

DEFF Research Database (Denmark)

Christiansen, Rasmus E.; Lazarov, Boyan S.; Jensen, Jakob S.

2015-01-01

Resonance and wave-propagation problems are known to be highly sensitive towards parameter variations. This paper discusses topology optimization formulations for creating designs that perform robustly under spatial variations for acoustic cavity problems. For several structural problems, robust...... and limitations are discussed. In addition, a known explicit penalization approach is considered for comparison. For near-uniform spatial variations it is shown that highly robust designs can be obtained using the double filter approach. It is finally demonstrated that taking non-uniform variations into account...... further improves the robustness of the designs....

Robust spatial memory maps in flickering neuronal networks: a topological model

Science.gov (United States)

Dabaghian, Yuri; Babichev, Andrey; Memoli, Facundo; Chowdhury, Samir; Rice University Collaboration; Ohio State University Collaboration

It is widely accepted that the hippocampal place cells provide a substrate of the neuronal representation of the environment--the ``cognitive map''. However, hippocampal network, as any other network in the brain is transient: thousands of hippocampal neurons die every day and the connections formed by these cells constantly change due to various forms of synaptic plasticity. What then explains the remarkable reliability of our spatial memories? We propose a computational approach to answering this question based on a couple of insights. First, we propose that the hippocampal cognitive map is fundamentally topological, and hence it is amenable to analysis by topological methods. We then apply several novel methods from homology theory, to understand how dynamic connections between cells influences the speed and reliability of spatial learning. We simulate the rat's exploratory movements through different environments and study how topological invariants of these environments arise in a network of simulated neurons with ``flickering'' connectivity. We find that despite transient connectivity the network of place cells produces a stable representation of the topology of the environment.

Nonlocal optical response in topological phase transitions in the graphene family

Science.gov (United States)

Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; Woods, Lilia M.

2018-01-01

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family and find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. We find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. The expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.

Univocally determining the cosmic topology from the detection of circles in the sky

International Nuclear Information System (INIS)

Mota, Bruno; Tavakol, Reza

2011-01-01

Full text: While the topology of the spatial sections of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a detectable non-trivial topology will generate pairs of matching circles of temperature fluctuations in maps of the cosmic microwave background, the so-called circles-in-the-sky. Each matching circle pair corresponds to an element of the holonomy group that determines the topology. However, generically, a complete set of generators for the holonomy group will not be detected, so it is not clear that the topology can be uniquely determined from such an observation. With that in mind, in the present work we seek to determine I) If, and how, the angular parameters of a correlated circle pair in a CMB map determines univocally the element in the holonomy group generating such correlation, irrespective of the observer's position in the manifold II) If, or to what extent, the detection of one or more elements of the spatial section's holonomy group univocally specifies the topology of the 3-manifold describing spatial sections of the Universe, and determines out position in it. III) If, or to what extent, the detection of one or more elements of the spatial section's holonomy group univocally specifies the geometry (namely, the sign of the curvature) of the 3-manifold describing spatial sections of the Universe IV) How the (possibly partial) determination of the topology of the 3-manifold describing spatial sections of the Universe from the detection of correlated circle pairs, combined with some other measure of its compactification lengths, constrains the cosmological density parameters. We show explicitly that, for many cases of flat manifolds, the full holonomy group, and by extension the full topology, can be completely determined, or severely constrained, by the determination of the geometrical parameters of a single matching circles pair associated with a non

Experimentally probing topological order and its breakdown through modular matrices

Science.gov (United States)

Luo, Zhihuang; Li, Jun; Li, Zhaokai; Hung, Ling-Yan; Wan, Yidun; Peng, Xinhua; Du, Jiangfeng

2018-02-01

The modern concept of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the following question: in principle, how much detail of the physics of topological orders can be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices--characterizing anyonic statistics that are some of the most fundamental fingerprints of topological orders--can be reconstructed with very good accuracy solely by experimental means. This is an experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle--that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications both in probing and realistically harnessing these exotic phases of matter.

Topological massive sigma models

International Nuclear Information System (INIS)

Lambert, N.D.

1995-01-01

In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the manifold to admit a Killing vector. We use the topological massive sigma model constructed here to simplify the calculation of the observables. Lastly it is noted that this model can be viewed as interpolating between topological massless sigma models and topological Landau-Ginzburg models. ((orig.))

Topics in general topology

CERN Document Server

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.

Evidence for fish dispersal from spatial analysis of stream network topology

Science.gov (United States)

Hitt, N.P.; Angermeier, P.L.

2008-01-01

Developing spatially explicit conservation strategies for stream fishes requires an understanding of the spatial structure of dispersal within stream networks. We explored spatial patterns of stream fish dispersal by evaluating how the size and proximity of connected streams (i.e., stream network topology) explained variation in fish assemblage structure and how this relationship varied with local stream size. We used data from the US Environmental Protection Agency's Environmental Monitoring and Assessment Program in wadeable streams of the Mid-Atlantic Highlands region (n = 308 sites). We quantified stream network topology with a continuous analysis based on the rate of downstream flow accumulation from sites and with a discrete analysis based on the presence of mainstem river confluences (i.e., basin area >250 km2) within 20 fluvial km (fkm) from sites. Continuous variation in stream network topology was related to local species richness within a distance of ???10 fkm, suggesting an influence of fish dispersal within this spatial grain. This effect was explained largely by catostomid species, cyprinid species, and riverine species, but was not explained by zoogeographic regions, ecoregions, sampling period, or spatial autocorrelation. Sites near mainstem river confluences supported greater species richness and abundance of catostomid, cyprinid, and ictalurid fishes than did sites >20 fkm from such confluences. Assemblages at sites on the smallest streams were not related to stream network topology, consistent with the hypothesis that local stream size regulates the influence of regional dispersal. These results demonstrate that the size and proximity of connected streams influence the spatial distribution of fish and suggest that these influences can be incorporated into the designs of stream bioassessments and reserves to enhance management efficacy. ?? 2008 by The North American Benthological Society.

Superconductivity and ferromagnetism in topological insulators

Science.gov (United States)

Zhang, Duming

exist when topological insulators are interfaced with superconductors. The observation of Majorana fermions would not only be fundamentally important, but would also lead to applications in fault-tolerant topological quantum computation. By interfacing topological insulator nanoribbons with superconducting electrodes, we observe distinct signatures of proximity-induced superconductivity, which is found to be present in devices with channel lengths that are much longer than the normal transport characteristic lengths. This might suggest preferential coupling of the proximity effect to a ballistic surface channel of the topological insulator. In addition, when the electrodes are in the superconducting state, we observe periodic magnetoresistance oscillations which suggest the formation of vortices in the proximity-induced region of the nanoribbons. Our results demonstrate that proximity-induced superconductivity and vortices can be realized in our nanoribbon geometry, which accomplishes a first important step towards the search for Majorana fermions in condensed matter. In Chapter 5, I will discuss experiments on a magnetically-doped topological insulator (Mn-doped Bi2Se3) to induce a surface state gap. The metallic Dirac cone surface states of a topological insulator are expected to be protected against small perturbations by time-reversal symmetry. However, these surface states can be dramatically modified and a finite energy gap can be opened at the Dirac point by breaking the time-reversal symmetry via magnetic doping. The interplay between magnetism and topological surface states is predicted to yield novel phenomena of fundamental interest such as a topological magneto-electric effect, a quantized anomalous Hall effect, and the induction of magnetic monopoles. Our systematic measurements reveal a close correlation between the onset of ferromagnetism and quantum corrections to diffusive transport, which crosses over from the symplectic (weak anti-localization) to the

Topological nearly entropy

Science.gov (United States)

Gulamsarwar, Syazwani; Salleh, Zabidin

2017-08-01

The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

Energy Technology Data Exchange (ETDEWEB)

Solbrig, Stefan

2008-07-01

In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

Topologically massive gravity and Ricci-Cotton flow

Energy Technology Data Exchange (ETDEWEB)

Lashkari, Nima; Maloney, Alexander, E-mail: lashkari@physics.mcgill.ca, E-mail: maloney@physics.mcgill.ca [McGill Physics Department, 3600 rue University, Montreal, QC H3A 2T8 (Canada)

2011-05-21

We consider topologically massive gravity (TMG), which is three-dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: anti-de Sitter space and warped anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly.

Topologically massive gravity and Ricci-Cotton flow

International Nuclear Information System (INIS)

Lashkari, Nima; Maloney, Alexander

2011-01-01

We consider topologically massive gravity (TMG), which is three-dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: anti-de Sitter space and warped anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly.

Generation of structural topologies using efficient technique based on sorted compliances

Science.gov (United States)

Mazur, Monika; Tajs-Zielińska, Katarzyna; Bochenek, Bogdan

2018-01-01

Topology optimization, although well recognized is still widely developed. It has gained recently more attention since large computational ability become available for designers. This process is stimulated simultaneously by variety of emerging, innovative optimization methods. It is observed that traditional gradient-based mathematical programming algorithms, in many cases, are replaced by novel and e cient heuristic methods inspired by biological, chemical or physical phenomena. These methods become useful tools for structural optimization because of their versatility and easy numerical implementation. In this paper engineering implementation of a novel heuristic algorithm for minimum compliance topology optimization is discussed. The performance of the topology generator is based on implementation of a special function utilizing information of compliance distribution within the design space. With a view to cope with engineering problems the algorithm has been combined with structural analysis system Ansys.

Metadynamics surfing on topology barriers: the CP{sup N−1} case

Energy Technology Data Exchange (ETDEWEB)

Laio, A. [SISSA,Via Bonomea 265, I-34136, Trieste (Italy); Martinelli, G. [SISSA,Via Bonomea 265, I-34136, Trieste (Italy); INFN - Sezione di Roma La Sapienza,Piazzale Aldo Moro 5, 00185 Roma (Italy); Sanfilippo, F. [School of Physics and Astronomy, University of Southampton,Southampton SO17 1BJ (United Kingdom)

2016-07-18

As one approaches the continuum limit, QCD systems, investigated via numerical simulations, remain trapped in sectors of field space with fixed topological charge. As a consequence the numerical studies of physical quantities may give biased results. The same is true in the case of two dimensional CP{sup N−1} models. In this paper we show that metadynamics, when used to simulate CP{sup N−1}, allows to address efficiently this problem. By studying CP{sup 20} we show that we are able to reconstruct the free energy of the topological charge F(Q) and compute the topological susceptibility as a function of the coupling and of the volume. This is a very important physical quantity in studies of the dynamics of the θ vacuum and of the axion. This method can in principle be extended to QCD applications.

Two-Loop Master Integrals for $\\gamma^{*} \\to 3$ Jets the Non-Planar Topologies

CERN Document Server

Gehrmann, T

2001-01-01

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

A derivation of the explicit structure of inner matrices for H∞-optimization

International Nuclear Information System (INIS)

Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

1991-05-01

One of the most important computational procedure in the solution of the H∞-minimization problems is the derivation of inner matrices. This report describes in detail Shaked's method to enable to obtain an explicit expression of the inner matrix and also summarizes in the form of computational procedure resulting from this method. In addition, a simple numerical example solved by this method is shown. (J.P.N.)

Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems

Science.gov (United States)

Cavaglieri, Daniele; Bewley, Thomas

2015-04-01

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.

Ultrafilters and topologies on groups

CERN Document Server

Zelenyuk, Yevhen

2011-01-01

This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results aboutultrafilters. Topics covered include: topological and left topological groups, ultrafilter semigroups, local homomorphisms and automorphisms, subgroups and ideal structure of ßG, almost maximal spaces and projectives of finite semigroups, resolvability of groups. This is a self-contained book aimed at graduate students and researchers working in to

An Efficient Topology-Based Algorithm for Transient Analysis of Power Grid

KAUST Repository

Yang, Lan

2015-08-10

In the design flow of integrated circuits, chip-level verification is an important step that sanity checks the performance is as expected. Power grid verification is one of the most expensive and time-consuming steps of chip-level verification, due to its extremely large size. Efficient power grid analysis technology is highly demanded as it saves computing resources and enables faster iteration. In this paper, a topology-base power grid transient analysis algorithm is proposed. Nodal analysis is adopted to analyze the topology which is mathematically equivalent to iteratively solving a positive semi-definite linear equation. The convergence of the method is proved.

Reconfigurable topological photonic crystal

Science.gov (United States)

Shalaev, Mikhail I.; Desnavi, Sameerah; Walasik, Wiktor; Litchinitser, Natalia M.

2018-02-01

Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topology of the band structure. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals (PCs) can serve as a platform for realizing a scatter-free propagation of light waves. In conventional PCs, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological PCs and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals (LCs), which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a LC background medium. Background index is changed depending on the orientation of a LC, while preserving the topology of the system. This results in a change of the spectral position of the photonic bandgap and the topological edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.

Topological materials discovery using electron filling constraints

Science.gov (United States)

Chen, Ru; Po, Hoi Chun; Neaton, Jeffrey B.; Vishwanath, Ashvin

2018-01-01

Nodal semimetals are classes of topological materials that have nodal-point or nodal-line Fermi surfaces, which give them novel transport and topological properties. Despite being highly sought after, there are currently very few experimental realizations, and identifying new materials candidates has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for filling-enforced nodal semimetals. We recast the previously derived constraints on the allowed band-insulator fillings in any space group into a new form, which enables effective screening of materials candidates based solely on their space group, electron count in the formula unit, and multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously synthesized compounds. As a demonstration, we focus on a few selected nonsymmorphic space groups which are predicted to host filling-enforced Dirac semimetals. Of the more than 30,000 entires listed, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. We discover a handful of candidates from this guided search; among them, the monoclinic crystal Ca2Pt2Ga is particularly promising.

Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons

International Nuclear Information System (INIS)

Nastase, Horatiu; Stephanov, Misha; Nieuwenhuizen, Peter van; Rebhan, Anton

1999-01-01

We fix the long-standing ambiguity in the one-loop contribution to the mass of a 1 + 1-dimensional supersymmetric soliton by adopting a set of boundary conditions which follow from the symmetries of the action and which depend only on the topology of the sector considered, and by invoking a physical principle that ought to hold generally in quantum field theories with a topological sector: for vanishing mass and other dimensionful constants, the vacuum energies in the trivial and topological sectors have to become equal. In the two-dimensional N = 1 supersymmetric case we find a result which for the supersymmetric sine-Gordon model agrees with the known exact solution of the S-matrix but seems to violate the BPS bound. We analyze the non-trivial relation between the quantum soliton mass and the quantum BPS bound and find a resolution. For N = 2 supersymmetric theories, there are no one-loop corrections to the soliton mass and to the central charge (and also no ambiguities) so that the BPS bound is always saturated. Beyond one-loop there are no ambiguities in any theory, which we explicitly check by a two-loop calculation in the sine-Gordon model

A New Topology for Interline Dynamic Voltage Restorer Based on Direct Three-Phase Converter

Directory of Open Access Journals (Sweden)

E. Babaei

2016-03-01

Full Text Available In this paper, a new topology for Interline Dynamic Voltage Restorer (IDVR is proposed. This topology contains two direct three-phase converters which have been connected together by a common fictitious dc-link. According to the kind of the disturbances, both of the converters can be employed as a rectifier or inverter. The converters receive the required compensation energy from the gird through the direct link which is provided by the dual-proposed switches. Due to the lack of the huge storage elements, the practical prototype of the proposed topology is more economical in comparison with the traditional structure. Moreover, compensating for long time duration is possible due to the unlimited eternal energy which is provided from the grids. The low volume, cost and weight are the additional features of the proposed topology in comparison with traditional types. This topology is capable to compensate both of the balanced and unbalanced disturbances. Furthermore, restoring the deep sags and power outages will be possible with the support from the other grid. Unlike the conventional topologies, the capability of compensation is independent from the power flow and the power factor of each grid. The performance of the proposed IDVR topology is validated by computer simulation with PSCAD/EMTDC software.

Industrial Application of Topology Optimization for Combined Conductive and Convective Heat Transfer Problems

DEFF Research Database (Denmark)

Zhou, Mingdong; Alexandersen, Joe; Sigmund, Ole

2016-01-01

This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systemes. The considered physical problem of steady......-state heat transfer under convection is simulated using SIMULIA-Abaqus. A corresponding topology optimization feature is provided by SIMULIA-Tosca. By following a standard workflow of design optimization, the proposed solution is able to accommodate practical design scenarios and results in efficient...

Computation of Groebner bases for two-loop propagator type integrals

International Nuclear Information System (INIS)

Tarasov, O.V.

2004-01-01

The Groebner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Groebner bases for all integrals with 1PI topologies and present explicit content of the Groebner bases

Computation of Groebner bases for two-loop propagator type integrals

Energy Technology Data Exchange (ETDEWEB)

Tarasov, O.V. [DESY Zeuthen, Theory Group, Deutsches Elektronen Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)]. E-mail: tarasov@ifh.de

2004-11-21

The Groebner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Groebner bases for all integrals with 1PI topologies and present explicit content of the Groebner bases.

Parallel PWTD-Accelerated Explicit Solution of the Time Domain Electric Field Volume Integral Equation

KAUST Repository

Liu, Yang

2016-03-25

A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.

Parallel PWTD-Accelerated Explicit Solution of the Time Domain Electric Field Volume Integral Equation

KAUST Repository

Liu, Yang; Al-Jarro, Ahmed; Bagci, Hakan; Michielssen, Eric

2016-01-01

A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.

Undergraduate topology a working textbook

CERN Document Server

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

A New Numerical Method for Z2 Topological Insulators with Strong Disorder

Science.gov (United States)

Akagi, Yutaka; Katsura, Hosho; Koma, Tohru

2017-12-01

We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.

Equivariant topological quantum field theory and symmetry protected topological phases

Energy Technology Data Exchange (ETDEWEB)

Kapustin, Anton [Division of Physics, California Institute of Technology,1200 E California Blvd, Pasadena, CA, 91125 (United States); Turzillo, Alex [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794 (United States)

2017-03-01

Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.

Estimating Turaev-Viro three-manifold invariants is universal for quantum computation

International Nuclear Information System (INIS)

Alagic, Gorjan; Reichardt, Ben W.; Jordan, Stephen P.; Koenig, Robert

2010-01-01

The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-dimensional topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a relation between the task of distinguishing nonhomeomorphic 3-manifolds and the power of a general quantum computer.

Spontaneous topological charging of tactoids in a living nematic

Science.gov (United States)

Genkin, Mikhail M.; Sokolov, Andrey; Aranson, Igor S.

2018-04-01

Living nematic is a realization of an active matter combining a nematic liquid crystal with swimming bacteria. The material exhibits a remarkable tendency towards spatio-temporal self-organization manifested in formation of dynamic textures of self-propelled half-integer topological defects (disclinations). Here we report on the study of such living nematic near normal inclusions, or tactoids, naturally realized in liquid crystals close to the isotropic-nematic (I–N) phase transition. On the basis of the computational analysis, we have established that tactoid’s I–N interface spontaneously acquire negative topological charge which is proportional to the tactoid’s size and depends on the concentration of bacteria. The observed negative charging is attributed to the drastic difference in the mobilities of +1/2 and ‑1/2 topological defects in active systems. The effect is described in the framework of a kinetic theory for point-like weakly-interacting defects with different mobilities. Our dedicated experiment fully confirmed the theoretical prediction. The results hint into new strategies for control of active matter.

Topologically massive supergravity

Directory of Open Access Journals (Sweden)

S. Deser

1983-01-01

Full Text Available The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The system's energy, as well as that of the original topological gravity, is therefore positive.

Topological pregauge-pregeometry

International Nuclear Information System (INIS)

Akama, Keiichi; Oda, Ichiro.

1990-12-01

The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions is investigated from the viewpoint of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale. (author)

Computing Tutte polynomials of contact networks in classrooms

Science.gov (United States)

Hincapié, Doracelly; Ospina, Juan

2013-05-01

Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network

Consequences of Common Topological Rearrangements for Partition Trees in Phylogenomic Inference.

Science.gov (United States)

Chernomor, Olga; Minh, Bui Quang; von Haeseler, Arndt

2015-12-01

In phylogenomic analysis the collection of trees with identical score (maximum likelihood or parsimony score) may hamper tree search algorithms. Such collections are coined phylogenetic terraces. For sparse supermatrices with a lot of missing data, the number of terraces and the number of trees on the terraces can be very large. If terraces are not taken into account, a lot of computation time might be unnecessarily spent to evaluate many trees that in fact have identical score. To save computation time during the tree search, it is worthwhile to quickly identify such cases. The score of a species tree is the sum of scores for all the so-called induced partition trees. Therefore, if the topological rearrangement applied to a species tree does not change the induced partition trees, the score of these partition trees is unchanged. Here, we provide the conditions under which the three most widely used topological rearrangements (nearest neighbor interchange, subtree pruning and regrafting, and tree bisection and reconnection) change the topologies of induced partition trees. During the tree search, these conditions allow us to quickly identify whether we can save computation time on the evaluation of newly encountered trees. We also introduce the concept of partial terraces and demonstrate that they occur more frequently than the original "full" terrace. Hence, partial terrace is the more important factor of timesaving compared to full terrace. Therefore, taking into account the above conditions and the partial terrace concept will help to speed up the tree search in phylogenomic inference.

Tunable Topological Phononic Crystals

KAUST Repository

Chen, Zeguo

2016-05-27

Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

Tunable Topological Phononic Crystals

KAUST Repository

Chen, Zeguo; Wu, Ying

2016-01-01

Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

A time-reversal invariant topological phase at the surface of a 3D topological insulator

International Nuclear Information System (INIS)

Bonderson, Parsa; Nayak, Chetan; Qi, Xiao-Liang

2013-01-01

A 3D fermionic topological insulator has a gapless Dirac surface state protected by time-reversal symmetry and charge conservation symmetry. The surface state can be gapped by introducing ferromagnetism to break time-reversal symmetry, introducing superconductivity to break charge conservation, or entering a topological phase. In this paper, we construct a minimal gapped topological phase that preserves both time-reversal and charge conservation symmetries and supports Ising-type non-Abelian anyons. This phase can be understood heuristically as emerging from a surface s-wave superconducting state via the condensation of eight-vortex composites. The topological phase inherits vortices supporting Majorana zero modes from the surface superconducting state. However, since it is time-reversal invariant, the surface topological phase is a distinct phase from the Ising topological phase, which can be viewed as a quantum-disordered spin-polarized p x + ip y superconductor. We discuss the anyon model of this topological phase and the manner in which time-reversal symmetry is realized in it. We also study the interfaces between the topological state and other surface gapped phases. (paper)

Topology optimized permanent magnet systems

DEFF Research Database (Denmark)

Bjørk, Rasmus; Bahl, Christian; Insinga, Andrea Roberto

2017-01-01

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron...... and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a ΛcoolΛcool figure of merit of 0...

On the role of topological complexity in spontaneous development of current sheets

Energy Technology Data Exchange (ETDEWEB)

Kumar, Sanjay; Bhattacharyya, R. [Udaipur Solar Observatory, Physical Research Laboratory, Dewali, Bari Road, Udaipur-313001 (India); Smolarkiewicz, P. K. [European Centre for Medium-Range Weather Forecasts, Reading RG2 9AX (United Kingdom)

2015-08-15

The computations presented in this work aim to asses the importance of field line interlacing on spontaneous development of current sheets. From Parker's magnetostatic theorem, such development of current sheets is inevitable in a topologically complex magnetofluid, with infinite electrical conductivity, at equilibrium. Relevant initial value problems are constructed by superposition of two untwisted component fields, each component field being represented by a pair of global magnetic flux surface. The intensity of field line interlacing is then specified by the relative amplitude of the two superposed fields. The computations are performed by varying this relative amplitude. Also to have a direct visualization of current sheet formation, we follow the evolution of flux surfaces instead of the vector magnetic field. An important finding of this paper is in the demonstration that initial field lines having intense interlacing tend to develop current sheets which are distributed throughout the computational domain with no preference for topologically favorable sites like magnetic nulls or field reversal layers. The onsets of these current sheets are attributed to favorable contortions of magnetic flux surfaces where two oppositely directed parts of the same field line or different field lines come to close proximity. However, for less intensely interlaced field lines, the simulations indicate development of current sheets at sites only where the magnetic topology is favorable. These current sheets originate as two sets of anti-parallel complimentary field lines press onto each other.

Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model

International Nuclear Information System (INIS)

Manabe, Masahide

2009-01-01

We study topological strings on local toric del Pezzo surfaces by a method called remodeling the B-model which was recently proposed by Bouchard, Klemm, Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we prove a functional formula of the Bergman kernel which is the basic constituent of the topological string amplitudes by the topological recursion relation of Eynard and Orantin. Because this formula is written as a functional of the period, we can obtain the topological string amplitudes at any point of the moduli space by a simple change of variables of the Picard-Fuchs equations for the period. By this formula and mirror symmetry we compute the A-model amplitudes on K F 2 , and predict the open orbifold Gromov-Witten invariants of C 3 /Z 4 .

Free Boolean Topological Groups

Directory of Open Access Journals (Sweden)

Ol’ga Sipacheva

2015-11-01

Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.

Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation

DEFF Research Database (Denmark)

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....

Exploitation of genetic interaction network topology for the prediction of epistatic behavior

KAUST Repository

Alanis Lobato, Gregorio

2013-10-01

Genetic interaction (GI) detection impacts the understanding of human disease and the ability to design personalized treatment. The mapping of every GI in most organisms is far from complete due to the combinatorial amount of gene deletions and knockdowns required. Computational techniques to predict new interactions based only on network topology have been developed in network science but never applied to GI networks.We show that topological prediction of GIs is possible with high precision and propose a graph dissimilarity index that is able to provide robust prediction in both dense and sparse networks.Computational prediction of GIs is a strong tool to aid high-throughput GI determination. The dissimilarity index we propose in this article is able to attain precise predictions that reduce the universe of candidate GIs to test in the lab. © 2013 Elsevier Inc.

Exploitation of genetic interaction network topology for the prediction of epistatic behavior

KAUST Repository

Alanis Lobato, Gregorio; Cannistraci, Carlo; Ravasi, Timothy

2013-01-01

Genetic interaction (GI) detection impacts the understanding of human disease and the ability to design personalized treatment. The mapping of every GI in most organisms is far from complete due to the combinatorial amount of gene deletions and knockdowns required. Computational techniques to predict new interactions based only on network topology have been developed in network science but never applied to GI networks.We show that topological prediction of GIs is possible with high precision and propose a graph dissimilarity index that is able to provide robust prediction in both dense and sparse networks.Computational prediction of GIs is a strong tool to aid high-throughput GI determination. The dissimilarity index we propose in this article is able to attain precise predictions that reduce the universe of candidate GIs to test in the lab. © 2013 Elsevier Inc.

Improving Topology Optimization using Games

DEFF Research Database (Denmark)

Nobel-Jørgensen, Morten; Christiansen, Asger Nyman; Bærentzen, J. Andreas

free of charge on iOS and Android devices1. The TopOptGame is inspired by puzzle-games (a genre of computer games), which constantly challenges the players and gives rewards when progress is made. This engagement loop will take the player on a journey starting with simple problems with few supports......, this will allow us to analyze the data to measure human performance of topology optimization and more importantly, in which cases people's intuition succeed or fail. The game is currently a working prototype and is scheduled for final release on both iOS and Android before WCSMO-10....

Topology general & algebraic

CERN Document Server

Chatterjee, D

2007-01-01

About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the

An explicit multi-time-stepping algorithm for aerodynamic flows

OpenAIRE

Niemann-Tuitman, B.E.; Veldman, A.E.P.

1997-01-01

An explicit multi-time-stepping algorithm with applications to aerodynamic flows is presented. In the algorithm, in different parts of the computational domain different time steps are taken, and the flow is synchronized at the so-called synchronization levels. The algorithm is validated for aerodynamic turbulent flows. For two-dimensional flows speedups in the order of five with respect to single time stepping are obtained.

Floquet topological insulators for sound

Science.gov (United States)

Fleury, Romain; Khanikaev, Alexander B.; Alù, Andrea

2016-06-01

The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential of topological acoustics. Here we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. We show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.

An Efficient Explicit-time Description Method for Timed Model Checking

Directory of Open Access Journals (Sweden)

Hao Wang

2009-12-01

Full Text Available Timed model checking, the method to formally verify real-time systems, is attracting increasing attention from both the model checking community and the real-time community. Explicit-time description methods verify real-time systems using general model constructs found in standard un-timed model checkers. Lamport proposed an explicit-time description method using a clock-ticking process (Tick to simulate the passage of time together with a group of global variables to model time requirements. Two methods, the Sync-based Explicit-time Description Method using rendezvous synchronization steps and the Semaphore-based Explicit-time Description Method using only one global variable were proposed; they both achieve better modularity than Lamport's method in modeling the real-time systems. In contrast to timed automata based model checkers like UPPAAL, explicit-time description methods can access and store the current time instant for future calculations necessary for many real-time systems, especially those with pre-emptive scheduling. However, the Tick process in the above three methods increments the time by one unit in each tick; the state spaces therefore grow relatively fast as the time parameters increase, a problem when the system's time period is relatively long. In this paper, we propose a more efficient method which enables the Tick process to leap multiple time units in one tick. Preliminary experimental results in a high performance computing environment show that this new method significantly reduces the state space and improves both the time and memory efficiency.

Efficient use of iterative solvers in nested topology optimization

DEFF Research Database (Denmark)

Amir, Oded; Stolpe, Mathias; 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, it is suggested to reduce this computational cost by using an approximation to the solution of the nested problem, generated...... measures. The approximation is shown to be sufficiently accurate for the practical purpose of optimization even though the nested equation system is not solved accurately. The approach is tested on several medium-scale topology optimization problems, including three dimensional minimum compliance problems...

Topological Acoustic Delay Line

Science.gov (United States)

Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Wei, Qi; Liu, Xiaojun; Christensen, Johan

2018-03-01

Topological protected wave engineering in artificially structured media is at the frontier of ongoing metamaterials research that is inspired by quantum mechanics. Acoustic analogues of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation with strikingly unconventional acoustic edge modes immune to backscattering. Earlier fabrications of topological insulators are characterized by an unreconfigurable geometry and a very narrow frequency response, which severely hinders the exploration and design of useful devices. Here we establish topologically protected sound in reconfigurable phononic crystals that can be switched on and off simply by rotating its three-legged "atoms" without altering the lattice structure. In particular, we engineer robust phase delay defects that take advantage of the ultrabroadband reflection-free sound propagation. Such topological delay lines serve as a paradigm in compact acoustic devices, interconnects, and electroacoustic integrated circuits.

Increasing the sampling efficiency of protein conformational transition using velocity-scaling optimized hybrid explicit/implicit solvent REMD simulation

Energy Technology Data Exchange (ETDEWEB)

Yu, Yuqi; Wang, Jinan; Shao, Qiang, E-mail: qshao@mail.shcnc.ac.cn, E-mail: Jiye.Shi@ucb.com, E-mail: wlzhu@mail.shcnc.ac.cn; Zhu, Weiliang, E-mail: qshao@mail.shcnc.ac.cn, E-mail: Jiye.Shi@ucb.com, E-mail: wlzhu@mail.shcnc.ac.cn [ACS Key Laboratory of Receptor Research, Drug Discovery and Design Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203 (China); Shi, Jiye, E-mail: qshao@mail.shcnc.ac.cn, E-mail: Jiye.Shi@ucb.com, E-mail: wlzhu@mail.shcnc.ac.cn [UCB Pharma, 216 Bath Road, Slough SL1 4EN (United Kingdom)

2015-03-28

The application of temperature replica exchange molecular dynamics (REMD) simulation on protein motion is limited by its huge requirement of computational resource, particularly when explicit solvent model is implemented. In the previous study, we developed a velocity-scaling optimized hybrid explicit/implicit solvent REMD method with the hope to reduce the temperature (replica) number on the premise of maintaining high sampling efficiency. In this study, we utilized this method to characterize and energetically identify the conformational transition pathway of a protein model, the N-terminal domain of calmodulin. In comparison to the standard explicit solvent REMD simulation, the hybrid REMD is much less computationally expensive but, meanwhile, gives accurate evaluation of the structural and thermodynamic properties of the conformational transition which are in well agreement with the standard REMD simulation. Therefore, the hybrid REMD could highly increase the computational efficiency and thus expand the application of REMD simulation to larger-size protein systems.

N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant