Reconfigurable topological photonic crystal
Shalaev, Mikhail I.; Desnavi, Sameerah; Walasik, Wiktor; Litchinitser, Natalia M.
2018-02-01
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topology of the band structure. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals (PCs) can serve as a platform for realizing a scatter-free propagation of light waves. In conventional PCs, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological PCs and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals (LCs), which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a LC background medium. Background index is changed depending on the orientation of a LC, while preserving the topology of the system. This results in a change of the spectral position of the photonic bandgap and the topological edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.
Photonic Floquet topological insulators
Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-09-01
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on the surface. In two dimensions, surface electrons in topological insulators do not scatter despite defects and disorder, providing robustness akin to superconductors. Topological insulators are predicted to have wideranging applications in fault-tolerant quantum computing and spintronics. Recently, large theoretical efforts were directed towards achieving topological insulation for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional, and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. However, since magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatterfree edge states requires a fundamentally different mechanism - one that is free of magnetic fields. Recently, a number of proposals for photonic topological transport have been put forward. Specifically, one suggested temporally modulating a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, where temporal variations in solidstate systems induce topological edge states. Here, we propose and experimentally demonstrate the first external field-free photonic topological insulator with scatter-free edge transport: a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate acts as `time'. Thus the waveguides
Topological Order in Silicon Photonics
2017-02-07
AFRL-AFOSR-VA-TR-2017-0037 Topological orders in Silicon photonics Mohammad Hafezi MARYLAND UNIV COLLEGE PARK 3112 LEE BLDG COLLEGE PARK, MD 20742...15 SEP 2016 4. TITLE AND SUBTITLE Topological Order in Silicon Photonics 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA-9550-14-1-0267 5c. PROGRAM...matter to ultra cold gases. Recently, photonic systems have been under investigation to explore various types of topological orders and to potentially
Two-dimensional topological photonics
Khanikaev, Alexander B.; Shvets, Gennady
2017-12-01
Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.
Topology Optimized Photonic Wire Splitters
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Borel, Peter Ingo; Jensen, Jakob Søndergaard
2006-01-01
Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm.......Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm....
Topological Photonics for Continuous Media
Silveirinha, Mario
Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.
Topology 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...
Elementary topology problem textbook
Viro, O Ya; Netsvetaev, N Yu; Kharlamov, V M
2008-01-01
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the pr
Lattice topology dictates photon statistics.
Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A
2017-08-21
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.
Topological photonic orbital-angular-momentum switch
Luo, Xi-Wang; Zhang, Chuanwei; Guo, Guang-Can; Zhou, Zheng-Wei
2018-04-01
The large number of available orbital-angular-momentum (OAM) states of photons provides a unique resource for many important applications in quantum information and optical communications. However, conventional OAM switching devices usually rely on precise parameter control and are limited by slow switching rate and low efficiency. Here we propose a robust, fast, and efficient photonic OAM switch device based on a topological process, where photons are adiabatically pumped to a target OAM state on demand. Such topological OAM pumping can be realized through manipulating photons in a few degenerate main cavities and involves only a limited number of optical elements. A large change of OAM at ˜10q can be realized with only q degenerate main cavities and at most 5 q pumping cycles. The topological photonic OAM switch may become a powerful device for broad applications in many different fields and motivate a topological design of conventional optical devices.
Two-dimensional topological photonic systems
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng
2017-09-01
The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.
Topology optimization of nano-photonic systems
DEFF Research Database (Denmark)
Elesin, Yuriy; Wang, Fengwen; Andkjær, Jacob Anders
2012-01-01
We describe recent developments within nano-photonic systems design based on topology optimization. Applications include linear and non-linear optical waveguides, slow-light waveguides, as well as all-dielectric cloaks that minimize scattering or back-scattering from hard obstacles.......We describe recent developments within nano-photonic systems design based on topology optimization. Applications include linear and non-linear optical waveguides, slow-light waveguides, as well as all-dielectric cloaks that minimize scattering or back-scattering from hard obstacles....
Transverse angular momentum in topological photonic crystals
Deng, Wei-Min; Chen, Xiao-Dong; Zhao, Fu-Li; Dong, Jian-Wen
2018-01-01
Engineering local angular momentum of structured light fields in real space enables applications in many fields, in particular, the realization of unidirectional robust transport in topological photonic crystals with a non-trivial Berry vortex in momentum space. Here, we show transverse angular momentum modes in silicon topological photonic crystals when considering transverse electric polarization. Excited by a chiral external source with either transverse spin angular momentum or transverse phase vortex, robust light flow propagating along opposite directions is observed in several kinds of sharp-turn interfaces between two topologically-distinct silicon photonic crystals. A transverse orbital angular momentum mode with alternating phase vortex exists at the boundary of two such photonic crystals. In addition, unidirectional transport is robust to the working frequency even when the ring size or location of the pseudo-spin source varies in a certain range, leading to the superiority of the broadband photonic device. These findings enable one to make use of transverse angular momentum, a kind of degree of freedom, to achieve unidirectional robust transport in the telecom region and other potential applications in integrated photonic circuits, such as on-chip robust delay lines.
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the thesis gives a proof-of-concept for the application of the method within fluid dynamic problems and it remains of interest for the design of microfluidic devices. Furthermore, the thesis contributes...... of the computed topology design using standard, credible analysis tools with a body-fitted mesh. Also, the thesis encompasses work on how to utilize the finite volume method (FVM) in the topology optimization context. This is motivated by the momentous position the FVM has in the fluid dynamics community...
Topology optimised planar photonic crystal building blocks
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Hede, K. K.; Borel, Peter Ingo
A photonic crystal waveguide (PhCW) 1x4 splitter has been constructed from PhCW 60° bends1 and Y-splitters2 that have been designed individually by utilising topology optimisation3. The splitter has been fabricated in a silicon-on-insulator material (Fig. 1) and exhibits a broadband splitting...... for the TE-polarisation with an average excess loss of 1.55±0.54 dB for a 110 nm bandwidth. The 1x4 splitter demonstrates that individual topology-optimised parts can be used as building blocks to realise high-performance nanophotonic circuits. 1L. H. Frandsen et al., Opt. Express 12, 5916-5921 (2004) 2P. I...
Design of photonic bandgap fibers by topology optimization
DEFF Research Database (Denmark)
Dühring, Maria Bayard; Sigmund, Ole; Feurer, Thomas
2010-01-01
A method based on topology optimization is presented to design the cross section of hollow-core photonic bandgap fibers for minimizing energy loss by material absorption. The optical problem is modeled by the timeharmonic wave equation and solved with the finite element program Comsol Multiphysics...... distribution and the lossy silica material is reduced and the energy flow is increased 375% in the core. Simplified designs inspired from optimized geometry are presented, which will be easier to fabricate. The energy flow is increased up to almost 300% for these cases....
Topology Optimised Broadband Photonic Crystal Y-Splitter
DEFF Research Database (Denmark)
Borel, Peter Ingo; Frandsen, Lars Hagedorn; Harpøth, Anders
2005-01-01
A planar photonic crystal waveguide Y-splitter that exhibits large-bandwidth low-loss 3 dB splitting for TE-polarised light has been fabricated in silicon-on-insulator material. The high performance is achieved by utilising topology optimisation to design the Y-junction and by using topology...
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
Topology optimization and fabrication of photonic crystal structures
DEFF Research Database (Denmark)
Borel, Peter Ingo; Harpøth, Anders; Frandsen, Lars Hagedorn
2004-01-01
Topology optimization is used to design a planar photonic crystal waveguide component resulting in significantly enhanced functionality. Exceptional transmission through a photonic crystal waveguide Z-bend is obtained using this inverse design strategy. The design has been realized in a silicon-on-insulator...
Tunable topological phases in photonic and phononic crystals
Chen, Zeguo
2018-02-18
Topological photonics/phononics, inspired by the discovery of topological insulators, is a prosperous field of research, in which remarkable one-way propagation edge states are robust against impurities or defect without backscattering. This dissertation discusses the implementation of multiple topological phases in specific designed photonic and phononic crystals. First, it reports a tunable quantum Hall phase in acoustic ring-waveguide system. A new three-band model focused on the topological transitions at the Γ point is studied, which gives the functionality that nontrivial topology can be tuned by changing the strengths of the couplings and/or the broken time-reversal symmetry. The resulted tunable topological edge states are also numerically verified. Second, based on our previous studied acoustic ring-waveguide system, we introduce anisotropy by tuning the couplings along different directions. We find that the bandgap topology is related to the frequency and directions. We report our proposal on a frequency filter designed from such an anisotropic topological phononic crystal. Third, motivated by the recent progress on quantum spin Hall phases, we propose a design of time-reversal symmetry broken quantum spin Hall insulators in photonics, in which a new quantum anomalous Hall phase emerges. It supports a chiral edge state with certain spin orientations, which is robust against the magnetic impurities. We also report the realization of the quantum anomalous Hall phase in phononics.
Topology optimization for acoustic problems
DEFF Research Database (Denmark)
Dühring, Maria Bayard
2006-01-01
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
.This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
Wavelength Selective 3D Topology Optimized Photonic Crystal Devices
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Elesin, Yuriy; Sigmund, Ole
2013-01-01
A compact photonic crystal drop filter has been designed using 3D topology optimization and fabricated in silicon-on-insulator material. Measurements and modeling are in excellent agreement showing a low-loss ~11nm 3dB bandwidth of the filter.......A compact photonic crystal drop filter has been designed using 3D topology optimization and fabricated in silicon-on-insulator material. Measurements and modeling are in excellent agreement showing a low-loss ~11nm 3dB bandwidth of the filter....
Observation of Topological Structures in Photonic Quantum Walks
Puentes, Graciana; Gerhardt, Ilja; Katzschmann, Fabian; Silberhorn, Christine; Wrachtrup, Jörg; Lewenstein, Maciej
2014-03-01
Phases of matter with nontrivial topological order are predicted to exhibit a variety of exotic phenomena, such as robust localized bound states in 1D systems, and edge states in 2D systems, which are expected to display spin helicity, immunity to backscattering, and weak antilocalization. In this Letter, we present an experimental observation of topological structures generated via the controlled implementation of two consecutive noncommuting rotations in photonic discrete-time quantum walks. The second rotation introduces valleylike Dirac points in the system, allowing us to create the nontrivial topological pattern. By choosing specific values for the rotations, it is possible to coherently drive the system between topological sectors characterized by different topological invariants. We probe the full topological landscape, demonstrating the emergence of localized bound states hosted at the topological boundaries, and the existence of extremely localized or delocalized non-Gaussian quantum states. Our results pave the way for the study of valley polarization and applications of topological mechanisms in robust optical-device engineering.
Topology-optimized silicon photonic wire mode (de)multiplexer
DEFF Research Database (Denmark)
Frellsen, Louise Floor; Frandsen, Lars Hagedorn; Ding, Yunhong
2015-01-01
We have designed and for the first time experimentally verified a topology optimized mode (de)multiplexer, which demultiplexes the fundamental and the first order mode of a double mode photonic wire to two separate single mode waveguides (and multiplexes vice versa). The device has a footprint...
Tailoring Dispersion properties of photonic crystal waveguides by topology optimization
DEFF Research Database (Denmark)
Stainko, Roman; Sigmund, Ole
2007-01-01
The paper describes a systematic method for the tailoring of dispersion properties of slab-based photonic crystal waveguides. The method is based on the topology optimization method which consists in repeated finite element frequency domain analyzes, analytical sensitivity analyzes and gradient...... curve and design of a wide bandwidth, constant low group velocity waveguide demonstrate the efficiency of the method....
Topology optimization of slow light coupling to photonic crystal waveguides
DEFF Research Database (Denmark)
Yang, Lirong; Lavrinenko, Andrei; Frandsen, Lars Hagedorn
2007-01-01
The slow light coupling efficiency in photonic crystal waveguides is enhanced by using the topology optimisation method. As much as 5 dB improvement in transmission can be achieved in the proximity of the spectrum cutoff. Moreover, the resemblance of the resulting two optimised spectra from...
Multiple topological phase transitions in a gyromagnetic photonic crystal
Chen, Zeguo
2017-04-19
We present the design of a tunable two-dimensional photonic crystal that exhibits multiple topological phases, including a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase under different combinations of geometric parameters and external magnetic fields. Our photonic crystal enables a platform to study the topology evolution attributed to the interplay between crystalline symmetry and time-reversal symmetry. A four-band tight-binding model unambiguously reveals that the topological property is associated with the pseudospin orientations and that it is characterized by the spin Chern number. The emerging quantum anomalous Hall phase features a single helical edge state that is locked by a specific pseudospin. Simulation results demonstrate that the propagation of such a single helical edge state is robust against magnetic impurities. Potential applications, such as spin splitters, are described.
Topology Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport in a sur......This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport...... in a surrounding uid, governed by a convection-diffusion equation, where the convective velocity field is found from solving the isothermal incompressible steady-state Navier-Stokes equations. Topology optimisation is also applied to steady-state natural convection problems. The modelling is done using stabilised...... finite element formulation is implemented in an object-oriented parallel finite element framework programmed in the C++ programming language, developed by the Top-Opt research group of the Department of Mechanical Engineering at The Technical University of Denmark. The presented work is seen...
Topological invariants in nonlinear boundary value problems
International Nuclear Information System (INIS)
Vinagre, Sandra; Severino, Ricardo; Ramos, J. Sousa
2005-01-01
We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions
Chong Li; Xiaoyong Hu; Hong Yang; Qihuang Gong
2017-01-01
We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, brin...
Topology optimization of fluid mechanics problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
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...
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.......This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness...
Topology optimized nanoparticles for near-infrared enhanced photon upconversion
DEFF Research Database (Denmark)
Vester-Petersen, Joakim; Christiansen, Rasmus E.; Julsgaard, Brian
)converted into photons with higher energies through absorption in rare earth ions (Er3+) followed by radiative decay.This process converts otherwise non-absorbed long wavelength photos to shorter wavelength photons able to bridge the band gap energy and contribute to the energy generation of the solar modules...... have shown that the intensity of the upconverted light is proportional to the intensity of the incident light raised to some power, n, [1]. Experimentally n is found to be 1.5 and the light intensity is proportional to the square of the electric field norm, |E|2. We aim to enhance the incident light...... using topology optimized nanoparticles. Here, the distribution of nanoparticle material is optimized to enhance |E|3 in a thin Er3+ doped TiO2 film. Topology optimization has previously proven successful for optimizing wave propagation in acoustics [2] and electromagnetics [3,4]. The governing physics...
Topological Phase Transitions in the Photonic Spin Hall Effect
Kort-Kamp, W. J. M.
2017-10-01
The recent synthesis of two-dimensional staggered materials opens up burgeoning opportunities to study optical spin-orbit interactions in semiconducting Dirac-like systems. We unveil topological phase transitions in the photonic spin Hall effect in the graphene family materials. It is shown that an external static electric field and a high frequency circularly polarized laser allow for active on-demand manipulation of electromagnetic beam shifts. The spin Hall effect of light presents a rich dependence with radiation degrees of freedom, and material properties, and features nontrivial topological properties. We discover that photonic Hall shifts are sensitive to spin and valley properties of the charge carriers, providing an unprecedented pathway to investigate spintronics and valleytronics in staggered 2D semiconductors.
Topology Optimization of Building Blocks for Photonic Integrated Circuits
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2005-01-01
Photonic integrated circuits are likely candidates as high speed replacements for the standard electrical integrated circuits of today. However, in order to obtain a satisfactorily performance many design prob- lems that up until now have resulted in too high losses must be resolved. In this work...... we demonstrate how the method of topology optimization can be used to design a variety of high performance building blocks for the future circuits....
2016-04-01
DEVELOPING TOPOLOGICAL INSULATOR FIBER BASED PHOTON PAIRS SOURCE FOR ULTRAFAST OPTOELECTRONIC APPLICATIONS NORTHWESTERN UNIVERSITY...REPORT TYPE FINAL TECHNICAL REPORT 3. DATES COVERED (From - To) APRIL 2015 – DEC 2015 4. TITLE AND SUBTITLE DEVELOPING TOPOLOGICAL INSULATOR FIBER BASED...in developing a new source for the production of correlated/entangled photon pairs based on the unique nanolayer properties of topological insulator
Topology optimization of Channel flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002......]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...... function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical...
Directory of Open Access Journals (Sweden)
Chong Li
2017-02-01
Full Text Available We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, bringing a topological phase reversal and results the topological edge mode arising at the interface which could transmit photons through the bandgaps both of the photonic crystal L and R. When the signal power intensity larger than a moderate low threshold value of 10.0 MW/cm2, the transmission contrast ratio could remain at 30 steadily.
Linux software for large topology optimization problems
DEFF Research Database (Denmark)
evolving product, which allows a parallel solution of the PDE, it lacks the important feature that the matrix-generation part of the computations is localized to each processor. This is well-known to be critical for obtaining a useful speedup on a Linux cluster and it motivates the search for a COMSOL......-like package for large topology optimization problems. One candidate for such software is developed for Linux by Sandia Nat’l Lab in the USA being the Sundance system. Sundance also uses a symbolic representation of the PDE and a scalable numerical solution is achieved by employing the underlying Trilinos...
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
as for vectorial elastic wave propagation problems using finite element analysis [P2], [P4]. The concept is implemented in a parallel computing code that includes efficient techniques for performing gradient based topology optimization. Using the developed computational framework the thesis considers four...... are derived by use of the adjoint variable method. Many wave propagation problems are open-region problems, i.e. the outer boundaries of the modeling domain must be re ection-less. The thesis contains new and independent developments within perfectly matched layer techniques for scalar as well......The study of elastic and optical waves together with intensive material research has revolutionized everyday as well as cutting edge technology in very tangible ways within the last century. Therefore it is important to continue the investigative work towards improving existing as well as innovate...
Topological methods for variational problems with symmetries
Bartsch, Thomas
1993-01-01
Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic a...
Topology optimization for transient heat transfer problems
DEFF Research Database (Denmark)
Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov
The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our......-stepping scheme. A PCM can efficiently absorb heat while keeping its temperature nearly unchanged [8]. The use of PCM ine.g. electronics [9] and mechanics [10], yields improved performance and lower costs depending on a.o., the spatial distribution of PCM.The considered problem consists in optimizing...... the distribution of PCM in a design domain, subject to a periodic heat influx. The objective is to stabilize the heat outflow. Application examples include keeping constant room temperature for oscilatory heat input or keeping constant working temperature of a CPU subjected to time varying computational load....
Electrically tunable robust edge states in graphene-based topological photonic crystal slabs
Song, Zidong; Liu, HongJun; Huang, Nan; Wang, ZhaoLu
2018-03-01
Topological photonic crystals are optical structures supporting topologically protected unidirectional edge states that exhibit robustness against defects. Here, we propose a graphene-based all-dielectric photonic crystal slab structure that supports two-dimensionally confined topological edge states. These topological edge states can be confined in the out-of-plane direction by two parallel graphene sheets. In the structure, the excitation frequency range of topological edge states can be dynamically and continuously tuned by varying bias voltage across the two parallel graphene sheets. Utilizing this kind of architecture, we construct Z-shaped channels to realize topological edge transmission with diffrerent frequencies. The proposal provides a new degree of freedom to dynamically control topological edge states and potential applications for robust integrated photonic devices and optical communication systems.
PHOTON PBL: problem-based learning in photonics technology education
Massa, Nicholas; Audet, Richard; Donnelly, Judith; Hanes, Fenna; Kehrhahn, Marijke
2007-06-01
Problem-based learning (PBL) is an educational approach whereby students learn course content by actively and collaboratively solving real-world problems presented in a context similar to that in which the learning is to be applied. Research shows that PBL improves student learning and retention, critical thinking and problem-solving skills, and the ability to skillfully apply knowledge to new situations - skills deemed critical to lifelong learning. Used extensively in medical education since the 1970's, and widely adopted in other fields including business, law, and education, PBL is emerging as an alternative to traditional lecture-based courses in engineering and technology education. In today's ever-changing global economy where photonics technicians are required to work productively in teams to solve complex problems across disciplines as well as cultures, PBL represents an exciting alternative to traditional lecture-based photonics education. In this paper we present the PHOTON PBL project, a National Science Foundation Advanced Technology Education (NSF-ATE) project aimed at creating, in partnership with the photonics industry and university research labs from across the US, a comprehensive series of multimedia-based PBL instructional resource materials and offering faculty professional development in the use of PBL in photonics technology education. Quantitative and qualitative research will be conducted on the effectiveness of PBL in photonics technician education.
Exploring photonic topological insulator states in a circuit-QED lattice
Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng
2018-04-01
We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.
Systematic and robust design of photonic crystal waveguides by topology optimization
DEFF Research Database (Denmark)
Wang, Fengwen; Jensen, Jakob Søndergaard; Sigmund, Ole
2010-01-01
A robust topology optimization method is presented to consider manufacturing uncertainties in tailoring dispersion properties of photonic crystal waveguides. The under, normal and over-etching scenarios in manufacturing process are represented by dilated, intermediate and eroded designs based on ...
Kuratowski, Kazimierz
1968-01-01
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connecte
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Elesin, Yuriy; Frellsen, Louise Floor
2014-01-01
We have designed and for the first time experimentally verified a topology optimized mode converter with a footprint of ∼6.3 μm × ∼3.6 μm which converts the fundamental even mode to the higher order odd mode of a dispersion engineered photonic crystal waveguide. 2D and 3D topology optimization...
Issues related to topology optimization of snap-through problems
DEFF Research Database (Denmark)
Lindgaard, Esben; Dahl, Jonas
2012-01-01
This work focuses on issues related to topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied to topology optimization of a point loaded curved beam problem with the aim...
Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua
2016-08-08
A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C6 point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.
Shvets, Gennady B.; Khanikaev, Alexander B.; Ma, Tzuhsuan; Lai, Kueifu
2015-09-01
Science thrives on analogies, and a considerable number of inventions and discoveries have been made by pursuing an unexpected connection to a very different field of inquiry. For example, photonic crystals have been referred to as "semiconductors of light" because of the far-reaching analogies between electron propagation in a crystal lattice and light propagation in a periodically modulated photonic environment. However, two aspects of electron behavior, its spin and helicity, escaped emulation by photonic systems until recent invention of photonic topological insulators (PTIs). The impetus for these developments in photonics came from the discovery of topologically nontrivial phases in condensed matter physics enabling edge states immune to scattering. The realization of topologically protected transport in photonics would circumvent a fundamental limitation imposed by the wave equation: inability of reflections-free light propagation along sharply bent pathway. Topologically protected electromagnetic states could be used for transporting photons without any scattering, potentially underpinning new revolutionary concepts in applied science and engineering. I will demonstrate that a PTI can be constructed by applying three types of perturbations: (a) finite bianisotropy, (b) gyromagnetic inclusion breaking the time-reversal (T) symmetry, and (c) asymmetric rods breaking the parity (P) symmetry. We will experimentally demonstrate (i) the existence of the full topological bandgap in a bianisotropic, and (ii) the reflectionless nature of wave propagation along the interface between two PTIs with opposite signs of the bianisotropy.
Topology Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe; Andreasen, Casper Schousboe; Aage, Niels
the widely used Brinkman-penalisation approach to fluid topology optimisation [2] combined with suitable interpolation functions for thermal conductivity. The Method of Moving Asymptotes (MMA) is used and density filtering is applied in order to ensure a minimum lengthscale. The results are generated using...
Valley photonic crystals for control of spin and topology.
Dong, Jian-Wen; Chen, Xiao-Dong; Zhu, Hanyu; Wang, Yuan; Zhang, Xiang
2017-03-01
Photonic crystals offer unprecedented opportunity for light manipulation and applications in optical communication and sensing. Exploration of topology in photonic crystals and metamaterials with non-zero gauge field has inspired a number of intriguing optical phenomena such as one-way transport and Weyl points. Recently, a new degree of freedom, valley, has been demonstrated in two-dimensional materials. Here, we propose a concept of valley photonic crystals with electromagnetic duality symmetry but broken inversion symmetry. We observe photonic valley Hall effect originating from valley-dependent spin-split bulk bands, even in topologically trivial photonic crystals. Valley-spin locking behaviour results in selective net spin flow inside bulk valley photonic crystals. We also show the independent control of valley and topology in a single system that has been long pursued in electronic systems, resulting in topologically-protected flat edge states. Valley photonic crystals not only offer a route towards the observation of non-trivial states, but also open the way for device applications in integrated photonics and information processing using spin-dependent transportation.
Valley photonic crystals for control of spin and topology
Energy Technology Data Exchange (ETDEWEB)
Dong, Jian-Wen; Chen, Xiao-Dong; Zhu, Hanyu; Wang, Yuan; Zhang, Xiang
2016-11-28
Photonic crystals offer unprecedented opportunity for light manipulation and applications in optical communication and sensing1,2,3,4. Exploration of topology in photonic crystals and metamaterials with non-zero gauge field has inspired a number of intriguing optical phenomena such as one-way transport and Weyl points5,6,7,8,9,10. Recently, a new degree of freedom, valley, has been demonstrated in two-dimensional materials11,12,13,14,15. Here, we propose a concept of valley photonic crystals with electromagnetic duality symmetry but broken inversion symmetry. We observe photonic valley Hall effect originating from valley-dependent spin-split bulk bands, even in topologically trivial photonic crystals. Valley–spin locking behaviour results in selective net spin flow inside bulk valley photonic crystals. We also show the independent control of valley and topology in a single system that has been long pursued in electronic systems, resulting in topologically-protected flat edge states. Valley photonic crystals not only offer a route towards the observation of non-trivial states, but also open the way for device applications in integrated photonics and information processing using spin-dependent transportation.
Topology Optimization Methods for Acoustic-Mechanical Coupling Problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Dilgen, Cetin Batur; Dilgen, Sümer Bartug
2017-01-01
A comparative overview of methods for topology optimization of acoustic mechanical coupling problems is provided. The goal is to pave the road for developing efficient optimization schemes for the design of complex acoustic devices such as hearingaids.......A comparative overview of methods for topology optimization of acoustic mechanical coupling problems is provided. The goal is to pave the road for developing efficient optimization schemes for the design of complex acoustic devices such as hearingaids....
Topologically protected bound states in photonic parity-time-symmetric crystals.
Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A
2017-04-01
Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.
Constraint interface preconditioning for topology optimization problems
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Loghin, D.; Turner, J.
2016-01-01
Roč. 38, č. 1 (2016), A128-A145 ISSN 1064-8275 R&D Projects: GA AV ČR IAA100750802 Grant - others:European Commission - EC(XE) 313781 Institutional support: RVO:67985556 Keywords : topology optimization * domain decomposition * Newton-Krylov Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/kocvara-0460325.pdf
Frequency response as a surrogate eigenvalue problem in topology optimization
DEFF Research Database (Denmark)
Andreassen, Erik; Ferrari, Federico; Sigmund, Ole
2017-01-01
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...... associated with computation of eigenvalues in very large problems....
Topological edge states of distorted photonic Kagome lattices
Ni, Xiang; Alu, Andrea; Khanikaev, Alexander B.
2017-08-01
We demonstrate that the distorted Kagome lattice formed by two-dimensional(2d) array of dielectric rods embedded in air exhibits a new class of topological states characterized by a topological invariant number in Pauli vector space. The Kagome lattice can be considered as a 2d analogue of the Su-Schrieffer-Heeger (SSH) model, which displays a phase transition by detuning the relative amplitudes of the inter-cell and intra-cell hopping terms. The phase transition is accompanied by the opening of a complete band gap in the Brillouin zone, which may host topological edge states on either the truncated end of the lattice or at the domain walls between topological nontrivial and trivial domains. To further reveal the connection between the bulk invariance and edge states, polarizations of shrunken and expanded effects are calculated. Our first-principles simulations based on finite element method (FEM) are used to design the lattice and confirm the analytic prediction.
Topology Optimization in wave-propagation and flow problems
DEFF Research Database (Denmark)
Sigmund, Ole; Jensen, Jakob Søndergaard; Gersborg-Hansen, A.
2004-01-01
We discuss recent extensions of the topology optimization method to wave-propagation and flow problems. More specifically, we optimize material distribution in scalar wave propagation problems modelled by Helmholtz equation. Moreover, we investigate the influence of the inertia term on the optimal...
A concept for global optimization of topology design problems
DEFF Research Database (Denmark)
Stolpe, Mathias; Achtziger, Wolfgang; Kawamoto, Atsushi
2006-01-01
We present a concept for solving topology design problems to proven global optimality. We propose that the problems are modeled using the approach of simultaneous analysis and design with discrete design variables and solved with convergent branch and bound type methods. This concept is illustrated...
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 Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe; Andreasen, Casper Schousboe; Aage, Niels
stabilised finite elements implemented in a parallel multiphysics analysis and optimisation framework DFEM [1], developed and maintained in house. Focus is put on control of the temperature field within the solid structure and the problems can therefore be seen as conjugate heat transfer problems, where heat...... conduction governs in the solid parts of the design domain and couples to convection-dominated heat transfer to a surrounding fluid. Both loosely coupled and tightly coupled problems are considered. The loosely coupled problems are convection-diffusion problems, based on an advective velocity field from...
Solving a Deconvolution Problem in Photon Spectrometry
Aleksandrov, D; Hille, P T; Polichtchouk, B; Kharlov, Y; Sukhorukov, M; Wang, D; Shabratova, G; Demanov, V; Wang, Y; Tveter, T; Faltys, M; Mao, Y; Larsen, D T; Zaporozhets, S; Sibiryak, I; Lovhoiden, G; Potcheptsov, T; Kucheryaev, Y; Basmanov, V; Mares, J; Yanovsky, V; Qvigstad, H; Zenin, A; Nikolaev, S; Siemiarczuk, T; Yuan, X; Cai, X; Redlich, K; Pavlinov, A; Roehrich, D; Manko, V; Deloff, A; Ma, K; Maruyama, Y; Dobrowolski, T; Shigaki, K; Nikulin, S; Wan, R; Mizoguchi, K; Petrov, V; Mueller, H; Ippolitov, M; Liu, L; Sadovsky, S; Stolpovsky, P; Kurashvili, P; Nomokonov, P; Xu, C; Torii, H; Il'kaev, R; Zhang, X; Peresunko, D; Soloviev, A; Vodopyanov, A; Sugitate, T; Ullaland, K; Huang, M; Zhou, D; Nystrand, J; Punin, V; Yin, Z; Batyunya, B; Karadzhev, K; Nazarov, G; Fil'chagin, S; Nazarenko, S; Buskenes, J I; Horaguchi, T; Djuvsland, O; Chuman, F; Senko, V; Alme, J; Wilk, G; Fehlker, D; Vinogradov, Y; Budilov, V; Iwasaki, T; Ilkiv, I; Budnikov, D; Vinogradov, A; Kazantsev, A; Bogolyubsky, M; Lindal, S; Polak, K; Skaali, B; Mamonov, A; Kuryakin, A; Wikne, J; Skjerdal, K
2010-01-01
We solve numerically a deconvolution problem to extract the undisturbed spectrum from the measured distribution contaminated by the finite resolution of the measuring device. A problem of this kind emerges when one wants to infer the momentum distribution of the neutral pions by detecting the it decay photons using the photon spectrometer of the ALICE LHC experiment at CERN {[}1]. The underlying integral equation connecting the sought for pion spectrum and the measured gamma spectrum has been discretized and subsequently reduced to a system of linear algebraic equations. The latter system, however, is known to be ill-posed and must be regularized to obtain a stable solution. This task has been accomplished here by means of the Tikhonov regularization scheme combined with the L-curve method. The resulting pion spectrum is in an excellent quantitative agreement with the pion spectrum obtained from a Monte Carlo simulation. (C) 2010 Elsevier B.V. All rights reserved.
3D Topology optimization of Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Dammann, Bernd
of energy efficient devices for 2D Stokes flow. Creeping flow problems are described by the Stokes equations which model very viscous fluids at macro scales or ordinary fluids at very small scales. The latter gives the motivation for topology optimization problems based on the Stokes equations being a model...... geometry is non-trivial as typically seen in topology design. The presentation elaborates on effects caused by 3D fluid modelling on the design. Numerical examples relevant for optimal micro fluidic mixer design are shown where the design is planar - compliant with micro fabrication techniques - and where...... fields as solid mechanics and optics and is due to the method's flexibility in the (rough) parametrization of the design, see [1] and the reference therein for an overview. Borrvall and Petersson [2] is the seminal reference for topology optimization in fluid flow problems. They considered design...
Broadband topology-optimized photonic crystal components for both TE and TM polarizations
DEFF Research Database (Denmark)
Têtu, A.; Kristensen, M.; Frandsen, Lars Hagedorn
2005-01-01
Several planar photonic crystal components topology-optimized for TE-polarized light, including 60º bends, Y-splitters, and 90º bends, have been characterized for the TM polarization. The experimental results are confirmed by finite-difference time-domain calculations. The surprising efficiency f...... for TM-polarized light is found and paves the way for photonic crystal components suitable for both polarizations....
Topological Valley Transport in Two-dimensional Honeycomb Photonic Crystals.
Yang, Yuting; Jiang, Hua; Hang, Zhi Hong
2018-01-25
Two-dimensional photonic crystals, in analogy to AB/BA stacking bilayer graphene in electronic system, are studied. Inequivalent valleys in the momentum space for photons can be manipulated by simply engineering diameters of cylinders in a honeycomb lattice. The inequivalent valleys in photonic crystal are selectively excited by a designed optical chiral source and bulk valley polarizations are visualized. Unidirectional valley interface states are proved to exist on a domain wall connecting two photonic crystals with different valley Chern numbers. With the similar optical vortex index, interface states can couple with bulk valley polarizations and thus valley filter and valley coupler can be designed. Our simple dielectric PC scheme can help to exploit the valley degree of freedom for future optical devices.
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.
particular at micro scales since they are easily manufacturable and maintenance free. Here we consider topology optimization of 3D Stokes flow problems which is a reasonable fluid model to use at small scales. The presentation elaborates on effects caused by 3D fluid modelling on the design. Numerical......The design of MEMS devices have benefitted from the topology optimization tool and complicated layout problems have been solved, see [1] for an overview. This research is aimed at micro fluidic devices known as micro-Total-Analysis-Systems (muTAS) where the main physical phenomena originate from...... fluid mechanics. In future practice a muTAS could be used by doctors, engineers etc. as a hand held device with short reaction time that provides on-site analysis of a flowing substance such as blood, polluted water or similar. Borrvall and Petersson [2] paved the road for using the topology...
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
flow [3]. Furthermore, it is questionable if such a coupling can be captured by a 2D model especially in non-trivial geometries as typically seen in topology design. This statement is widely accepted in the fluid mechanics community, i.e. that planar fluid models are useful for academic test problems...... fundamental aspects of the topology optimization method applied to the Stokes equations as described below. This work consists of two parts. The main part elaborates on effects caused by 3D fluid modelling on the design. Numerical examples are shown where the design is planar - relevant to micro fluidic...... are discussed which is the critical bottleneck for the 3D problem. The implementation uses semi--analytical sensitivities to drive a gradient based optimization algorithm. [1] M. P. Bendsøe and O. Sigmund, Topology Optimization - Theory, Methods and Applications, Springer Verlag, Berlin Heidelberg, 2003. [2] T...
Topology Optimization for Wave Propagation Problems with Experimental Validation
DEFF Research Database (Denmark)
Christiansen, Rasmus Ellebæk
discussion of the finite element method and a hybrid ofa wave based method and the finite element method, used to discretize the modelproblems under consideration. A short discussion of the benefits and drawbacks of applying the hybrid method compared to the finite element method, used in conjunction......This Thesis treats the development and experimental validation of density-based topology optimization methods for wave propagation problems. Problems in the frequency regime where design dimensions are between approximately one fourth and ten wavelengths are considered. All examples treat problems...... from acoustics, however problems for TE or TM polarized electromagnetic waves and shear waves in solids in two dimensions may be treated using the proposed methods with minor modifications. A brief introduction to wave problems and to density-based topology optimizationis included, as is a brief...
Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Harpøth, Anders; Borel, Peter Ingo
2004-01-01
Topology optimization has been used to design a 60° bend in a single-mode planar photonic crystal waveguide. The design has been realized in a silicon-on-insulator material and we demonstrate a record-breaking 200-nm transmission bandwidth with an average bend loss of 0.43±0.27 dB for the TE...
Flat-top Drop Filter based on a Single Topology Optimized Photonic Crystal Cavity
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Elesin, Yuriy; Guan, Xiaowei
2015-01-01
Outperforming conventional design concepts, a flat-top drop filter has been designed byapplying 3D topology optimization to a single waveguide-coupled L3 photonic crystal cavity.Measurements on the design fabricated in silicon-on-insulator material reveal that the pass-band ofthe drop channel...
Topology optimization: a systematic method to improve the performance of photonic crystal structures
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2004-01-01
The method of topology optimization has previously been used to design exotic materials, MEMS and thermo-elastic mechanisms, as well as several other devices in mechanics and multi-physics applications [1]. Recently, the method was applied to design photonic and phononic crystals with maximum siz...
Topology optimization of dynamics problems with Padé approximants
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
An efficient procedure for topology optimization of dynamics problems is proposed. The method is based on frequency responses represented by Padé approximants and analytical sensitivity analysis derived using the adjoint method. This gives an accurate approximation of the frequency response over ...
Topological spin transport of photons: the optical Magnus effect and Berry phase
International Nuclear Information System (INIS)
Bliokh, K.Yu.; Bliokh, Yu.P.
2004-01-01
The Letter develops a modified geometrical optics (GO) of smoothly inhomogeneous isotropic medium, which takes into account two topological phenomena: Berry phase and the optical Magnus effect. Taking into account the correspondence between a quasi-classical motion of a quantum particle with a spin and GO of an electromagnetic wave in smoothly inhomogeneous media, we have introduced the standard gauge potential associated with the degeneracy in the wave momentum space. This potential corresponds to the magnetic-monopole-like field (Berry curvature), which causes the topological spin (polarization) transport of photons. The deviations of waves of right-hand and left-hand polarization occur in the opposite directions and orthogonally to the principal direction of motion. This produces a spin current directed across the principal motion. The situation is similar to the anomalous Hall effect for electrons. In addition, a simple scheme of the experiment allowing one to observe the topological spin splitting of photons has been suggested
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...
Topology optimization applied to room acoustic problems and surface acoustic wave devices
DEFF Research Database (Denmark)
Dühring, Maria Bayard; Sigmund, Ole; Jensen, Jakob Søndergaard
of the project is concerned with simulation and optimization of surface acoustic wave (SAW) devices [4]. SAWs are for instance used in filters and resonators in mobile phones and to modulate light waves [5], and it is here essential to obtain waves with a high intensity, to direct the waves or to optimize...... of engineering fields such as mechanism design, fluid problems and photonic and phononic band-gap materials and structures [1,2]. In this project topology optimization is first applied to control acoustic properties in a room [3]. It is shown how the squared sound pressure amplitude in a certain part of a room...
Unidirectional edge states in topological honeycomb-lattice membrane photonic crystals.
Anderson, P Duke; Subramania, Ganapathi
2017-09-18
Photonic analogs of electronic systems with topologically non-trivial behavior such as unidirectional scatter-free propagation has tremendous potential for transforming photonic systems. Like in electronics topological behavior can be observed in photonics for systems either preserving time-reversal (TR) symmetry or explicitly breaking it. TR symmetry breaking requires magneto-optic photonics crystals (PC) or generation of synthetic gauge fields. For on-chip photonics that operate at optical frequencies both are quite challenging because of poor magneto-optic response of materials or substantial nanofabrication challenges in generating synthetic gauge fields. A recent work by Ma, et al. [Phys. Rev. Lett.114, 223901 (2015)] based on preserving pseudo TR symmetry offers a promising design scheme for observing unidirectional edge states in a modified honeycomb photonic crystal (PC) lattice of circular rods that offers encouraging alternatives. Here we propose through bandstructure calculations the inverse system of modified honeycomb PC of circular holes in a dielectric membrane which is more attractive from fabrication standpoint for on-chip applications. We observe trivial and non-trivial bandgaps as well as unidirectional edge states of opposite helicity propagating in opposite directions at the interface of a trivial and non-trivial PC structures. Around 1550nm operating wavelength ~55nm of bandwidth is possible for practicable values of design parameters (lattice constant, hole radii, membrane thickness, scaling factor etc.) and robust to reasonable variations in those parameters.
Topological classification of Chern-type insulators by means of the photonic Green function
Silveirinha, Mário G.
2018-03-01
The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to calculate the gap Chern numbers of a photonic platform without having any detailed knowledge of its band structure, relying simply on the system photonic Green function. It is shown that the gap Chern number is given by an integral of the photonic Green function along a line of the complex frequency plane parallel to the imaginary axis. Our theory applies to arbitrary frequency dispersive fully three-dimensional photonic crystals, as well as to the case of electromagnetic continua with no intrinsic periodicity.
On topological derivatives for contact problems in elasticity
Czech Academy of Sciences Publication Activity Database
Giusti, S.M.; Sokolowski, S.; Stebel, Jan
2015-01-01
Roč. 165, č. 1 (2015), s. 279-294 ISSN 0022-3239 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : topological derivative * static frictionless contact problem * asymptotic analysis Subject RIV: BA - General Mathematics Impact factor: 1.160, year: 2015 http://link.springer.com/article/10.1007%2Fs10957-014-0594-7
Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides
DEFF Research Database (Denmark)
Frellsen, Louise Floor; Ding, Yunhong; Sigmund, Ole
2016-01-01
We design and experimentally verify a topology optimized low-loss and broadband two-mode (de-)multiplexer, which is (de-)multiplexing the fundamental and the first-order transverse-electric modes in a silicon photonic wire. The device has a footprint of 2.6 μm x 4.22 μm and exhibits a loss 14 d...
Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods
Chan, Hsun-Chi; Guo, Guang-Yu
2018-01-01
In this paper we study topological phases in a two-dimensional photonic crystal with broken time (T ) and parity (P ) symmetries by performing calculations of band structures, Berry curvatures, Chern numbers, edge states, and also numerical simulations of light propagation in the edge modes. Specifically, we consider a hexagonal lattice consisting of triangular gyromagnetic rods. Here the gyromagnetic material breaks T symmetry while the triangular rods break P symmetry. Interestingly, we find that the crystal could host quantum anomalous Hall (QAH) phases with different gap Chern numbers (Cg) including | Cg|>1 as well as quantum valley Hall (QVH) phases with contrasting valley Chern numbers (Cv), depending on the orientation of the triangular rods. Furthermore, phase transitions among these topological phases, such as from QAH to QVH and vice versa, can be engineered by a simple rotation of the rods. Our band theoretical analyses reveal that the Dirac nodes at the K and K' valleys in the momentum space are produced and protected by the mirror symmetry (my) instead of the P symmetry, and they become gapped when either T or my symmetry is broken, resulting in a QAH or QVH phase, respectively. Moreover, a high Chern number (Cg=-2 ) QAH phase is generated by gapping triply degenerate nodal points rather than pairs of Dirac points by breaking T symmetry. Our proposed photonic crystal thus provides a platform for investigating intriguing topological phenomena which may be challenging to realize in electronic systems, and also has promising potentials for device applications in photonics such as reflection-free one-way waveguides and topological photonic circuits.
Photonic topological boundary pumping as a probe of 4D quantum Hall physics.
Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P; Kraus, Yaacov E; Rechtsman, Mikael C
2018-01-03
When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.
Efficient topology optimisation of multiscale and multiphysics problems
DEFF Research Database (Denmark)
Alexandersen, Joe
the computational cost of treating structures with fully-resolved microstructural details. The methodology is further applied to examples, where it is shown that it ensures connectivity of the microstructural details and that forced periodicity of the microstructural details can yield an implicit robustness to load...... to describe heat transfer and fluid flow are outlined, describing both a commonly-used simplified convection model and the full natural convection model. Topology optimisation using the simplified model is investigated as a means to reduce the computational time of optimising heat sinks. The model is shown...... sinks, a full conjugate heat transfer model is introduced. Optimised heat sinks are presented for both two- and three-dimensional natural convection problems, where similarities and differences are discussed. Generally, the observations are in line with classical heat sink design, but topology...
OPEN PROBLEM: Some problems in differential geometry and topology
Donaldson, S. K.
2008-09-01
This does not attempt to be a systematic overview or to present a comprehensive list of problems. We outline some questions in three different areas which seem interesting to the author. Experts will learn little that is new; our goal is to give some picture of the fields for non-specialists.
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...... structure of the problem. In both solvers, information of the exact Hessian is considered. A robust iterative method is implemented to efficiently solve large-scale linear systems. Both TopSQP and TopIP have successful results in terms of convergence, number of iterations, and objective function values....... Thanks to the use of the iterative method implemented, TopIP is able to solve large-scale problems with more than three millions degrees of freedom....
Topological approach to the generalized n-centre problem
Bolotin, S. V.; Kozlov, V. V.
2017-06-01
This paper considers a natural Hamiltonian system with two degrees of freedom and Hamiltonian H=\\Vert p\\Vert^2/2+V(q). The configuration space M is a closed surface (for non-compact M certain conditions at infinity are required). It is well known that if the potential energy V has n>2χ(M) Newtonian singularities, then the system is not integrable and has positive topological entropy on the energy level H=h>\\sup V. This result is generalized here to the case when the potential energy has several singular points a_j of type V(q)∼ -\\operatorname{dist}(q,a_j)-α_j. Let A_k=2-2k-1, k\\in{N}, and let n_k be the number of singular points with A_k≤slant α_jk+1. It is proved that if \\displaystyle \\sum2≤slant k≤slant∞n_kA_k>2χ(M), then the system has a compact chaotic invariant set of collision-free trajectories on any energy level H=h>\\sup V. This result is purely topological: no analytical properties of the potential energy are used except the presence of singularities. The proofs are based on the generalized Levi-Civita regularization and elementary topology of coverings. As an example, the plane n-centre problem is considered. Bibliography: 29 titles.
Topology optimization of mass distribution problems in Stokes flow
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Berggren, Martin; Dammann, Bernd
enabled an evaluation of the design with a body fitted mesh in a standard analysis software relevant in engineering practice prior to design manufacturing. This work investigates the proper choice of a maximum penalization value during the optimization process that ensures that the target outflow rates......We consider topology optimization of mass distribution problems in 2D and 3D Stokes flow with the aim of designing devices that meet target outflow rates. For the purpose of validation, the designs have been post processed using the image processing tools available in FEMLAB. In turn, this has...
Topology optimization problems for reflection and dissipation of elastic waves
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
This paper is devoted to topology optimization problems for elastic wave propagation. The objective of the study is to maximize the reflection or the dissipation in a finite slab of material for pressure and shear waves in a range of frequencies. The optimized designs consist of two or three...... material phases: a host material and scattering and/or absorbing inclusions. The capabilities of the optimization algorithm are demonstrated with two numerical examples in which the reflection and dissipation of ground-borne wave pulses are maximized....
Topology optimization problems with design-dependent sets of constraints
DEFF Research Database (Denmark)
Schou, Marie-Louise Højlund
for all elements independently of the values of the design variables. The investigations include validating constraint qualifications, attacking the problem formulations directly, and bounding the objective function value. We consider different constraint qualifications and whether they hold for the MPEC...... that a general nonlinear interior-point algorithm applied to the MPEC formulations outperforms a general nonlinear active-set sequential quadratic programming method. Inspired by this, we implement an interior-point algorithm such that we have full control of all aspects of the code. Solving the stress...... constrained structural topology optimization problem is computationally challenging. We therefore present a technique that decides whether it may pay-off to actually treat the stress constrained problem. The technique finds lower and upper bounds on the objective function value of the stress constrained...
The ATLAS collaboration
2017-01-01
The electron and photon reconstruction in ATLAS has moved towards the use of a dynamical, topo- logical cell-based approach for cluster building, owing to advancements in the calibration procedure which allow for such a method to be applied. The move to this new technique allows for improved measurements of electron and photon energies, particularly in situations where an electron radiates a bremsstrahlung photon, or a photon converts to an electron-poistron pair. This note details the changes to the ATLAS electron and photon reconstruction software, and assesses its performance under current LHC luminosity conditions using simulated data. Changes to the converted photon reconstruction are also detailed, which improve the reconstruction efficiency of double-track converted photons, as well as reducing the reconstruction of spurious one-track converted photons. The performance of the new reconstruction algorithm is also presented in a number of important topologies relevant to precision Standard Model physics,...
A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal
Wu, Ying
2014-01-01
Accidental degeneracy in a photonic crystal consisting of a square array of elliptical dielectric cylinders leads to both a semi-Dirac point at the center of the Brillouin zone and an electromagnetic topological transition (ETT). A perturbation method is deduced to affirm the peculiar linear-parabolic dispersion near the semi-Dirac point. An effective medium theory is developed to explain the simultaneous semi-Dirac point and ETT and to show that the photonic crystal is either a zero-refractive-index material or an epsilon-near-zero material at the semi-Dirac point. Drastic changes in the wave manipulation properties at the semi-Dirac point, resulting from ETT, are described.©2014 Optical Society of America.
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
Hassani Gangaraj, Seyyed Ali
analysis of the Green's function for the surface plasmonic wave contribution of the Sommerfeld integral. The Sommerfeld integral form of the Green's function can be time-consuming to evaluate, and here, it has been shown that for the surface waves, this integral can be evaluated efficiently as a mixture of continuous and discrete spectrums associated to the radiation of the source into the ambient space and energy coupled to the SPPs. Graphene strip arrays provide directive surface waves in the low THz regime, and unperturbed black phosphorus provides a similar response for higher frequency ranges. All plasmonic devices are impacted by SPP diffraction at surface defects and discontinuities. In particular, for reciprocal materials a surface defect/discontinuity can both scatter a forward mode into a backward mode (and vice versa) and cause significant radiation/diffraction of the SPP. The presence of a backward state comes from time reversal (TR) symmetry; when broken, a backward state may be absent, and reflection at a discontinuity can be suppressed. As a result, surface energy becomes unidirectional and follows the contour of the interface. This type of system can be broadly classified as a photonic topological insulators (PTIs). The properties of PTIs are quantified by the Berry phase, Berry connection, and an invariant known as the Chern number. Also the physical meaning of the Berry phase, connection, and curvature, how these quantities arise in electromagnetic problems, and the significance of Chern numbers for unidirectional, scattering-immune surface wave propagation are discussed. The Chern numbers for the electromagnetic modes supported by a biased plasma have been calculated. It has been demonstrated that the modes supported by biased plasmas indeed possess non-trivial Chern numbers, which leads to the propagation of a topologically protected and unidirectional surface modes (energy) at the interface between the biased plasma and topologically trivial material
Solving a deconvolution problem in photon spectrometry
Czech Academy of Sciences Publication Activity Database
Aleksandrov, D.; Alme, J.; Basmanov, V.; Mareš, Jiří A.; Polák, Karel
2010-01-01
Roč. 620, 2-3 (2010), s. 526-533 ISSN 0168-9002 Institutional research plan: CEZ:AV0Z10100502 Keywords : deconvolution * ALICE experiment * photon spectrometer * Tikhonov regularization Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.142, year: 2010
Topologically protected refraction of robust kink states in valley photonic crystals
Gao, Fei; Xue, Haoran; Yang, Zhaoju; Lai, Kueifu; Yu, Yang; Lin, Xiao; Chong, Yidong; Shvets, Gennady; Zhang, Baile
2018-02-01
Recently discovered valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials. Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling efficiency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an effective spin-orbit coupling in one of the VPC domains. This also constitutes the first realization of spin-valley locking for topological valley transport.
Topological inversion for solution of geodesy-constrained geophysical problems
Saltogianni, Vasso; Stiros, Stathis
2015-04-01
Geodetic data, mostly GPS observations, permit to measure displacements of selected points around activated faults and volcanoes, and on the basis of geophysical models, to model the underlying physical processes. This requires inversion of redundant systems of highly non-linear equations with >3 unknowns; a situation analogous to the adjustment of geodetic networks. However, in geophysical problems inversion cannot be based on conventional least-squares techniques, and is based on numerical inversion techniques (a priori fixing of some variables, optimization in steps with values of two variables each time to be regarded fixed, random search in the vicinity of approximate solutions). Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solutions with poor error control (usually sampling-based approaches). To overcome these problems, a numerical-topological, grid-search based technique in the RN space is proposed (N the number of unknown variables). This technique is in fact a generalization and refinement of techniques used in lighthouse positioning and in some cases of low-accuracy 2-D positioning using Wi-Fi etc. The basic concept is to assume discrete possible ranges of each variable, and from these ranges to define a grid G in the RN space, with some of the gridpoints to approximate the true solutions of the system. Each point of hyper-grid G is then tested whether it satisfies the observations, given their uncertainty level, and successful grid points define a sub-space of G containing the true solutions. The optimal (minimal) space containing one or more solutions is obtained using a trial-and-error approach, and a single optimization factor. From this essentially deterministic identification of the set of gridpoints satisfying the system of equations, at a following step, a stochastic optimal solution is computed corresponding to the center of gravity of this set of gridpoints. This solution corresponds to a
Problem-based learning in photonics technology education
Massa, Nicholas M.; Dischino, Michele; Donnelly, Judith; Hanes, Fenna
2008-08-01
Problem-based learning (PBL) is an instructional approach in which students learn by actively and collaboratively solving authentic problems encountered in real-world situations. Research demonstrates that PBL improves students' learning and retention, motivation, critical thinking and problem-solving skills, and their ability to skillfully apply knowledge in new and novel situations - skills deemed critical for lifelong learning. In this paper, we present the Photon PBL project, a three-year National Science Foundation Advanced Technological Education (NSF-ATE) project aimed at developing, in partnership with photonics industry and university partners, a comprehensive series of multimedia PBL instructional materials and training for photonics technology educators from across the US and abroad. Results from first-year pilot testing of multimedia PBL instructional materials, problem development and implementation strategies are detailed.
A dimensionality reduction technique for scattering problems in photonics
Ivanova, Alyona; Stoffer, Remco; Hammer, Manfred
2008-01-01
Optical scattering problems in guided wave photonics are addressed. We represent the unknown optical fields as superpositions of 1D slab modes bounded by PMLs. By applying a variational principle, the problems are reduced to lower dimensional systems of differential equations for the unknown
Method to optimize optical switch topology for photonic network-on-chip
Zhou, Ting; Jia, Hao
2018-04-01
In this paper, we propose a method to optimize the optical switch by substituting optical waveguide crossings for optical switching units and an optimizing algorithm to complete the optimization automatically. The functionality of the optical switch remains constant under optimization. With this method, we simplify the topology of optical switch, which means the insertion loss and power consumption of the whole optical switch can be effectively minimized. Simulation result shows that the number of switching units of the optical switch based on Spanke-Benes can be reduced by 16.7%, 20%, 20%, 19% and 17.9% for the scale from 4 × 4 to 8 × 8 respectively. As a proof of concept, the experimental demonstration of an optimized six-port optical switch based on Spanke-Benes structure by means of silicon photonics chip is reported.
Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2005-01-01
A T junction in a photonic crystal waveguide is designed with the topology-optimization method. The gradientbased optimization tool is used to modify the material distribution in the junction area so that the power transmission in the output ports is maximized. To obtain high transmission...
Fuzzy Generalized Variational Like Inequality problems in Topological Vector Spaces
Directory of Open Access Journals (Sweden)
M. K. Ahmad
2013-01-01
Full Text Available This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.
Newton-type method for the variational discretization of topology optimization problems
DEFF Research Database (Denmark)
Evgrafov, Anton
2013-01-01
We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, ...
Reduced order modeling in topology optimization of vibroacoustic problems
DEFF Research Database (Denmark)
Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas
2017-01-01
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...... suffer from the curse of dimensionality. Moreover, the fact that the nature of the elements changes throughout the optimization (material to void or material to air) makes it more difficult to create a global basis that is accurate throughout the whole design space. In this work, these challenges...
Efficient methods for solving discrete topology design problems in the PLATO-N project
DEFF Research Database (Denmark)
Canh, Nam Nguyen; Stolpe, Mathias
This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global optimizat......This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global...
PROBLEMS IN TOPOLOGICAL GRAPH THEORY : QUESTIONS I CAN'T ANSWER
Archdeacon, Dan
1999-01-01
This paper describes my Problems in Topological Graph Theory, which can be accessed through the world-wide-web at http: //www.emba .uvm.edu/~arcceack/problems/problems.html This list of problems is constantly being revised; the interested reader is encouraged to submit additions and updates.
DEFF Research Database (Denmark)
Stolpe, Mathias; Stidsen, Thomas K.
2005-01-01
In this paper we present a hierarchical optimization method for finding feasible true 0-1 solutions to finite element based topology design problems. The topology design problems are initially modeled as non-convex mixed 0-1 programs. The hierarchical optimization method is applied to the problem...... from global optimization, which have only recently become available, for solving the problems in the sequence. Numerical examples of topology design problems of continuum structures with local stress and displacement constraints are presented.......In this paper we present a hierarchical optimization method for finding feasible true 0-1 solutions to finite element based topology design problems. The topology design problems are initially modeled as non-convex mixed 0-1 programs. The hierarchical optimization method is applied to the problem...... of minimizing the weight of a structure subject to displacement and local design-dependent stress constraints. The method iteratively solves a sequence of problems of increasing size of the same type as the original problem. The problems are defined on a design mesh which is initially coarse...
Benefits and Challenges when Performing Robust Topology Optimization for Interior Acoustic Problems
DEFF Research Database (Denmark)
Christiansen, Rasmus Ellebæk; Jensen, Jakob Søndergaard; Lazarov, Boyan Stefanov
The objective of this work is to present benets and challenges of using robust topology optimization techniques for minimizing the sound pressure in interior acoustic problems. The focus is on creating designs which maintain high performance under uniform spatial variations. This work takes offset...... in previous work considering topology optimization for interior acoustic problems, [1]. However in the previous work the robustness of the designs was not considered....
Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method
DEFF Research Database (Denmark)
Goo, Seongyeol; Wang, Semyung; Kook, Junghwan
2017-01-01
This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which...... is limited to low frequency applications due to considerable computational efforts. To this end, we propose a gradient-based topology optimization method that uses the hybrid FE-WBM whereby the entire domain of a problem is partitioned into design and non-design domains. In this respect, the FEM is used...... as a design domain of topology optimization, and the WBM is used as a non-design domain to increase computational efficiency. The adjoint variable method based on the hybrid FE-WBM is also proposed as a means of computing design sensitivities. Numerical examples are presented to demonstrate the effectiveness...
DEFF Research Database (Denmark)
Sugimoto, Y; Watanabe, Y; Ikeda, N
2006-01-01
Numerical and experimental studies on the photonic crystal waveguide intersection based on the topology optimization design method are reported and the effectiveness is shown by achieving high transmission spectra with low crosstalk for the straightforward beam-propagation line....
Optimal calculational schemes for solving multigroup photon transport problem
International Nuclear Information System (INIS)
Dubinin, A.A.; Kurachenko, Yu.A.
1987-01-01
A scheme of complex algorithm for solving multigroup equation of radiation transport is suggested. The algorithm is based on using the method of successive collisions, the method of forward scattering and the spherical harmonics method, and is realized in the FORAP program (FORTRAN, BESM-6 computer). As an example the results of calculating reactor photon transport in water are presented. The considered algorithm being modified may be used for solving neutron transport problems
Solving stress constrained problems in topology and material optimization
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Stingl, M.
2012-01-01
Roč. 46, č. 1 (2012), s. 1-15 ISSN 1615-147X R&D Projects: GA AV ČR IAA100750802 Grant - others:EU FP6(XE) 30717 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Topology optimization * Material Optimization * Stress based design * Nonlinear semidefinite programming Subject RIV: BA - General Mathematics Impact factor: 1.728, year: 2012 http://library.utia.cas.cz/separaty/2013/MTR/kocvara-0421362.pdf
Optimization of photonic crystal cavities
DEFF Research Database (Denmark)
Wang, Fengwen; Sigmund, Ole
2017-01-01
We present optimization of photonic crystal cavities. The optimization problem is formulated to maximize the Purcell factor of a photonic crystal cavity. Both topology optimization and air-hole-based shape optimization are utilized for the design process. Numerical results demonstrate...... that the Purcell factor of the photonic crystal cavity can be significantly improved through optimization....
The world problem: on the computability of the topology of 4-manifolds
vanMeter, J. R.
2005-01-01
Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.
Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang
2017-10-01
The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.
DEFF Research Database (Denmark)
Stolpe, Mathias; Stidsen, Thomas K.
2007-01-01
and then successively refined as needed. At each level of design mesh refinement, a neighbourhood optimization method is used to treat the problem considered. The non-convex topology design problems are equivalently reformulated as convex all-quadratic mixed 0-1 programs. This reformulation enables the use of methods...
Topology optimization of heat conduction problems using the finite volume method
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole
2006-01-01
This note addresses the use of the finite volume method (FVM) for topology optimization of a heat conduction problem. Issues pertaining to the proper choice of cost functions, sensitivity analysis and example test problems are used to illustrate the effect of applying the FVM as an analysis tool ...
On Compliance and Buckling Objective Functions in Topology Optimization of Snap-Through Problems
DEFF Research Database (Denmark)
Lindgaard, Esben; Dahl, Jonas
2013-01-01
This paper deals with topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied for topology optimization of a point loaded curved beam problem with the aim of maximizing...... the snap-through buckling load. The response of the optimized structures obtained using the considered objective functions are evaluated and compared. Due to the intrinsic nonlinear nature of the problem, the load level at which the objective function is evaluated has a tremendous effect on the resulting...... optimized design. A well-known issue in buckling topology optimization is artificial buckling modes in low density regions. The typical remedy applied for linear buckling does not have a natural extension to nonlinear problems, and we propose an alternative approach. Some possible negative implications...
Topology optimization of fluid-structure-interaction problems in poroelasticity
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe; Sigmund, Ole
2013-01-01
with the deformation of the elastic skeleton through a macroscopic Darcy-type flow law. The method allows to impose pressure loads for static problems through a one way coupling, while transient problems are fully coupled modeling the interaction between fluid and solid. The material distribution is determined...
Riemann problem for the photon fluid: Self-steepening effects
Ivanov, S. K.; Kamchatnov, A. M.
2017-11-01
We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear Schrödinger (NLS) equation with self-steepening term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. It is shown that evolution dynamics in this case is much richer than that for the NLS equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity.
On some problems of descriptive set theory in topological spaces
International Nuclear Information System (INIS)
Choban, M M
2005-01-01
Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katetov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute B-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated
On some problems of descriptive set theory in topological spaces
Energy Technology Data Exchange (ETDEWEB)
Choban, M M [Tiraspol State University, Chisinau (Moldova, Republic of)
2005-08-31
Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katetov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute B-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated.
DEFF Research Database (Denmark)
Rasmussen, Marie-Louise Højlund; Stolpe, Mathias
2008-01-01
The subject of this article is solving discrete truss topology optimization problems with local stress and displacement constraints to global optimum. We consider a formulation based on the Simultaneous ANalysis and Design (SAND) approach. This intrinsically non-convex problem is reformulated...... to a mixed-integer linear program, which is solved with a parallel implementation of branch-and-bound. Additional valid inequalities and cuts are introduced to give a stronger representation of the problem, which improves convergence and speed up of the parallel method. The valid inequalities represent...... the physics, and the cuts (Combinatorial Benders’ and projected Chvátal–Gomory) come from an understanding of the particular mathematical structure of the reformulation. The impact of a stronger representation is investigated on several truss topology optimization problems in two and three dimensions....
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jens Stissing; Sigmund, Ole
2007-01-01
The paper presents a gradient-based topology optimization formulation that allows to solve acoustic-structure (vibro-acoustic) interaction problems without explicit boundary interface representation. In acoustic-structure interaction problems, the pressure and displacement fields are governed...... given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u/p-formulation). The Helmholtz equation is obtained as a special case of the mixed formulation...... for the elastic shear modulus equating to zero. Hence, by spatial variation of the mass density, shear and bulk moduli we are able to solve the coupled problem by the mixed formulation. Using this modelling approach, the topology optimization procedure is simply implemented as a standard density approach. Several...
Topology-optimized mode converter in a silicon-on-insulator photonic wire waveguide
DEFF Research Database (Denmark)
Frellsen, Louise Floor; Ding, Yunhong; Sigmund, Ole
2016-01-01
A 1.4 μm × 3.4 μm fundamental to first order mode converter for the transverse electric polarization was designed using topology optimization. Insertion loss <2 dB (100 nm bandwidth) and extinction ratio >9.5 dB.......A 1.4 μm × 3.4 μm fundamental to first order mode converter for the transverse electric polarization was designed using topology optimization. Insertion loss 9.5 dB....
Topology Optimization of Nanophotonic Devices
DEFF Research Database (Denmark)
Yang, Lirong
This thesis explores the various aspects of utilizing topology optimization in designing nanophotonic devices. Either frequency-domain or time-domain methods is used in combination with the optimization algorithms, depending on various aims of the designing problems. The frequency-domain methods...... lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses....
DEFF Research Database (Denmark)
Jensen, Kristian
2018-01-01
Topology optimization was recently combined with anisotropic mesh adaptation to solve 3D minimum compliance problems in a fast and robust way. This paper demonstrates that the methodology is also applicable to 2D/3D heat conduction problems. Nodal design variables are used and the objective...... function is chosen such that the problem is self-adjoint. There is no way around the book keeping associated with mesh adaptation, so the whole 5527 line MATLAB code is published (https://github.com/kristianE86/trullekrul). The design variables as well as the sensitivities have to be interpolated between...
Topological Design for Acoustic-Structure Interaction Problems with a Mixed Finite Element Method
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...... acoustic-structure interaction problems are optimized to show the validity of the proposed method....
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....
Topological regularizations of the triple collision singularity in the 3-vortex problem
International Nuclear Information System (INIS)
Hiraoka, Yasuaki
2008-01-01
The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail
Topology-optimized and dispersion-tailored photonic crystal slow-light devices
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Lavrinenko, Andrei; Borel, Peter Ingo
2007-01-01
not guarantee optimal solutions. The systematic design method based on topology optimization [1] allows creation of improved PhCW components with previously unseen low transmission losses, high operational bandwidths,and/or with wavelength selective functionalities. The method was originally developed...... distribution for the target mode and through a simple structural tuning of the waveguide geometry [3]. In this way, it is possible to realize a silicon-on-insulator PhCW with semi-slow light having a group velocity in the range ~(c0/15 – c0/100); vanishing, positive, or negative group velocity dispersion (GVD......); and low-loss propagation in a practical ~5-15 nm bandwidth. Such simple PhCW component may find widespread use in passive integrated circuits. The talk will present examples of topology-optimized PhCW components for broadband use and for narrowband use in the slow-light regime of PhCWs and exemplify how...
Condensed history Monte Carlo methods for photon transport problems
International Nuclear Information System (INIS)
Bhan, Katherine; Spanier, Jerome
2007-01-01
We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods - called Condensed History (CH) methods - have been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models - one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes - can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions
Measurement problem and local hidden variables with entangled photons
Muchowski, Eugen
2017-12-01
It is shown that there is no remote action with polarization measurements of photons in singlet state. A model is presented introducing a hidden parameter which determines the polarizer output. This model is able to explain the polarization measurement results with entangled photons. It is not ruled out by Bell's Theorem.
Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
Bradlyn, Barry; Elcoro, L.; Vergniory, M. G.; Cano, Jennifer; Wang, Zhijun; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei
2018-01-01
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k .p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.
Crystalline metamaterials for topological properties at subwavelength scales.
Yves, Simon; Fleury, Romain; Berthelot, Thomas; Fink, Mathias; Lemoult, Fabrice; Lerosey, Geoffroy
2017-07-18
The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have so far only been observed in photonic crystals and waveguide arrays, which are inherently physically wavelength scaled, hindering their application in compact subwavelength systems. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices, and create crystalline metamaterials that can develop complex nonlocal properties due to multiple scattering, despite their very subwavelength spatial scale that usually implies to disregard their structure. These spatially dispersive systems can support subwavelength topological phases, as we demonstrate at microwaves by direct field mapping. Our approach gives a straightforward tabletop platform for the study of photonic topological phases, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.
A Branch and Bound Approach for Truss Topology Design Problems with Valid Inequalities
International Nuclear Information System (INIS)
Cerveira, Adelaide; Agra, Agostinho; Bastos, Fernando; Varum, Humberto
2010-01-01
One of the classical problems in the structural optimization field is the Truss Topology Design Problem (TTDP) which deals with the selection of optimal configuration for structural systems for applications in mechanical, civil, aerospace engineering, among others. In this paper we consider a TTDP where the goal is to find the stiffest truss, under a given load and with a bound on the total volume. The design variables are the cross-section areas of the truss bars that must be chosen from a given finite set. This results in a large-scale non-convex problem with discrete variables. This problem can be formulated as a Semidefinite Programming Problem (SDP problem) with binary variables. We propose a branch and bound algorithm to solve this problem. In this paper it is considered a binary formulation of the problem, to take advantage of its structure, which admits a Knapsack problem as subproblem. Thus, trying to improve the performance of the Branch and Bound, at each step, some valid inequalities for the Knapsack problem are included.
Fluctuation-induced forces on an atom near a photonic topological material
Silveirinha, Mário G.; Gangaraj, S. Ali Hassani; Hanson, George W.; Antezza, Mauro
2018-02-01
We theoretically study the Casimir-Polder force on an atom in an arbitrary initial state in a rather general electromagnetic environment wherein the materials may have a nonreciprocal bianisotropic dispersive response. It is shown that under the Markov approximation the force has resonant and nonresonant contributions. We obtain explicit expressions for the optical force both in terms of the system Green function and of the electromagnetic modes. We apply the theory to the particular case wherein a two-level system interacts with a topological gyrotropic material, showing that the nonreciprocity enables exotic light-matter interactions and the opportunity to sculpt and tune the Casimir-Polder forces on the nanoscale. With a quasistatic approximation, we obtain a simple analytical expression for the optical force and unveil the crucial role of surface plasmons in fluctuation-induced forces. Finally, we derive the Green function for a gyrotropic material half-space in terms of a Sommerfeld integral.
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, Takahiro [Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Ibaraki (Japan) and Liquid-Crystal Nano-System Project, ERATO/SORST, Japan Science and Technology, Agency, 5-9-9 Tokodai, Tsukuba 300-2635, Ibaraki (Japan)]. E-mail: takahiro.yamamoto@aist.go.jp; Tabe, Yuka [Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Ibaraki (Japan); Liquid-Crystal Nano-System Project, ERATO/SORST, Japan Science and Technology, Agency, 5-9-9 Tokodai, Tsukuba 300-2635, Ibaraki (Japan); Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjyuku, 169-8555, Tokyo (Japan); Yokoyama, Hiroshi [Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Ibaraki (Japan); Liquid-Crystal Nano-System Project, ERATO/SORST, Japan Science and Technology, Agency, 5-9-9 Tokodai, Tsukuba 300-2635, Ibaraki (Japan)
2006-06-19
By modulating liquid-crystal alignment on a colloidal sphere, we successfully manipulated topological defects in glycerol-droplet/liquid-crystal emulsions doped with amphiphilic azobenzene derivatives. At an initial state, a disclination loop (Saturn ring) could be observed around the droplet, in which the azobenzene molecules should adsorb onto the droplet and liquid crystal molecules align normally to the surface of the droplet. On irradiation with ultra-violet light ({lambda} = 365 nm), the disclination loop was unfastened and transformed into two point defects called boojums. This should be attributed to the alignment change of the liquid crystal molecules from normal to planar arrangement triggered by trans-to-cis photoisomerization of the adsorbed azo-dyes. On irradiation with visible light causing cis-to-trans photoisomerization ({lambda} = 435 nm), the boojums went back to the Saturn ring reversibly.
A note on the consensus finding problem in communication networks with switching topologies
Haskovec, Jan
2014-05-07
In this note, we discuss the problem of consensus finding in communication networks of agents with dynamically switching topologies. In particular, we consider the case of directed networks with unbalanced matrices of communication rates. We formulate sufficient conditions for consensus finding in terms of strong connectivity of the underlying directed graphs and prove that, given these conditions, consensus is found asymptotically. Moreover, we show that this consensus is an emergent property of the system, being encoded in its dynamics and not just an invariant of its initial configuration. © 2014 © 2014 Taylor & Francis.
Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem
Raman, Aaswath
2010-02-26
We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.
A new approach to the photon localization problem
Han, D.; Kim, Y. S.; Noz, Marilyn E.
1994-01-01
Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.
Directory of Open Access Journals (Sweden)
Yu-Shan Chen
2015-04-01
Full Text Available We reported that the photonic crystal fiber (PCF filled with TI:Bi2Te3 nanosheets solution could act as an effective saturable absorber (SA. Employing this TI-PCF SA device; we constructed an ytterbium-doped all-fiber laser oscillator and achieved the evanescent wave mode-locking operation. Due to the large cavity dispersion; the fundamental mode-locking pulse had the large full width at half maximum (FWHM of 2.33 ns with the repetition rate of ~1.11 MHz; and the radio frequency (RF spectrum with signal-to-noise ratio (SNR of 61 dB. In addition; the transition dynamics from a bunched state of pulses to harmonic mode-locking (HML was also observed; which was up to 26th order.
Carrier and photon dynamics in a topological insulator Bi2Te3/GaN type II staggered heterostructure
Chaturvedi, P.; Chouksey, S.; Banerjee, D.; Ganguly, S.; Saha, D.
2015-11-01
We have demonstrated a type-II band-aligned heterostructure between pulsed laser deposited topological insulator bismuth telluride and metal organic-chemical-vapour deposited GaN on a sapphire substrate. The heterostructure shows a large valence band-offset of 3.27 eV as determined from x-ray photoelectron spectroscopy, which is close to the bandgap of GaN (3.4 eV). Further investigation using x-ray diffraction, Raman spectroscopy, and energy-dispersive x-ray spectrum reveals the stoichiometric and material properties of bismuth telluride on GaN. Steady state photon emission from GaN is found to be modulated by the charge transfer process due to diffusion across the junction. The time constant involved with the charge transfer process is found to be 0.6 ns by transient absorption spectroscopy. The heterostructure can be used for designing devices with different functionalities and improving the performance of the existing devices on GaN.
Andrews, David L
2015-01-01
Discusses the basic physical principles underlying thescience and technology of nanophotonics, its materials andstructures This volume presents nanophotonic structures and Materials.Nanophotonics is photonic science and technology that utilizeslight/matter interactions on the nanoscale where researchers arediscovering new phenomena and developing techniques that go wellbeyond what is possible with conventional photonics andelectronics.The topics discussed in this volume are: CavityPhotonics; Cold Atoms and Bose-Einstein Condensates; Displays;E-paper; Graphene; Integrated Photonics; Liquid Cry
Andrews, David L
2015-01-01
Discusses the basic physical principles underlying Biomedical Photonics, spectroscopy and microscopy This volume discusses biomedical photonics, spectroscopy and microscopy, the basic physical principles underlying the technology and its applications. The topics discussed in this volume are: Biophotonics; Fluorescence and Phosphorescence; Medical Photonics; Microscopy; Nonlinear Optics; Ophthalmic Technology; Optical Tomography; Optofluidics; Photodynamic Therapy; Image Processing; Imaging Systems; Sensors; Single Molecule Detection; Futurology in Photonics. Comprehensive and accessible cov
Andrews, David L
2015-01-01
This book covers modern photonics accessibly and discusses the basic physical principles underlying all the applications and technology of photonicsThis volume covers the basic physical principles underlying the technology and all applications of photonics from statistical optics to quantum optics. The topics discussed in this volume are: Photons in perspective; Coherence and Statistical Optics; Complex Light and Singular Optics; Electrodynamics of Dielectric Media; Fast and slow Light; Holography; Multiphoton Processes; Optical Angular Momentum; Optical Forces, Trapping and Manipulation; Pol
Andrews, David L
2015-01-01
Discusses the basic physical principles underlying the technology instrumentation of photonics This volume discusses photonics technology and instrumentation. The topics discussed in this volume are: Communication Networks; Data Buffers; Defense and Security Applications; Detectors; Fiber Optics and Amplifiers; Green Photonics; Instrumentation and Metrology; Interferometers; Light-Harvesting Materials; Logic Devices; Optical Communications; Remote Sensing; Solar Energy; Solid-State Lighting; Wavelength Conversion Comprehensive and accessible coverage of the whole of modern photonics Emphas
DEFF Research Database (Denmark)
Stolpe, Mathias
2007-01-01
linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...
Topological insulators and topological superconductors
Bernevig, Andrei B
2013-01-01
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topolo...
A dimensionality reduction technique for 2D scattering problems in photonics
Ivanova, Alyona; Stoffer, Remco; Hammer, Manfred
2010-01-01
This paper describes a simulation method for 2D frequency domain scattering problems in photonics. The technique reduces the spatial dimensionality of the problem by means of global, continuous mode expansion combined with a variational formalism; the resulting equations are solved using a finite
Ivanova, Alyona; Stoffer, Remco; Kauppinen, L.J.; Hammer, Manfred
2009-01-01
In order to reduce the computational effort we develop a method for 3D-to-2D dimensionality reduction of scattering problems in photonics. Contrary to the `standard' Effective Index Method the effective parameters of the reduced problem are always rigorously defined using the variational technique,
DEFF Research Database (Denmark)
Stolpe, Mathias
2004-01-01
We consider equivalent reformulations of nonlinear mixed 0-1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. It is shown that the considered problems may equivalently be cast as either...... linear or as convex quadratic mixed 0-1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...... of structures subjected to either static or periodic loads, design of composite materials with prescribed homogenized properties using the inverse homogenization approach, optimization of fluids in Stokes flow, design of band gap structures, and multi-physics problems involving coupled steady-state heat...
Analytical Approaches to Improve Accuracy in Solving the Protein Topology Problem.
Al Nasr, Kamal; Yousef, Feras; Jebril, Ruba; Jones, Christopher
2018-01-23
To take advantage of recent advances in genomics and proteomics it is critical that the three-dimensional physical structure of biological macromolecules be determined. Cryo-Electron Microscopy (cryo-EM) is a promising and improving method for obtaining this data, however resolution is often not sufficient to directly determine the atomic scale structure. Despite this, information for secondary structure locations is detectable. De novo modeling is a computational approach to modeling these macromolecular structures based on cryo-EM derived data. During de novo modeling a mapping between detected secondary structures and the underlying amino acid sequence must be identified. DP-TOSS ( D ynamic P rogramming for determining the T opology O f S econdary S tructures) is one tool that attempts to automate the creation of this mapping. By treating the correspondence between the detected structures and the structures predicted from sequence data as a constraint graph problem DP-TOSS achieved good accuracy in its original iteration. In this paper, we propose modifications to the scoring methodology of DP-TOSS to improve its accuracy. Three scoring schemes were applied to DP-TOSS and tested: (i) a skeleton-based scoring function; (ii) a geometry-based analytical function; and (iii) a multi-well potential energy-based function. A test of 25 proteins shows that a combination of these schemes can improve the performance of DP-TOSS to solve the topology determination problem for macromolecule proteins.
Student reactions to problem-based learning in photonics technician education
Massa, Nicholas M.; Donnelly, Judith; Hanes, Fenna
2014-07-01
Problem-based learning (PBL) is an instructional approach in which students learn problem-solving and teamwork skills by collaboratively solving complex real-world problems. Research shows that PBL improves student knowledge and retention, motivation, problem-solving skills, and the ability to skillfully apply knowledge in new and novel situations. One of the challenges faced by students accustomed to traditional didactic methods, however, is acclimating to the PBL process in which problem parameters are often ill-defined and ambiguous, often leading to frustration and disengagement with the learning process. To address this problem, the New England Board of Higher Education (NEBHE), funded by the National Science Foundation Advanced Technological Education (NSF-ATE) program, has created and field tested a comprehensive series of industry-based multimedia PBL "Challenges" designed to scaffold the development of students' problem solving and critical thinking skills. In this paper, we present the results of a pilot study conducted to examine student reactions to the PBL Challenges in photonics technician education. During the fall 2012 semester, students (n=12) in two associate degree level photonics courses engaged in PBL using the PBL Challenges. Qualitative and quantitative methods were used to assess student motivation, self-efficacy, critical thinking, metacognitive self-regulation, and peer learning using selected scales from the Motivated Strategies for Learning Questionnaire (MSLQ). Results showed positive gains in all variables. Follow-up focus group interviews yielded positive themes supporting the effectiveness of PBL in developing the knowledge, skills and attitudes of photonics technicians.
Creating and using industry-based problem-based learning challenges in photonics: lessons learned
Donnelly, Judith; Dischino, Michele; Hanes, Fenna; Massa, Nicholas
2009-06-01
Problem-based learning (PBL) is an educational approach whereby students learn course content by actively and collaboratively solving real-world problems presented in a context similar to that in which the learning is to be applied. Project PHOTON PBL, in collaboration with photonics industry and research university partners, created eight interdisciplinary multi-media Challenges to be used in high school and community college math, science and technology courses. Each Challenge was recorded on location and features the scientists, engineers and technicians who originally solved the problem engaged in authentic problem solving. In this paper we describe the evolution of the development of the Challenges and we provide instructions on creating a Challenge and using it in the classroom to enhance student learning.
A dimensionality reduction technique for 2D scattering problems in photonics
Alyona Ivanova, O. V.; Stoffer, Remco; Hammer, Manfred
2010-03-01
This paper describes a simulation method for 2D frequency domain scattering problems in photonics. The technique reduces the spatial dimensionality of the problem by means of global, continuous mode expansion combined with a variational formalism; the resulting equations are solved using a finite element method. Transparent influx boundary conditions and perfectly matched layers are employed at the computational window boundaries. Numerical examples validate the method.
Poulin, Vivian; Serpico, Pasquale Dario
2015-03-06
The standard theory of electromagnetic cascades onto a photon background predicts a quasiuniversal shape for the resulting nonthermal photon spectrum. This has been applied to very disparate fields, including nonthermal big bang nucleosynthesis (BBN). However, once the energy of the injected photons falls below the pair-production threshold the spectral shape is much harder, a fact that has been overlooked in past literature. This loophole may have important phenomenological consequences, since it generically alters the BBN bounds on nonthermal relics; for instance, it allows us to reopen the possibility of purely electromagnetic solutions to the so-called "cosmological lithium problem," which were thought to be excluded by other cosmological constraints. We show this with a proof-of-principle example and a simple particle physics model, compared with previous literature.
Problem-based learning in photonics technology education: assessing student learning
Massa, Nicholas; Dischino, Michele; Donnelly, Judith; Hanes, Fenna
2009-06-01
Problem-based learning (PBL) is an instructional approach whereby students learn course content by collaboratively solving complex real-world problems and reflecting on their experience. Research shows that PBL improves student knowledge and retention, motivation, problem-solving skills, and the ability to skillfully apply knowledge in new situations. One of the challenges with PBL, however, is that real-world problems are typically open-ended with more than one possible solution, which poses a challenge to educators with regard to assessing student performance. In this paper, we describe an approach to assessing student performance in PBL developed by the Photon PBL Project, a three-year National Science Foundation Advanced Technological Education (NSF-ATE) project in which eight interdisciplinary multimedia PBL "Challenges" were created in collaboration with photonics industry and university partners for use in high school and college math, science and technology courses. Assessment included measures of content knowledge, conceptual knowledge, problem-solving skills, motivation, self-efficacy, and metacognitive ability. Results from pilot testing at four community college photonics technology programs are presented.
Statistical method for resolving the photon-photoelectron-counting inversion problem
International Nuclear Information System (INIS)
Wu Jinlong; Li Tiejun; Peng, Xiang; Guo Hong
2011-01-01
A statistical inversion method is proposed for the photon-photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.
The shortest path problem in the stochastic networks with unstable topology.
Shirdel, Gholam H; Abdolhosseinzadeh, Mohsen
2016-01-01
The stochastic shortest path length is defined as the arrival probability from a given source node to a given destination node in the stochastic networks. We consider the topological changes and their effects on the arrival probability in directed acyclic networks. There is a stable topology which shows the physical connections of nodes; however, the communication between nodes does not stable and that is defined as the unstable topology where arcs may be congested. A discrete time Markov chain with an absorbing state is established in the network according to the unstable topological changes. Then, the arrival probability to the destination node from the source node in the network is computed as the multi-step transition probability of the absorption in the final state of the established Markov chain. It is assumed to have some wait states, whenever there is a physical connection but it is not possible to communicate between nodes immediately. The proposed method is illustrated by different numerical examples, and the results can be used to anticipate the probable congestion along some critical arcs in the delay sensitive networks.
DEFF Research Database (Denmark)
Zhou, Mingdong; Alexandersen, Joe; Sigmund, Ole
2016-01-01
-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...
Systematic design of microstructures by topology optimization
DEFF Research Database (Denmark)
Sigmund, Ole
2003-01-01
The topology optimization method can be used to determine the material distribution in a design domain such that an objective function is maximized and constraints are fulfilled. The method which is based on Finite Element Analysis may be applied to all kinds of material distribution problems like...... extremal material design, sensor and actuator design and MEMS synthesis. The state-of-the-art in topology optimization will be reviewed and older as well as new applications in phononic and photonic crystals design will be presented....
DEFF Research Database (Denmark)
Bendsøe, Martin P.; Sigmund, Ole
2007-01-01
Taking as a starting point a design case for a compliant mechanism (a force inverter), the fundamental elements of topology optimization are described. The basis for the developments is a FEM format for this design problem and emphasis is given to the parameterization of design as a raster image...
International Nuclear Information System (INIS)
Burke, D.L.
1982-10-01
Studies of photon-photon collisions are reviewed with particular emphasis on new results reported to this conference. These include results on light meson spectroscopy and deep inelastic e#betta# scattering. Considerable work has now been accumulated on resonance production by #betta##betta# collisions. Preliminary high statistics studies of the photon structure function F 2 /sup #betta#/(x,Q 2 ) are given and comments are made on the problems that remain to be solved
Choong, Zhengyang
2017-08-01
Student research projects are increasingly common at the K-12 level. However, students often face difficulties in the course of their school research projects such as setting realistic timelines and expectations, handling problems stemming from a lack of self-confidence, as well as being sufficiently disciplined for sustained communication and experimentation. In this work, we explore manifestations of these problems in the context of a photonics project, characterising the spectrum of the breakdown flash from Silicon Avalanche Photodiodes. We report on the process of planning and building the setup, data collection, analysis and troubleshooting, as well as the technical and human problems at each step. Approaches that were found to be helpful in managing the aforementioned problems are discussed, including an attention to detail during experimental work, as well as communicating in a forthcoming manner. e former allowed for clearer planning and the setting of quantifiable proximal goals; the latter helped in motivating discipline, and also helped in the understanding of research as an iterative learning process without a clear definition of success or failure.
Stress-constrained truss topology optimization problems that can be solved by linear programming
DEFF Research Database (Denmark)
Stolpe, Mathias; Svanberg, Krister
2004-01-01
We consider the problem of simultaneously selecting the material and determining the area of each bar in a truss structure in such a way that the cost of the structure is minimized subject to stress constraints under a single load condition. We show that such problems can be solved by linear...... programming to give the global optimum, and that two different materials are always sufficient in an optimal structure....
Global optimization of truss topology with discrete bar areas—Part I: Theory of relaxed problems
DEFF Research Database (Denmark)
Achtziger, Wolfgang; Stolpe, Mathias
2008-01-01
. The main issue of the paper and of the approach lies in the fact that the relaxed nonlinear optimization problem can be formulated as a quadratic program (QP). Here the paper generalizes and extends the available theory from the literature. Although the Hessian of this QP is indefinite, it is possible...... to circumvent the non-convexity and to calculate global optimizers. Moreover, the QPs to be treated in the branch-and-bound search tree differ from each other just in the objective function. In Part I we give an introduction to the problem and collect all theory and related proofs for the treatment...
Newton-type method for the variational discretization of topology optimization problems
DEFF Research Database (Denmark)
Evgrafov, Anton
2013-01-01
, which we achieve by inverting a part of perturbed optimality conditions for the problem. In this way, the computational bottleneck is conveniently shifted from evaluating the merit function to a direction finding subproblem. The latter involves solving certain linearized PDEs, and the computational...
Action minimizers under topological constraints in the planar equal-mass four-body problem
Yan, Duokui
2018-04-01
It is shown that in the planar equal-mass four-body problem, there exist two sets of action minimizers connecting two planar boundary configurations with fixed symmetry axes and specific order constraints: a double isosceles configuration and an isosceles trapezoid configuration, while order constraints are introduced on the boundary configurations. By applying the level estimate method, these minimizers are shown to be collision-free and they can be extended to two new sets of periodic or quasi-periodic orbits.
Topology optimised wavelength dependent splitters
DEFF Research Database (Denmark)
Hede, K. K.; Burgos Leon, J.; Frandsen, Lars Hagedorn
A photonic crystal wavelength dependent splitter has been constructed by utilising topology optimisation1. The splitter has been fabricated in a silicon-on-insulator material (Fig. 1). The topology optimised wavelength dependent splitter demonstrates promising 3D FDTD simulation results....... This complex photonic crystal structure is very sensitive against small fabrication variations from the expected topology optimised design. A wavelength dependent splitter is an important basic building block for high-performance nanophotonic circuits. 1J. S. Jensen and O. Sigmund, App. Phys. Lett. 84, 2022...
Neutron radiography imaging with 2-dimensional photon counting method and its problems
International Nuclear Information System (INIS)
Ikeda, Y.; Kobayashi, H.; Niwa, T.; Kataoka, T.
1988-01-01
A ultra sensitive neutron imaging system has been deviced with a 2-dimensional photon counting camara (ARGUS 100). The imaging system is composed by a 2-dimensional single photon counting tube and a low background vidicon followed with an image processing unit and frame memories. By using the imaging system, electronic neutron radiography (NTV) has been possible under the neutron flux less than 3 x 10 4 n/cm 2 ·s. (author)
A topological quantum optics interface.
Barik, Sabyasachi; Karasahin, Aziz; Flower, Christopher; Cai, Tao; Miyake, Hirokazu; DeGottardi, Wade; Hafezi, Mohammad; Waks, Edo
2018-02-09
The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored. We demonstrate a strong interface between single quantum emitters and topological photonic states. Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals. We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends. This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
DEFF Research Database (Denmark)
This paper is concerned with topology optimization of a coupled optical and mechanical wave propagation problem in photonic crystals. It is motivated by the potential gain in functionality of optical devices where mechanical Rayleigh waves (travelling in the surface of the material) play a leading...
Maximizing the Optical Band Gap in 2D Photonic Crystals
DEFF Research Database (Denmark)
Hougaard, Kristian G.; Sigmund, Ole
Topology optimization is used to find the 2D photonic crystal designs with the largest relative photonic band gaps. Starting points for the topology optimization are found with an exhaustive binary search on a low resolution grid.......Topology optimization is used to find the 2D photonic crystal designs with the largest relative photonic band gaps. Starting points for the topology optimization are found with an exhaustive binary search on a low resolution grid....
Why do I need to know this? Optics/photonics problem-based learning in the math classroom
Donnelly, Matthew J.; Donnelly, Judith F.; Donnelly, Stephanie
2017-08-01
A common complaint of engineering managers is that new employees at all levels, technician through engineer, tend to have rote calculation ability but are unable to think critically and use structured problem solving techniques to apply mathematical concepts. Further, they often have poor written and oral communication skills and difficulty working in teams. Ironically, a common question of high school mathematics students is "Why do I need to know this?" In this paper we describe a project using optics/photonics and Problem Based Learning (PBL) to address these issues in a high school calculus classroom.
Wilansky, Albert
2008-01-01
Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.
Topological Phases of Sound and Light
Directory of Open Access Journals (Sweden)
V. Peano
2015-07-01
Full Text Available Topological states of matter are particularly robust, since they exploit global features of a material’s band structure. Topological states have already been observed for electrons, atoms, and photons. It is an outstanding challenge to create a Chern insulator of sound waves in the solid state. In this work, we propose an implementation based on cavity optomechanics in a photonic crystal. The topological properties of the sound waves can be wholly tuned in situ by adjusting the amplitude and frequency of a driving laser that controls the optomechanical interaction between light and sound. The resulting chiral, topologically protected phonon transport can be probed completely optically. Moreover, we identify a regime of strong mixing between photon and phonon excitations, which gives rise to a large set of different topological phases and offers an example of a Chern insulator produced from the interaction between two physically distinct particle species, photons and phonons.
Frank-Kamenetskiĭ, M. D.; Vologodskiĭ, A. V.
1981-08-01
The formation of polymer ring structures leads to new physical effects that arise from topological restrictions. These restrictions consist of the fact that the topological state of a ring polymer molecule cannot vary. Interest in this type of object has increased sharply since the proof that in most cases the molecules of DNA function in the cell in a closed circular form. This review presents the necessary information on the physical properties of circular DNAs. The mathematical basis of the theory of knots and linkages are briefly presented, together with the theory of ribbons. This apparatus is employed to obtain quantitative data on the behavior of closed polymer chains by Monte Carlo calculations on a computer. The results of the calculations are compared with the experimental data for circular DNAs. This comparison has made it possible to obtain valuable information on the properties of the double helix, such as its torsional rigidity. The biological role of the topological restrictions in DNA is discussed, as well as the significance of the recently discovered enzymes, topoisomerases, which alter the topological state of circular DNAs.
Tunable Topological Phononic Crystals
Chen, Zeguo
2016-05-27
Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.
International Nuclear Information System (INIS)
Gapp, C.
1990-03-01
The pointlike γ-parton interactions in γ-proton reactions are evaluated in terms of energy-flows. Only charged particles in the forward hemisphere of the overall CM-system (i.e. χ F >> 0) are used. The pointlike processes should exhibit '2-jetlike' structures. To disentangle the pointlike component from hadronlike photon interactions hadron and photon induced interactions have been studied. The experiment was carried out by the WA69 collaboration using the facilities of the CERN-Ω spectrometer. Both datasets were recorded with identical detector setups in order to minimize systematic effects. A tagged photon beam with energies between 65 and 175 GeV and mixed hadron beams (π + /K + , π - /K - ) at fixed energies of 80 and 140 GeV were used. For high transverse momenta the pointlike interactions are calculable in QCD at lowest order (α.α s ). Since energy-flows depend on all final state particles a collective measure for the hardness of an event has been introduced (Σip 2 perpendicular to in eventplane ). Only the energy-flows from photoproduction give evidence for the presence of 2-jetlike processes. The hadron induced distributions are scaled in order to emulate the behaviour of a hadronlike photon. The difference between the photon and scaled hadroninduced distributions is compared to a Monte Carlo calculation of the pointlike processes. (orig.) [de
Sacramento, P. D.; Vieira, V. R.
2018-04-01
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.
Topological properties of instantons
International Nuclear Information System (INIS)
Mello, E.R.B. de.
1978-07-01
The pure Yang-Mills theory defined in R 4 space is considered and some relevant properties of gauge field like Instanton are shown. The vacuum structure of the theory is discussed, as well as the problem of topological numbers associated with the Instantons and anti-Instantons solutions. A procedure is presented showing how we can alter this topological number by of any variation in the field parameters. (Author) [pt
Directory of Open Access Journals (Sweden)
Emre Biyikli
Full Text Available A new topology optimization method called the Proportional Topology Optimization (PTO is presented. As a non-sensitivity method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing optimality criteria method which computes sensitivities. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.
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.
International Nuclear Information System (INIS)
Attalla, E.M.; Lotayef, M.M.; Khalil, E.M.; El-Hosiny, H.A.
2007-01-01
The purpose of this study was to quantify dose distribution errors by comparing actual dose measurements with the calculated values done by the software. To evaluate the outcome of radiation overexposure related to Panama's accident and in response to ensure that the treatment planning systems (T.P.S.) are being operated in accordance with the appropriate quality assurance programme, we studied the central axis and pripheral depth dose data using complex field shaped with blocks to quantify dose distribution errors. Material and Methods: Multi data T.P.S. software versions 2.35 and 2.40 and Helax T.P.S. software version 5.1 B were assesed. The calculated data of the software treatment planning systems were verified by comparing these data with the actual dose measurements for open and blocked high energy photon fields (Co-60, 6MV and 18MV photons). Results: Close calculated and measured results were obtained for the 2-D (Multi data) and 3-D treatment planning (TMS Helax). These results were correct within 1 to 2% for open fields and 0.5 to 2.5% for peripheral blocked fields. Discrepancies between calculated and measured data ranged between 13. to 36% along the central axis of complex blocked fields when normalisation point was selected at the Dmax, when the normalisation point was selected near or under the blocks, the variation between the calculated and the measured data was up to 500% difference. Conclusions: The present results emphasize the importance of the proper selection of the normalization point in the radiation field, as this facilitates detection of aberrant dose distribution (over exposure or under exposure)
Attalla, Ehab M; Lotayef, Mohamed M; Khalil, Ehab M; El-Hosiny, Hesham A; Nazmy, Mohamed S
2007-06-01
The purpose of this study was to quantify dose distribution errors by comparing actual dose measurements with the calculated values done by the software. To evaluate the outcome of radiation overexposure related to Panama's accident and in response to ensure that the treatment planning systems (T.P.S.) are being operated in accordance with the appropriate quality assurance programme, we studied the central axis and pripheral depth dose data using complex field shaped with blocks to quantify dose distribution errors. Multidata T.P.S. software versions 2.35 and 2.40 and Helax T.P.S. software version 5.1 B were assesed. The calculated data of the software treatment planning systems were verified by comparing these data with the actual dose measurements for open and blocked high energy photon fields (Co-60, 6MV & 18MV photons). Close calculated and measured results were obtained for the 2-D (Multidata) and 3-D treatment planning (TMS Helax). These results were correct within 1 to 2% for open fields and 0.5 to 2.5% for peripheral blocked fields. Discrepancies between calculated and measured data ranged between 13. to 36% along the central axis of complex blocked fields when normalisation point was selected at the Dmax, when the normalisation point was selected near or under the blocks, the variation between the calculated and the measured data was up to 500% difference. The present results emphasize the importance of the proper selection of the normalization point in the radiation field, as this facilitates detection of aberrant dose distribution (over exposure or under exposure).
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
Charges and Electromagnetic Radiation as Topological Excitations
Directory of Open Access Journals (Sweden)
Manfried Faber
2017-01-01
Full Text Available We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.
On topological spaces whose topology is induced by a binary relation
African Journals Online (AJOL)
We study the problem of characterizing which topologies on a nonemptybset are generated by a binary relation by means of its lower and upper contour sets. In this direction we consider different classical categories of topological spaces whose topology is defined by at least one binary relation. Given a topology defined by ...
Indian Academy of Sciences (India)
Topology is usually taught in India in the second year of a master's degree programme. Much of the time is spent on developing such basic notions as connectedness, compactness, product topology, and the course ends with. Tychonov's theorem or Urysohn's lemma. At best, the student learns a bit about the fundamental ...
Nonreciprocal lasing in topological cavities of arbitrary geometries
Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe; El Amili, Abdelkrim; Fainman, Yeshaiahu; Kanté, Boubacar
2017-11-01
Resonant cavities are essential building blocks governing many wave-based phenomena, but their geometry and reciprocity fundamentally limit the integration of optical devices. We report, at telecommunication wavelengths, geometry-independent and integrated nonreciprocal topological cavities that couple stimulated emission from one-way photonic edge states to a selected waveguide output with an isolation ratio in excess of 10 decibels. Nonreciprocity originates from unidirectional edge states at the boundary between photonic structures with distinct topological invariants. Our experimental demonstration of lasing from topological cavities provides the opportunity to develop complex topological circuitry of arbitrary geometries for the integrated and robust generation and transport of photons in classical and quantum regimes.
International Nuclear Information System (INIS)
Burkhart, A.; Charlot, J.M.; Roumeguere, M.
1982-10-01
After recalling the effects of irradiation on semi-conductors, some problems appearing in the use of such components in a radiatif context are presented. Reliability of components under irradiation is treated in the sense of unexpected or not easily predictable behaviour. It is important that a rigorous control of components, having to work under irradiation, be realised [fr
Filters in topology optimization
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...
Buchstaber, Victor M
2015-01-01
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v
Franz, Marcel
2013-01-01
Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was
International Nuclear Information System (INIS)
Gal'berg, V.P.
1981-01-01
Some optimization problems occurring in developing the automatic control system (ASC) of a commercial amalgamation (ACS-ATOM), assessments of economically optimal structure of location of computation centres and means of data transmission in particular are considered [ru
Topological arguments for Kolmogorov complexity
Directory of Open Access Journals (Sweden)
Alexander Shen
2012-08-01
Full Text Available We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.
Directory of Open Access Journals (Sweden)
Serkan Karatas
2016-12-01
Full Text Available In this paper, we redefine the neutrosophic set operations and, by using them, we introduce neutrosophic topology and investigate some related properties such as neutrosophic closure, neutrosophic closure, neutrosophic interior, neutrosophic exterior, neutrosophic boundary and neutrosophic subspace.
Slope constrained Topology Optimization
DEFF Research Database (Denmark)
Petersson, J.; Sigmund, Ole
1998-01-01
The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density-energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing...
Steen, Lynn Arthur
1978-01-01
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.
Directory of Open Access Journals (Sweden)
Muhammad Iqbal
2017-01-01
Full Text Available We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative. The proposed problem is as follows: D cαxt-ft,xt=gt,yt,Iαyt, t∈J=[0,1],D cαyt-ft,yt=gt,xt,Iαxt, t∈J=0,1, D cpx0=ψxη1, x′0=0,…,xn-20=0, D cpx1=ψxη2, D cpy0=ψyη1, y′0=0,…,yn-20=0, D cpy1=ψyη2, where p,η1,η2∈0,1, ψ is linear, D cα is Caputo fractional derivative of order α, with n-1<α≤n, n∈N, and Iα is fractional integral of order α. The nonlinear functions f, g are continuous. For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory. Finally, we illustrated the main results by a concrete example.
Topology Discovery Using Cisco Discovery Protocol
Rodriguez, Sergio R.
2009-01-01
In this paper we address the problem of discovering network topology in proprietary networks. Namely, we investigate topology discovery in Cisco-based networks. Cisco devices run Cisco Discovery Protocol (CDP) which holds information about these devices. We first compare properties of topologies that can be obtained from networks deploying CDP versus Spanning Tree Protocol (STP) and Management Information Base (MIB) Forwarding Database (FDB). Then we describe a method of discovering topology ...
Riemann, topology, and physics
Monastyrsky, Michael I
2008-01-01
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...
Topological Fidelity in Sensor Networks
Chintakunta, Harish; Krim, Hamid
2011-01-01
Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection ...
Topology optimization for coated structures
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik; Sigmund, Ole
2015-01-01
This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....
Topological Rankings in Communication Networks
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard; Træholt, Chresten
2015-01-01
In the theory of communication the central problem is to study how agents exchange information. This problem may be studied using the theory of connected spaces in topology, since a communication network can be modelled as a topological space such that agents can communicate if and only...... if they belong to the same path connected component of that space. In order to study combinatorial properties of such a communication network, notions from algebraic topology are applied. This makes it possible to determine the shape of a network by concrete invariants, e.g. the number of connected components...
Milewski, Emil G
2013-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, co
Arnold, Vladimir; Zorich, Anton
1999-01-01
This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors … have done much to s
Warner, S
1993-01-01
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn''s Lemma, is also expected.
Algebraic topology of finite topological spaces and applications
Barmak, Jonathan A
2011-01-01
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen’s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon
2006-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Indian Academy of Sciences (India)
TOPOLOGY. Allen Hatcher. October 2004 Volume 9 Number 10. GENERAL ARTICLES. 10 Taylor the Sailor. V Radhakrishnan. 19 Twisted Winged Endoparasitoids. An Enigma for Entomologists. Alpana Mazumdar. 25 Xanthan - A Versatile Gum. Anil Lachke. 34 From Natural Numbers to Numbers and. Curves in Nature - II.
Frank-Kamenetskii, Maxim D.
2013-01-01
A new variety on non-coding RNA has been discovered by several groups: circular RNA (circRNA). This discovery raises intriguing questions about the possibility of the existence of knotted RNA molecules and the existence of a new class of enzymes changing RNA topology, RNA topoisomerases.
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
Concept Model on Topological Learning
Ae, Tadashi; Kioi, Kazumasa
2010-11-01
We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.
Fomenko, Anatoly
2016-01-01
This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role ...
Bistable Topological Insulator with Exciton-Polaritons
Kartashov, Yaroslav V.; Skryabin, Dmitry V.
2017-12-01
The functionality of many nonlinear and quantum optical devices relies on the effect of optical bistability. Using microcavity exciton-polaritons in a honeycomb arrangement of microcavity pillars, we report the resonance response and bistability of topological edge states. A balance between the pump, loss, and nonlinearity ensures a broad range of dynamical stability and controls the distribution of power between counterpropagating states on the opposite edges of the honeycomb lattice stripe. Tuning energy and polarization of the pump photons, while keeping their momentum constant, we demonstrate control of the propagation direction of the dominant edge state. Our results facilitate the development of practical applications of topological photonics.
DEFF Research Database (Denmark)
Schwerdtfeger, Peter; Wirz, Lukas; Avery, James Emil
2014-01-01
Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar g....... In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems....
The Teaching of Mathematics: Universal Topological Spaces.
Magill, K. D., Jr.
1988-01-01
The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)
International Nuclear Information System (INIS)
Haissinski, J.
1986-06-01
The discussions presented in this paper deal with the following points: distinctive features of gamma-gamma collisions; related processes; photon-photon elastic scattering in the continuum and γγ →gg; total cross section; γγ → V 1 V 2 (V=vector meson); radiative width measurements and light meson spectroscopy; exclusive channels at large /t/; jets and inclusive particle distribution in γγ collisions; and, the photon structure function F γ 2
Energy Technology Data Exchange (ETDEWEB)
Sessler, A.M.
1995-04-01
Since the seminal work by Ginsburg, et at., the subject of giving the Next Linear Collider photon-photon capability, as well as electron-positron capability, has drawn much attention. A 1990 article by V.I. Teinov describes the situation at that time. In March 1994, the first workshop on this subject was held. This report briefly reviews the physics that can be achieved through the photon-photon channel and then focuses on the means of achieving such a collider. Also reviewed is the spectrum of backscattered Compton photons -- the best way of obtaining photons. We emphasize the spectrum actually obtained in a collider with both polarized electrons and photons (peaked at high energy and very different from a Compton spectrum). Luminosity is estimated for the presently considered colliders, and interaction and conversion-point geometries are described. Also specified are laser requirements (such as wavelength, peak power, and average power) and the lasers that might be employed. These include conventional and free-electron lasers. Finally, we describe the R&D necessary to make either of these approaches viable and explore the use of the SLC as a test bed for a photon-photon collider of very high energy.
Guillemin, Victor
2010-01-01
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main
Photonic crystal fibres and effective index approaches
DEFF Research Database (Denmark)
Riishede, Jesper; Libori, Stig E. Barkou; Bjarklev, Anders Overgaard
2001-01-01
Photonic crystal fibres are investigated with an effective index approach. The effective index of both core and cladding is found to be wavelength dependent. Accurate modelling must respect the rich topology of these fibres.......Photonic crystal fibres are investigated with an effective index approach. The effective index of both core and cladding is found to be wavelength dependent. Accurate modelling must respect the rich topology of these fibres....
Quantum field theory in topology changing spacetimes
International Nuclear Information System (INIS)
Bauer, W.
2007-03-01
The goal of this diploma thesis is to present an overview of how to reduce the problem of topology change of general spacetimes to the investigation of elementary cobordisms. In the following we investigate the possibility to construct quantum fields on elementary cobordisms, in particular we discuss the trousers topology. Trying to avoid the problems occuring at spacetimes with instant topology change we use a model for simulating topology change. We construct the algebra of observables for a free scalar field with the algebraic approach to quantum field theory. Therefore we determine a fundamental solution of the eld equation. (orig.)
Independent Study Project, Topic: Topology.
Notre Dame High School, Easton, PA.
Using this guide and the four popular books noted in it, a student, working independently, will learn about some of the classical ideas and problems of topology: the Meobius strip and Klein bottle, the four color problem, genus of a surface, networks, Euler's formula, and the Jordan Curve Theorem. The unit culminates in a project of the students'…
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J.
1988-07-01
Highlights of the VIIIth International Workshop on Photon-Photon Collisions are reviewed. New experimental and theoretical results were reported in virtually every area of ..gamma gamma.. physics, particularly in exotic resonance production and tests of quantum chromodynamics where asymptotic freedom and factorization theorems provide predictions for both inclusive and exclusive ..gamma gamma.. reactions at high momentum transfer. 73 refs., 12 figs.
Computational differential topology
Directory of Open Access Journals (Sweden)
Denis Blackmore
2007-04-01
Full Text Available Some of the more differential aspects of the nascent field of computational topology are introduced and treated in considerable depth. Relevant categories based upon stratified geometric objects are proposed, and fundamental problems are identified and discussed in the context of both differential topology and computer science. New results on the triangulation of objects in the computational differential categories are proven, and evaluated from the perspective of effective computability (algorithmic solvability. In addition, the elements of innovative, effectively computable approaches for analyzing and obtaining computer generated representations of geometric objects based upon singularity/stratification theory and obstruction theory are formulated. New methods for characterizing complicated intersection sets are proven using differential analysis and homology theory. Also included are brief descriptions of several implementation aspects of some of the approaches described, as well as applications of the results in such areas as virtual sculpting, virtual surgery, modeling of heterogeneous biomaterials, and high speed visualizations.
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.
Margalef-Roig, J
1992-01-01
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Improving Topology Optimization using Games
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten; Christiansen, Asger Nyman; Bærentzen, J. Andreas
structures. Consequently, we have created a game, the TopOptGame, which improves the player's topology optimization intuition in a fun and engaging way while collecting data about the users performance. Technically, the TopOptGame builds on the TopOptApp [1] - an interactive topology optimization application...... designed for hand-held devices. The TopOptApp solves the 2D minimum compliance problem with interactive control of loads, supports and volume fraction, and thus the TopOptApp allows the user to change the problem on the y and watch the design evolve to a new optimum in real time. TopOptApp is available...
Optimal Topology Design of Discrete Structures Resisting Degradation Effects
DEFF Research Database (Denmark)
Achtziger, W.; Bendsøe, Martin P.
1999-01-01
In this technical note we treat the problem of finding the optimal topology of a truss, so that stiffness after degradation is maximized. It is shown that for the problem setting at hand, the optimal topology has uniform relative degradation in all bars and the topology is unchanged from the topo...... the topology for a truss not undergoing degradation. As is well-known such a design can be realized as a fully stressed, statically determinate truss....
Emerging Trends in Topological Insulators and Topological ...
Indian Academy of Sciences (India)
Moreover, proximity induced superconductivity in these systemscan lead to a state that supports zero energy Majoranafermions, and the phase is known as topological superconductors.In this article, the basic idea of topological insulatorsand topological superconductors are presented alongwith their experimental ...
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
Quantum dots in photonic crystals for integrated quantum photonics
Kim, Je-Hyung; Richardson, Christopher J. K.; Leavitt, Richard P.; Waks, Edo
2017-08-01
Integrated quantum photonic technologies hold a great promise for application in quantum information processing. A major challenge is to integrate multiple single photon sources on a chip. Quantum dots are bright sources of high purity single photons, and photonic crystals can provide efficient photonic platforms for generating and manipulating single photons from integrated quantum dots. However, integrating multiple quantum dots with photonic crystal devices still remains as a challenging task due to the spectral randomness of the emitters. Here, we present the integration of multiple quantum dots with individual photonic crystal cavities and report quantum interference from chip-integrated multiple quantum dots. To solve the problem of spectral randomness, we introduce local engineering techniques for tuning multiple quantum dots and cavities. From integrated quantum dot devices we observe indistinguishable nature of single photons from individual quantum dots on the same chip. Therefore, our approach paves the way for large-scale quantum photonics with integrated quantum emitters.
4D topological mass by gauging spin
Choudhury, I. D.; Diamantini, M. Cristina; Guarnaccia, Giuseppe; Lahiri, A.; Trugenberger, Carlo A.
2015-06-01
We propose a spin gauge field theory in which the curl of a Dirac fermion current density plays the role of the pseudovector charge density. In this field-theoretic model, spin interactions are mediated by a single scalar gauge boson in its antisymmetric tensor formulation. We show that these long range spin interactions induce a gauge invariant photon mass in the one-loop effective action. The fermion loop generates a coupling between photons and the spin gauge boson, which acquires thus charge. This coupling represents also an induced, gauge invariant, topological mass for the photons, leading to the Meissner effect. The one-loop effective equations of motion for the charged spin gauge boson are the London equations. We propose thus spin gauge interactions as an alternative, topological mechanism for superconductivity in which no spontaneous symmetry breaking is involved.
4D topological mass by gauging spin
Energy Technology Data Exchange (ETDEWEB)
Choudhury, I.D. [S.N. Bose National Centre for Basic Sciences,Block JD, Sector III, Salt Lake, Kolkata, 700098 (India); Diamantini, M. Cristina [NiPS Laboratory, INFN and Dipartimento di Fisica, University of Perugia,via A. Pascoli, Perugia, I-06100 (Italy); Guarnaccia, Giuseppe [Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno,via Giovanni Paolo II, Fisciano, Salerno, I-84084 (Italy); Lahiri, A. [S.N. Bose National Centre for Basic Sciences,Block JD, Sector III, Salt Lake, Kolkata, 700098 (India); Trugenberger, Carlo A. [SwissScientific,chemin Diodati 10, Cologny, CH-1223 (Switzerland)
2015-06-12
We propose a spin gauge field theory in which the curl of a Dirac fermion current density plays the role of the pseudovector charge density. In this field-theoretic model, spin interactions are mediated by a single scalar gauge boson in its antisymmetric tensor formulation. We show that these long range spin interactions induce a gauge invariant photon mass in the one-loop effective action. The fermion loop generates a coupling between photons and the spin gauge boson, which acquires thus charge. This coupling represents also an induced, gauge invariant, topological mass for the photons, leading to the Meissner effect. The one-loop effective equations of motion for the charged spin gauge boson are the London equations. We propose thus spin gauge interactions as an alternative, topological mechanism for superconductivity in which no spontaneous symmetry breaking is involved.
4D topological mass by gauging spin
International Nuclear Information System (INIS)
Choudhury, I.D.; Diamantini, M. Cristina; Guarnaccia, Giuseppe; Lahiri, A.; Trugenberger, Carlo A.
2015-01-01
We propose a spin gauge field theory in which the curl of a Dirac fermion current density plays the role of the pseudovector charge density. In this field-theoretic model, spin interactions are mediated by a single scalar gauge boson in its antisymmetric tensor formulation. We show that these long range spin interactions induce a gauge invariant photon mass in the one-loop effective action. The fermion loop generates a coupling between photons and the spin gauge boson, which acquires thus charge. This coupling represents also an induced, gauge invariant, topological mass for the photons, leading to the Meissner effect. The one-loop effective equations of motion for the charged spin gauge boson are the London equations. We propose thus spin gauge interactions as an alternative, topological mechanism for superconductivity in which no spontaneous symmetry breaking is involved.
Axion topological field theory of topological superconductors
Qi, Xiao-Liang; Witten, Edward; Zhang, Shou-Cheng
2013-04-01
Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal invariant topological superconductors. In our theory the topological superconductor is characterized by a topological coupling between the electromagnetic field and the superconducting phase fluctuation, which has the same form as the coupling of “axions” with an Abelian gauge field. As a physical consequence of our theory, we predict the level crossing induced by the crossing of special “chiral” vortex lines, which can be realized by considering s-wave superconductors in proximity with the topological superconductor. Our theory can also be generalized to the coupling with a gravitational field.
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon
2007-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features...
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Sporring, Jon; Fogh Olsen, Ole
2008-01-01
. To address this problem, we introduce a photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way, we preserve important illumination features, while...
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....
Optical image encryption topology.
Yong-Liang, Xiao; Xin, Zhou; Qiong-Hua, Wang; Sheng, Yuan; Yao-Yao, Chen
2009-10-15
Optical image encryption topology is proposed based on the principle of random-phase encoding. Various encryption topological units, involving peer-to-peer, ring, star, and tree topologies, can be realized by an optical 6f system. These topological units can be interconnected to constitute an optical image encryption network. The encryption and decryption can be performed in both digital and optical methods.
Topological theory of dynamical systems recent advances
Aoki, N
1994-01-01
This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.
International Nuclear Information System (INIS)
Va'vra, J.
1995-10-01
J. Seguinot and T. Ypsilantis have recently described the theory and history of Ring Imaging Cherenkov (RICH) detectors. In this paper, I will expand on these excellent review papers, by covering the various photon detector designs in greater detail, and by including discussion of mistakes made, and detector problems encountered, along the way. Photon detectors are among the most difficult devices used in physics experiments, because they must achieve high efficiency for photon transport and for the detection of single photo-electrons. For gaseous devices, this requires the correct choice of gas gain in order to prevent breakdown and wire aging, together with the use of low noise electronics having the maximum possible amplification. In addition, the detector must be constructed of materials which resist corrosion due to photosensitive materials such as, the detector enclosure must be tightly sealed in order to prevent oxygen leaks, etc. The most critical step is the selection of the photocathode material. Typically, a choice must be made between a solid (CsI) or gaseous photocathode (TMAE, TEA). A conservative approach favors a gaseous photocathode, since it is continuously being replaced by flushing, and permits the photon detectors to be easily serviced (the air sensitive photocathode can be removed at any time). In addition, it can be argued that we now know how to handle TMAE, which, as is generally accepted, is the best photocathode material available as far as quantum efficiency is concerned. However, it is a very fragile molecule, and therefore its use may result in relatively fast wire aging. A possible alternative is TEA, which, in the early days, was rejected because it requires expensive CaF 2 windows, which could be contaminated easily in the region of 8.3 eV and thus lose their UV transmission
International Nuclear Information System (INIS)
Field, J.H.
1984-01-01
The current status, both theoretical and experimental, of two photon collision physics is reviewed with special emphasis on recent experimental results from e + e - storage rings. After a complete presentation of the helicity amplitude formalism for the general process e + e - → Xe + e - , various approximations (transverse photon, Weisaecker Williams) are discussed. Beam polarisation effects and radiative corrections are also briefly considered. A number of specific processes, for which experimental results are now available, are then described. In each case existing theoretical prediction are confronted with experimental results. The processes described include single resonance production, lepton and hadron pair production, the structure functions of the photon, the production of high Psub(T) jets and the total photon photon cross section. In the last part of the review the current status of the subject is summarised and some comments are made on future prospects. These include both extrapolations of current research to higher energy machines (LEP, HERA) as well as a brief mention of both the technical realisation and the physics interest of the real γγ and eγ collisions which may be possible using linear electron colliders in the 1 TeV energy range
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J.
1985-01-01
The study of photon-photon collisions has progressed enormously, stimulated by new data and new calculational tools for QCD. In the future we can expect precise determinations of ..cap alpha../sub s/ and ..lambda../sup ms/ from the ..gamma..*..gamma.. ..-->.. ..pi../sup 0/ form factor and the photon structure function, as well as detailed checks of QCD, determination of the shape of the hadron distribution amplitudes from ..gamma gamma.. ..-->.. H anti H, reconstruction of sigma/sub ..gamma gamma../ from exclusive channels at low W/sub ..gamma gamma../, definitive studies of high p/sub T/ hadron and jet production, and studies of threshold production of charmed systems. Photon-photon collisions, along with radiative decays of the psi and UPSILON, are ideal for the study of multiquark and gluonic resonances. We have emphasized the potential for resonance formation near threshold in virtually every hadronic exclusive channel, including heavy quark states c anti c c anti c, c anti c u anti u, etc. At higher energies SLC, LEP, ...) parity-violating electroweak effects and Higgs production due to equivalent Z/sup 0/ and W/sup + -/ beams from e ..-->.. eZ/sup 0/ and e ..-->.. nu W will become important. 44 references.
International Nuclear Information System (INIS)
Brodsky, S.J.
1985-01-01
The study of photon-photon collisions has progressed enormously, stimulated by new data and new calculational tools for QCD. In the future we can expect precise determinations of α/sub s/ and Λ/sup ms/ from the γ*γ → π 0 form factor and the photon structure function, as well as detailed checks of QCD, determination of the shape of the hadron distribution amplitudes from γγ → H anti H, reconstruction of sigma/sub γγ/ from exclusive channels at low W/sub γγ/, definitive studies of high p/sub T/ hadron and jet production, and studies of threshold production of charmed systems. Photon-photon collisions, along with radiative decays of the psi and UPSILON, are ideal for the study of multiquark and gluonic resonances. We have emphasized the potential for resonance formation near threshold in virtually every hadronic exclusive channel, including heavy quark states c anti c c anti c, c anti c u anti u, etc. At higher energies SLC, LEP, ...) parity-violating electroweak effects and Higgs production due to equivalent Z 0 and W +- beams from e → eZ 0 and e → nu W will become important. 44 references
Strongly Correlated Topological Insulators
2016-02-03
Strongly Correlated Topological Insulators In the past year, the grant was used for work in the field of topological phases, with emphasis on finding...surface of topological insulators. In the past 3 years, we have started a new direction, that of fractional topological insulators. These are materials...in which a topologically nontrivial quasi-flat band is fractionally filled and then subject to strong interactions. The views, opinions and/or
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.
Wave Manipulation by Topology Optimization
DEFF Research Database (Denmark)
Andkjær, Jacob Anders
topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable...
Topological methods in Euclidean spaces
Naber, Gregory L
2000-01-01
Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem, the Lefschetz Fixed Point Theorem, the Stone-Weierstrass Theorem, and Morse functions. Includes new section of solutions to selected problems.
Transportation Network Topologies
Holmes, Bruce J.; Scott, John
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21st thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which
Weighted spectral distribution for internet topology analysis: Theory and applications
Fay, D.; Haddadi, H.; Thomason, A.; Moore, A.W.; Mortier, R.; Jamakovic, A.; Uhlig, S.; Rio, M.
2010-01-01
Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We
Topological Modeling and Stochastic Analysis of Images
National Research Council Canada - National Science Library
Krim, Hamid
2004-01-01
.... Concepts in classification and recognition problems. 1. We have explored the potential of combining geometrical as well as topological information in capturing the essence of an object for classification and recognition purposes...
Topological visual mapping in robotics.
Romero, Anna; Cazorla, Miguel
2012-08-01
A key problem in robotics is the construction of a map from its environment. This map could be used in different tasks, like localization, recognition, obstacle avoidance, etc. Besides, the simultaneous location and mapping (SLAM) problem has had a lot of interest in the robotics community. This paper presents a new method for visual mapping, using topological instead of metric information. For that purpose, we propose prior image segmentation into regions in order to group the extracted invariant features in a graph so that each graph defines a single region of the image. Although others methods have been proposed for visual SLAM, our method is complete, in the sense that it makes all the process: it presents a new method for image matching; it defines a way to build the topological map; and it also defines a matching criterion for loop-closing. The matching process will take into account visual features and their structure using the graph transformation matching (GTM) algorithm, which allows us to process the matching and to remove out the outliers. Then, using this image comparison method, we propose an algorithm for constructing topological maps. During the experimentation phase, we will test the robustness of the method and its ability constructing topological maps. We have also introduced new hysteresis behavior in order to solve some problems found building the graph.
Lattice QCD without topology barriers
Lüscher, Martin
2011-01-01
As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.
Hidden topological constellations and polyvalent charges in chiral nematic droplets.
Posnjak, Gregor; Čopar, Simon; Muševič, Igor
2017-02-21
Topology has an increasingly important role in the physics of condensed matter, quantum systems, material science, photonics and biology, with spectacular realizations of topological concepts in liquid crystals. Here we report on long-lived hidden topological states in thermally quenched, chiral nematic droplets, formed from string-like, triangular and polyhedral constellations of monovalent and polyvalent singular point defects. These topological defects are regularly packed into a spherical liquid volume and stabilized by the elastic energy barrier due to the helical structure and confinement of the liquid crystal in the micro-sphere. We observe, for the first time, topological three-dimensional point defects of the quantized hedgehog charge q=-2, -3. These higher-charge defects act as ideal polyvalent artificial atoms, binding the defects into polyhedral constellations representing topological molecules.
First Meeting in Topology and Functional Analysis
López-Pellicer, Manuel
2014-01-01
Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.
Topology optimization based on the harmony search method
International Nuclear Information System (INIS)
Lee, Seung-Min; Han, Seog-Young
2017-01-01
A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclu- sions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.
Topology optimization based on the harmony search method
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung-Min; Han, Seog-Young [Hanyang University, Seoul (Korea, Republic of)
2017-06-15
A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclu- sions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.
CONFERENCE: Photon-photon collisions
International Nuclear Information System (INIS)
Anon.
1983-01-01
Despite being difficult to observe, photon-photon collisions have opened up a range of physics difficult, or even impossible, to access by other methods. The progress which has been made in this field was evident at the fifth international workshop on photon-photon collisions, held in Aachen from 13-16 April and attended by some 120 physicists
Emerging Trends in Topological Insulators and Topological ...
Indian Academy of Sciences (India)
Emerging Trends in Topological Insulators and. Topological Superconductors. Arijit Saha and Arun M Jayannavar. Arijit Saha is a Reader-F at the Institute of Physics,. Bhubaneswar. His research interest lies broadly in the areas of mesoscopic physics and strongly correlated electrons. Arun M Jayannavar is a.
A topological derivative method for topology optimization
DEFF Research Database (Denmark)
Norato, J.; Bendsøe, Martin P.; Haber, RB
2007-01-01
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...
Observation of a phononic quadrupole topological insulator
Serra-Garcia, Marc; Peri, Valerio; Süsstrunk, Roman; Bilal, Osama R.; Larsen, Tom; Villanueva, Luis Guillermo; Huber, Sebastian D.
2018-03-01
The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.
Book Review: Computational Topology
DEFF Research Database (Denmark)
Raussen, Martin
2011-01-01
Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5......Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5...
Photon technology. Hard photon technology; Photon technology. Hard photon gijutsu
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-03-01
Research results of hard photon technology have been summarized as a part of novel technology development highly utilizing the quantum nature of photon. Hard photon technology refers to photon beam technologies which use photon in the 0.1 to 200 nm wavelength region. Hard photon has not been used in industry due to the lack of suitable photon sources and optical devices. However, hard photon in this wavelength region is expected to bring about innovations in such areas as ultrafine processing and material synthesis due to its atom selective reaction, inner shell excitation reaction, and spatially high resolution. Then, technological themes and possibility have been surveyed. Although there are principle proposes and their verification of individual technologies for the technologies of hard photon generation, regulation and utilization, they are still far from the practical applications. For the photon source technology, the laser diode pumped driver laser technology, laser plasma photon source technology, synchrotron radiation photon source technology, and vacuum ultraviolet photon source technology are presented. For the optical device technology, the multi-layer film technology for beam mirrors and the non-spherical lens processing technology are introduced. Also are described the reduction lithography technology, hard photon excitation process, and methods of analysis and measurement. 430 refs., 165 figs., 23 tabs.
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see......, e.g. [2]) in order to develop methods for topology design for applications where conservation laws are critical such that element--wise conservation in the discretized models has a high priority. This encompasses problems involving for example mass and heat transport. The work described...... 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...
Elementary concepts of topology
Alexandroff, Paul
1961-01-01
Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.
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.
Energy Management Dynamic Control Topology In MANET
Madhusudan, G.; Kumar, TNR
2017-08-01
Topology management via per-node transmission power adjustment has been shown effective in extending network lifetime. The existing algorithms constructs static topologies which fail to take the residual energy of network nodes, and cannot balance energy consumption efficiently. To address this problem, a Light Weighted Distributed Topology Control algorithm EMDCT(Energy Management Dynamic Control Topology ) is proposed in this paper. Based on the link metric of the network, both the energy consumption rate level and residual energy levels at the two end nodes are considered. EMDCT generates a Dynamic Topology that changes with the variation of node energy without the aid of location information, each node determines its transmission power according to local network information, which reduces the overhead complexity of EMDCT greatly. The experiment results show that EMDCT preserves network connectivity and manitains minimum-cost property of the network also it can extend network lifetime more remarkably.
Topology-Based Methods in Visualization 2015
Garth, Christoph; Weinkauf, Tino
2017-01-01
This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volum...
International Nuclear Information System (INIS)
Ulmer, W; Kaissl, W
2003-01-01
A Gaussian convolution kernel K is deduced as a Green's function of a Lie operator series. The deconvolution of a Gaussian kernel is developed by the inverse Green's function K -1 . A practical application is the deconvolution of measured profiles D m (x) of photons and protons with finite detector size to determine the profiles D p (x) of point-detectors or Monte Carlo Bragg curves of protons. The presented algorithms work if D m (x) is either an analytical function or only given in a numerical form. Some approximation methods of the deconvolution are compared (differential operator expansion to analytical adaptations of 2 x 2 cm 2 and 4 x 4 cm 2 profiles, Hermite expansions to measured 6 x 6 cm 2 and 20 x 20 cm 2 profiles and Bragg curves of 80/180 MeV protons, FFT to an analytical 4 x 4 cm 2 profile). The inverse problem may imply ill-posed problems, and, in particular, the use of FFT may be susceptible to them
Tierny, Julien; Favelier, Guillaume; Levine, Joshua A; Gueunet, Charles; Michaux, Michael
2017-08-29
This system paper presents the Topology ToolKit (TTK), a software platform designed for the topological analysis of scalar data in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. TTK aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependency-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions
Topological antiferromagnetic spintronics
Šmejkal, Libor; Mokrousov, Yuriy; Yan, Binghai; MacDonald, Allan H.
2018-03-01
The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field that is exploring the links between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topological superconductors, to control topological protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.
Time domain topology optimization of 3D nanophotonic devices
DEFF Research Database (Denmark)
Elesin, Yuriy; Lazarov, Boyan Stefanov; Jensen, Jakob Søndergaard
2014-01-01
We present an efficient parallel topology optimization framework for design of large scale 3D nanophotonic devices. The code shows excellent scalability and is demonstrated for optimization of broadband frequency splitter, waveguide intersection, photonic crystal-based waveguide and nanowire......-based waveguide. The obtained results are compared to simplified 2D studies and we demonstrate that 3D topology optimization may lead to significant performance improvements. © 2013 Elsevier B.V. All rights reserved....
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.
Real Topological Cyclic Homology
DEFF Research Database (Denmark)
Høgenhaven, Amalie
The main topics of this thesis are real topological Hochschild homology and real topological cyclic homology. If a ring or a ring spectrum is equipped with an anti-involution, then it induces additional structure on the topological Hochschild homology spectrum. The group O(2) acts on the spectrum......, where O(2) is the semi-direct product of T, the multiplicative group of complex number of modulus 1, by the group G=Gal(C/R). We refer to this O(2)-spectrum as the real topological Hochschild homology. This generalization leads to a G-equivariant version of topological cyclic homology, which we call...... real topological cyclic homology. The first part of the thesis computes the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings at a prime p with anti-involution induced by taking inverses in the group. The second part of the thesis investigates the derived G...
Triple Point Topological Metals
Directory of Open Access Journals (Sweden)
Ziming Zhu
2016-07-01
Full Text Available Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.
On the Hardness of Topology Inference
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.
Topology Optimization of Continuum Structures with Local Stress Constraints
DEFF Research Database (Denmark)
Duysinx, Pierre; Bendsøe, Martin P
1998-01-01
of topology problems are considered. To deal with the so-called 'singularity' phenomenon of stress constraints in topology design, an epsilon-constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems...
Cultural Topology of Creativity
Directory of Open Access Journals (Sweden)
L. M. Andryukhina
2012-01-01
Full Text Available The man in the modern culture faces the challenge of either being creative or forced to leave the stage, which reflects the essential basics of life. The price of lost opportunities, caused by mental stereotypes and encapsulation, is gradually rising. The paper reveals the socio-cultural conditions and the necessary cultural topology of creativity development, as well as the man’s creative potential in the 21st century. The content of the creativity concept is specified along with the phenomenon of its fast expansion in the modern discourse. That results from the global spreading of numerous creative practices in various spheres of life, affecting the progress directions in economics, business, industrial technologies, labor, employment and social stratification. The author emphasizes the social features of creativity, the rising number of, so called, creative class, and outlines the two opposing strategies influencing the topology modification of the social and cultural environment. The first one, applied by the developed countries, facilitates the development of the creative human potential, whereas the other one, inherent in our country, holds that a creative person is able to make progress by himself. However, for solving the urgent problem of innovative development, the creative potential of modern Russia is not sufficient, and following the second strategy will result in unrealized social opportunities and ever lasting social and cultural situation demanding further investment. According to the author, to avoid such a perspective, it is necessary to overcome the three deeply rooted archetypes: the educational disciplinary centrism, organizational absolutism and cultural ostracism.
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.
Differential topology an introduction
Gauld, David B
2006-01-01
Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curv
Directory of Open Access Journals (Sweden)
S. Nazmul
2014-03-01
Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.
Topological Foundations of Electromagnetism
Barrett, Terrence W
2008-01-01
Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic field
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.
Topological Gyroscopic Metamaterials
Nash, Lisa Michelle
Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.
The ABCD of topological recursion
DEFF Research Database (Denmark)
Andersen, Jorgen Ellegaard; Borot, Gaëtan; Chekhov, Leonid O.
an interesting problem which we study here. We provide some elementary, Lie-algebraic tools to address this problem, and give some elements of classification for dim V = 2. We also describe four more interesting classes of quantum Airy structures, coming from respectively Frobenius algebras (here we retrieve...... the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a Z2-invariant version of the latter. This Z2-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of math-ph/0702045....
Explorations in topology map coloring, surfaces and knots
Gay, David
2013-01-01
Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigation
General Topology of the Universe
Pandya, Aalok
2002-01-01
General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded.
Design of acoustic devices by topology optimization
DEFF Research Database (Denmark)
Sigmund, Ole; Jensen, Jakob Søndergaard
2003-01-01
The goal of this study is to design and optimize structures and devices that are subjected to acoustic waves. Examples are acoustic lenses, sound walls, waveguides and loud speakers. We formulate the design problem as a topology optimization problem, i.e. distribute material in a design domain...
Moduli spaces of curves and enumerative geometry via topological recursion
Lewański, D.
2017-01-01
The thesis considers several enumerative geometric problems concerning the topology of the moduli space of curves and their combinatorics. These enumerative geometric problems are analysed from different intertwined points of view and using different mathematical tools, including Hurwitz theory,
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Liu, Jia-Ming
2016-01-01
With this self-contained and comprehensive text, students will gain a detailed understanding of the fundamental concepts and major principles of photonics. Assuming only a basic background in optics, readers are guided through key topics such as the nature of optical fields, the properties of optical materials, and the principles of major photonic functions regarding the generation, propagation, coupling, interference, amplification, modulation, and detection of optical waves or signals. Numerous examples and problems are provided throughout to enhance understanding, and a solutions manual containing detailed solutions and explanations is available online for instructors. This is the ideal resource for electrical engineering and physics undergraduates taking introductory, single-semester or single-quarter courses in photonics, providing them with the knowledge and skills needed to progress to more advanced courses on photonic devices, systems and applications.
Directory of Open Access Journals (Sweden)
Evgenii E. Narimanov
2014-10-01
Full Text Available We introduce a new “universality class” of artificial optical media—photonic hypercrystals. These hyperbolic metamaterials, with periodic spatial variation of dielectric permittivity on subwavelength scale, combine the features of optical metamaterials and photonic crystals. In particular, surface waves supported by a hypercrystal possess the properties of both the optical Tamm states in photonic crystals and surface-plasmon polaritons at the metal-dielectric interface.
Canonical Duality Theory for Topology Optimization
Gao, David Yang
2016-01-01
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer nonlinear programming problem (MINLP), i.e. for a given deformation, the first-level optimization is a typical linear constrained 0-1 programming problem, while for a given structure, the second-level optimization is a general nonlinear continuous minimization pro...
Lee, Chi H
2006-01-01
Wireless, optical, and electronic networks continue to converge, prompting heavy research into the interface between microwave electronics, ultrafast optics, and photonic technologies. New developments arrive nearly as fast as the photons under investigation, and their commercial impact depends on the ability to stay abreast of new findings, techniques, and technologies. Presenting a broad yet in-depth survey, Microwave Photonics examines the major advances that are affecting new applications in this rapidly expanding field.This book reviews important achievements made in microwave photonics o
Reconstruction of topology and geometry from digitisations
DEFF Research Database (Denmark)
Christensen, Sabrina Tang
2016-01-01
Elucidation of the relation between real world objects and their digitisations is an inherent challenge of image analysis. This thesis addresses the reconstruction of topological as well as geometrical features of sets in Euclidean 3-space respectively the Euclidean plane from binary images....... The first problem, the reconstruction of topology in dimension three, is approached using combinatorics of voxel reconstructions in combination with differential topology results. An improved digital re-construction based on binary images of objects with sufficiently smooth boundary is proposed. It is shown......, and it is argued that this is the best possible bound for which topological equivalence is guaranteed. Making no restrictions on the classical reconstruction, similar results can be proved for slightly stronger assumptions on the resolution. It is conjectured that the lower of the bounds on the resolution also...
Optimization-based topology identification of complex networks
International Nuclear Information System (INIS)
Tang Sheng-Xue; Chen Li; He Yi-Gang
2011-01-01
In many cases, the topological structures of a complex network are unknown or uncertain, and it is of significance to identify the exact topological structure. An optimization-based method of identifying the topological structure of a complex network is proposed in this paper. Identification of the exact network topological structure is converted into a minimal optimization problem by using the estimated network. Then, an improved quantum-behaved particle swarm optimization algorithm is used to solve the optimization problem. Compared with the previous adaptive synchronization-based method, the proposed method is simple and effective and is particularly valid to identify the topological structure of synchronization complex networks. In some cases where the states of a complex network are only partially observable, the exact topological structure of a network can also be identified by using the proposed method. Finally, numerical simulations are provided to show the effectiveness of the proposed method. (general)
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole
2005-01-01
Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, s......: the Finite Volume Method. London: Longman Scientific Technical......Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see......, e.g. [2]) in order to develop methods for topology design for applications where conservation laws are critical such that element--wise conservation in the discretized models has a high priority. This encompasses problems involving for example mass and heat transport. The work described...
Modeling Internet Topology Dynamics
Haddadi, H.; Uhlig, S.; Moore, A.; Mortier, R.; Rio, M.
Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements,
Topology optimization approaches
DEFF Research Database (Denmark)
Sigmund, Ole; Maute, Kurt
2013-01-01
Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary...
Manufacturing tolerant topology optimization
DEFF Research Database (Denmark)
Sigmund, Ole
2009-01-01
(dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization...
Mendelson, Bert
1990-01-01
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.
Distributed topology control algorithm to conserve energy in heterogeneous wireless mesh networks
CSIR Research Space (South Africa)
Aron, FO
2008-07-01
Full Text Available to increasing the network capacity via better spatial bandwidth reuse. In this work, the problem of topology control in a hybrid WMN of heterogeneous wireless devices with varying maximum transmission ranges is considered. A localized distributed topology...
Amorphous Gyroscopic Topological Metamaterials
Mitchell, Noah P.; Nash, Lisa M.; Hexner, Daniel; Turner, Ari M.; Irvine, William T. M.
Mechanical topological metamaterials display striking mechanical responses, such as unidirectional surface modes that are impervious to disorder. This behavior arises from the topology of their vibrational spectra. All examples of topological metamaterials to date are finely-tuned structures such as crystalline lattices or jammed packings. Here, we present robust recipes for building amorphous topological metamaterials with arbitrary underlying structure and no long-range order. Using interacting gyroscopes as a model system, we demonstrate through experiment, simulation, and theoretical methods that the local geometry and interactions are sufficient to generate topological mobility gaps, allowing for spatially-resolved, real-space calculations of the Chern number. The robustness of our approach enables the design and self-assembly of non-crystalline materials with protected, unidirectional waveguides on the micro and macro scale.
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...... in an interactive and intuitive way. By creating such applications with an intuitive and simple user interface we allow non-engineers like designers and architects to easily experiment with boundary conditions, design domains and other optimization settings. This is in contrast to commercial topology optimization...... software where the users are assumed to be well-educated both in the finite element method and topology optimization. This dissertation describes how various topology optimization methods have been used for creating cross-platform applications with high performance. The user interface design is based...
Stochastic stabilization of cosmological photons
International Nuclear Information System (INIS)
Dettmann, C P; Keating, J P; Prado, S D
2004-01-01
The stability of photon trajectories in models of the universe that have constant spatial curvature is determined by the sign of the curvature: they are exponentially unstable if the curvature is negative and stable if it is positive or zero. We demonstrate that random fluctuations in the curvature provide an additional stabilizing mechanism. This mechanism is analogous to the one responsible for stabilizing the stochastic Kapitsa pendulum. When the mean curvature is negative it is capable of stabilizing the photon trajectories; when the mean curvature is zero or positive it determines the characteristic frequency with which neighbouring trajectories oscillate about each other. In constant negative curvature models of the universe that have compact topology, exponential instability implies chaos (e.g. mixing) in the photon dynamics. We discuss some consequences of stochastic stabilization in this context. (letter to the editor)
Machine learning topological states
Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
2017-11-01
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.
DEFF Research Database (Denmark)
Keller, Ole
2002-01-01
A review is given of the space-time wave mechanics of single photons, a subject with an almost century long history. The Landau-Peierls photon wave function, which is related nonlocally to the electromagnetic field is first described, and thereafter the so-called energy wave function, based...... on the positive-frequency Riemann-Silberstein vectors, is discussed. Recent attempts to understand the birth process of a photon emerging from a single atom are summarized. The polychromatic photon concept is introduced, and it is indicated how the wave mechanics of polychromatic photons can be upgraded to wave...... in a hyperfine spin transition shows an exponential falloff with the distance from the atomic nucleus. The length parameter in this falloff is the Bohr radius....
Robust quantum network architectures and topologies for entanglement distribution
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.
Topological dynamics of gyroscopic and Floquet lattices from Newton's laws
Lee, Ching Hua; Li, Guangjie; Jin, Guliuxin; Liu, Yuhan; Zhang, Xiao
2018-02-01
Despite intense interest in realizing topological phases across a variety of electronic, photonic, and mechanical platforms, the detailed microscopic origin of topological behavior often remains elusive. To bridge this conceptual gap, we show how hallmarks of topological modes—boundary localization and chirality—emerge from Newton's laws in mechanical topological systems. We first construct a gyroscopic lattice with analytically solvable edge modes, and show how the Lorentz and spring restoring forces conspire to support very robust "dangling bond" boundary modes. The chirality and locality of these modes intuitively emerges from microscopic balancing of restoring forces and cyclotron tendencies. Next, we introduce the highlight of this work, an experimentally realistic mechanical nonequilibrium (Floquet) Chern lattice driven by ac electromagnets. Through appropriate synchronization of the ac driving protocol, the Floquet lattice is "pushed around" by a rotating potential analogous to an object washed ashore by water waves. Besides hosting "dangling bond" chiral modes analogous to the gyroscopic boundary modes, our Floquet Chern lattice also supports peculiar half-period chiral modes with no static analog, i.e., analogs of anomalous Floquet Chern insulators edge modes. With key parameters controlled electronically, our setup has the advantage of being dynamically tunable for applications involving arbitrary Floquet modulations. The physical intuition gleaned from our two prototypical topological systems is applicable not just to arbitrarily complicated mechanical systems, but also photonic and electrical topological setups.
State space Newton's method for topology optimization
DEFF Research Database (Denmark)
Evgrafov, Anton
2014-01-01
We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem in the algori......We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem...
Topology Optimization of Structure Using Differential Evolution
Directory of Open Access Journals (Sweden)
Chun-Yin Wu
2008-02-01
Full Text Available The population-based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems. A promising new evolutionary algorithm, differential evolution, has garnered significant attention in the engineering optimization research. Differential evolution has the advantage of incorporating a relatively simple and efficient form of mutation and crossover. This paper aims at introducing differential evolution as an alternative approach for topology optimization of truss and continuous structure with stress and displacement constraints. In comparison the results with other studies, it shows that differential evolution algorithms are very effective and efficient in solving topology optimization problem of structure.
Algebraic topology a first course
Fulton, William
1995-01-01
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: ...
International Nuclear Information System (INIS)
Bergqvist, I.
1976-01-01
Methods for extracting photon strength functions are briefly discussed. We follow the Brink-Axel approach to relate the strength functions to the giant resonances observed in photonuclear work and summarize the available data on the E1, E2 and M1 resonances. Some experimental and theoretical problems are outlined. (author)
Elements of differential topology
Shastri, Anant R
2011-01-01
Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topology, algebraic/differential geometry, and Lie groups.The first two chapters review differential and integral calculus of several variables and present fundamental results that are used throughout the text. The next few chapters focus on smooth manifo
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
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
2016-10-31
AFRL-AFOSR-UK-TR-2017-0002 Global Topology Optimisation Robert Jack UNIVERSITY OF BATH Final Report 10/31/2016 DISTRIBUTION A: Distribution approved...01 Aug 2015 to 31 Jul 2016 4. TITLE AND SUBTITLE Global Topology Optimisation 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-15-1-0317 5c...future work. 15. SUBJECT TERMS EOARD, Topology Optimization, Non Convex 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18
Algebraic topology and concurrency
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric
2006-01-01
We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Plasmonics in Topological Insulators
Directory of Open Access Journals (Sweden)
Yi-Ping Lai
2014-04-01
Full Text Available With strong spin-orbit coupling, topological insulators have an insulating bulk state, characterized by a band gap, and a conducting surface state, characterized by a Dirac cone. Plasmons in topological insulators show high frequency-tunability in the mid-infrared and terahertz spectral regions with transverse spin oscillations, also called “spin-plasmons”. This paper presents a discussion and review of the developments in this field from the fundamental theory of plasmons in bulk, thin-film, and surface-magnetized topological insulators to the techniques of plasmon excitation and future applications.
Barr, Stephen
1989-01-01
""A mathematician named KleinThought the Moebius band was divine.Said he: 'If you glueThe edges of two,You'll get a weird bottle like mine.' "" - Stephen BarrIn this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics:New Surfaces (Orientability, Dimension, The Klein Bottle, etc.)The Shortest Moebius StripThe
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)
Scalable quantum information processing with photons and atoms
Pan, Jian-Wei
Over the past three decades, the promises of super-fast quantum computing and secure quantum cryptography have spurred a world-wide interest in quantum information, generating fascinating quantum technologies for coherent manipulation of individual quantum systems. However, the distance of fiber-based quantum communications is limited due to intrinsic fiber loss and decreasing of entanglement quality. Moreover, probabilistic single-photon source and entanglement source demand exponentially increased overheads for scalable quantum information processing. To overcome these problems, we are taking two paths in parallel: quantum repeaters and through satellite. We used the decoy-state QKD protocol to close the loophole of imperfect photon source, and used the measurement-device-independent QKD protocol to close the loophole of imperfect photon detectors--two main loopholes in quantum cryptograph. Based on these techniques, we are now building world's biggest quantum secure communication backbone, from Beijing to Shanghai, with a distance exceeding 2000 km. Meanwhile, we are developing practically useful quantum repeaters that combine entanglement swapping, entanglement purification, and quantum memory for the ultra-long distance quantum communication. The second line is satellite-based global quantum communication, taking advantage of the negligible photon loss and decoherence in the atmosphere. We realized teleportation and entanglement distribution over 100 km, and later on a rapidly moving platform. We are also making efforts toward the generation of multiphoton entanglement and its use in teleportation of multiple properties of a single quantum particle, topological error correction, quantum algorithms for solving systems of linear equations and machine learning. Finally, I will talk about our recent experiments on quantum simulations on ultracold atoms. On the one hand, by applying an optical Raman lattice technique, we realized a two-dimensional spin-obit (SO
Protection of surface states in topological nanoparticles
Siroki, Gleb; Haynes, Peter D.; Lee, Derek K. K.; Giannini, Vincenzo
2017-07-01
Topological insulators host protected electronic states at their surface. These states show little sensitivity to disorder. For miniaturization one wants to exploit their robustness at the smallest sizes possible. This is also beneficial for optical applications and catalysis, which favor large surface-to-volume ratios. However, it is not known whether discrete states in particles share the protection of their continuous counterparts in large crystals. Here we study the protection of the states hosted by topological insulator nanoparticles. Using both analytical and tight-binding simulations, we show that the states benefit from the same level of protection as those on a planar surface. The results hold for many shapes and sustain surface roughness which may be useful in photonics, spectroscopy, and chemistry. They complement past studies of large crystals—at the other end of possible length scales. The protection of the nanoparticles suggests that samples of all intermediate sizes also possess protected states.
Basis for calculations in the topological expansion
International Nuclear Information System (INIS)
Levinson, M.A.
1982-12-01
Investigations aimed at putting the topological theory of particles on a more quantitative basis are described. First, the incorporation of spin into the topological structure is discussed and shown to successfully reproduce the observed lowest mass hadron spectrum. The absence of parity-doubled states represents a significant improvement over previous efforts in similar directions. This theory is applied to the lowest order calculation of elementary hadron coupling constant ratios. SU(6)/sub W/ symmetry is maintained and extended via the notions of topological supersymmetry and universality. Finally, efforts to discover a perturbative basis for the topological expansion are described. This has led to the formulation of off-shell Feynman-like rules which provide a calculational scheme for the strong interaction components of the topological expansion once the zero-entropy connected parts are known. These rules are shown to imply a topological asymptotic freedom. Even though the nonlinear zero-entropy problem cannot itself be treated perturbatively, plausible general assumptions about zero-entropy amplitudes allow immediate qualitative inferences concerning physical hadrons. In particular, scenarios for mass splittings beyond the supersymmetric level are described
Topological systems versus attachment relations | Guido ...
African Journals Online (AJOL)
... localification procedure introduced by S. Vickers for topological systems. Keywords: Adjoint functor, algebra, attachment relation, embedding functor, localification of topological systems, spatialization of topological systems, topological system, topological theory, variety of algebras. Quaestiones Mathematicae 37(2014), ...
Time relative single-photon (photoelectron) method
International Nuclear Information System (INIS)
Luo Binqiao
1988-01-01
A single-photon (photoelectron) measuring system is designed. It researches various problems in single-photon (photoelectron) method. The electronic resolving time is less than 25 ps. The resolving time of single-photon (photoelectron) measuring system is 25 to 65 ps
Efficient reanalysis techniques for robust topology optimization
DEFF Research Database (Denmark)
Amir, Oded; Sigmund, Ole; Lazarov, Boyan Stefanov
2012-01-01
The article focuses on the reduction of the computational effort involved in robust topology optimization procedures. The performance of structures designed by means of topology optimization may be seriously degraded due to fabrication errors. Robust formulations of the optimization problem were...... shown to yield optimized designs that are tolerant with respect to such manufacturing uncertainties. The main drawback of such procedures is the added computational cost associated with the need to evaluate a set of designs by performing multiple finite element analyses. In this article, we propose...... efficient robust topology optimization procedures based on reanalysis techniques. The approach is demonstrated on two compliant mechanism design problems where robust design is achieved by employing either a worst case formulation or a stochastic formulation. It is shown that the time spent on finite...
On the epireflective hull of topological nearness groups in the ...
African Journals Online (AJOL)
To find the specific nature of the objects that are in the epireflective hull of the symmetric topological spaces in the category of nearness spaces is a long open problem. See [BCH05]for more information. Here we consider topological nearness groups as a full subcategory of nearness groups and ask the analogous question ...
A new compactness type topological property | Zhao | Quaestiones ...
African Journals Online (AJOL)
By a gauge on a topological space we shall mean a mapping that assigns each element in the space an open neighbourhood. We investigate some topological properties which can be characterized using gauges. The main property we will consider is the gauge compactness. Some problems and possible future work are ...
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 ...
Topology and condensed matter physics
Mj, Mahan; Bandyopadhyay, Abhijit
2017-01-01
This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a qui...
Topology Optimization for Additive Manufacturing
DEFF Research Database (Denmark)
Clausen, Anders
microstructure for a material with programmable, nearly constant Poisson’s ratio for large deformations may be designed and fabricated using direct ink writing. Structures are generated for the full interval [−0.8, 0.8], all with uniform feature size and a continuous print path, ensuring the potential...... for scalable manufacturing. In relation to interface problems it is shown how a flexible void area may be included into a standard minimum compliance problem by employing an additional design variable field and a sensitivity filter. Furthermore, it is shown how the design of coated structures may be modeled...... as a differentiable topology optimization problem. This is done partly by using spatial gradients of the density variable in the interpolation function between the design variable field and physical variables, partly by employing a two-step filtering scheme in order to control the gradient field. The approach...
Hallo photons calls photon; Allo photon appelle photon
Energy Technology Data Exchange (ETDEWEB)
Anon.
1997-09-01
When a pair of photons is created, it seems that these 2 photons are bound together by a mysterious link. This phenomenon has been discovered at the beginning of the seventies. In this new experiment the 2 photons are separated and have to follow different ways through optic cables until they face a quantum gate. At this point they have to chose between a short and a long itinerary. Statistically they have the same probability to take either. In all cases the 2 photons agree to do the same choice even if the 2 quantum gates are distant of about 10 kilometers. Some applications in ciphering and coding of messages are expected. (A.C.)
Topological Solitons in Physics.
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
Topological susceptibility from slabs
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Forcrand, Philippe de [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); CERN, Physics Department, TH Unit, CH-1211 Geneva 23 (Switzerland); Gerber, Urs [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Apdo. Postal 2-82, Morelia, Michoacán, C.P. 58040 (Mexico)
2015-12-14
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ{sub t}. In principle it seems straightforward to measure χ{sub t} by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ{sub t} even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ{sub t}, as we demonstrate with numerical results for non-linear σ-models.
Topological Susceptibility from Slabs
Bietenholz, Wolfgang; Gerber, Urs
2015-01-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.
Games for topological fixpoint logic
Bezhanishvili, N.; Kupke, C.
2016-01-01
Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators
Lee, Chi H
2013-01-01
Microwave photonics continues to see rapid growth. The integration of optical fiber and wireless networks has become a commercial reality and is becoming increasingly pervasive. Such hybrid technology will lead to many innovative applications, including backhaul solutions for mobile networks and ultrabroadband wireless networks that can provide users with very high bandwidth services. Microwave Photonics, Second Edition systematically introduces important technologies and applications in this emerging field. It also reviews recent advances in micro- and millimeter-wavelength and terahertz-freq
Tensor Network Wavefunctions for Topological Phases
Ware, Brayden Alexander
The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for
The refined topological vertex
International Nuclear Information System (INIS)
Iqbal, Amer; Kozcaz, Can; Vafa, Cumrun
2009-01-01
We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov. The refined vertex is also expected to be related to Khovanov knot invariants.
Manufacturing tolerant topology optimization
Sigmund, Ole
2009-01-01
In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining an...
Noncommutative topological dynamics
International Nuclear Information System (INIS)
Ramos, C. Correia; Martins, Nuno; Severino, Ricardo; Ramos, J. Sousa
2006-01-01
We study noncommutative dynamical systems associated to unimodal and bimodal maps of the interval. To these maps we associate subshifts and the correspondent AF-algebras and Cuntz-Krieger algebras. As an example we consider systems having equal topological entropy log(1 + φ), where φ is the golden number, but distinct chaotic behavior and we show how a new numerical invariant allows to distinguish that complexity. Finally, we give a statistical interpretation to the topological numerical invariants associated to bimodal maps
Hodge, John
2009-11-01
In current light models, a particle-like model of light is inconsistent with diffraction observations. A model of light is proposed wherein photon inferences are combined with the cosmological scalar potential model (SPM). That the photon is a surface with zero surface area in the travel direction is inferred from the Michelson-Morley experiment. That the photons in slits are mathematically treated as a linear antenna array (LAA) is inferred from the comparison of the transmission grating interference pattern and the single slit diffraction pattern. That photons induce a LAA wave into the plenum is inferred from the fractal model. Similarly, the component of the photon (the hod) is treated as a single antenna radiating a potential wave into the plenum. That photons are guided by action on the surface of the hod is inferred from the SPM. The plenum potential waves are a real field (not complex) that forms valleys, consistent with the pilot waves of the Bohm interpretation of quantum mechanics. Therefore, the Afshar experiment result is explained, supports Bohm, and falsifies Copenhagen. The papers may be viewed at http://web.citcom.net/˜scjh/.
Pseudospins and Topological Effects of Phonons in a Kekulé Lattice
Liu, Yizhou; Lian, Chao-Sheng; Li, Yang; Xu, Yong; Duan, Wenhui
2017-12-01
The search for exotic topological effects of phonons has attracted enormous interest for both fundamental science and practical applications. By studying phonons in a Kekulé lattice, we find a new type of pseudospin characterized by quantized Berry phases and pseudoangular momenta, which introduces various novel topological effects, including topologically protected pseudospin-polarized interface states and a phonon pseudospin Hall effect. We further demonstrate a pseudospin-contrasting optical selection rule and a pseudospin Zeeman effect, giving a complete generation-manipulation-detection paradigm of the phonon pseudospin. The pseudospin and topology-related physics revealed for phonons is general and applicable for electrons, photons, and other particles.
Inferring network topology from complex dynamics
International Nuclear Information System (INIS)
Shandilya, Srinivas Gorur; Timme, Marc
2011-01-01
Inferring the network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method for inferring the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is hardly restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology from observing a time series of state variables only. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstructing both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of external noise that distorts the original dynamics substantially. The method provides a conceptually new step towards reconstructing a variety of real-world networks, including gene and protein interaction networks and neuronal circuits.
Essentials of topology with applications
Krantz, Steven G
2009-01-01
Fundamentals What Is Topology? First Definitions Mappings The Separation Axioms Compactness Homeomorphisms Connectedness Path-Connectedness Continua Totally Disconnected Spaces The Cantor Set Metric Spaces Metrizability Baire's Theorem Lebesgue's Lemma and Lebesgue NumbersAdvanced Properties of Topological Spaces Basis and Sub-Basis Product Spaces Relative Topology First Countable, Second Countable, and So ForthCompactifications Quotient Topologies Uniformities Morse Theory Proper Mappings Paracompactness An Application to Digital ImagingBasic Algebraic Topology Homotopy Theory Homology Theory
Routing in Networks with Random Topologies
Bambos, Nicholas
1997-01-01
We examine the problems of routing and server assignment in networks with random connectivities. In such a network the basic topology is fixed, but during each time slot and for each of tis input queues, each server (node) is either connected to or disconnected from each of its queues with some probability.
Topologies on uniform hyperspaces | Hitchcock | Quaestiones ...
African Journals Online (AJOL)
This paper includes the proofs of results announced in [3], as well as other results deriving from the Isbell-Smith-Ward problem of comparability of Hausdorff uniform topologies on hyperspaces of uniform spaces. In particular we give (in Theorem 6) simple conditions on a uniform space sufficient for H-singularity (no other ...
Improving topology optimization intuition through games
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten; Malmgren-Hansen, David; Bærentzen, J. Andreas
2016-01-01
as well asto train human intuition of topology optimization. The players are challenged to solve the standard minimum compliance problem in 2D by distributing material in a design domain given a number of loads and supports with a material constraint. A statistical analysis of the gameplay data shows...
Applications of automatic differentiation in topology optimization
DEFF Research Database (Denmark)
Nørgaard, Sebastian A.; Sagebaum, Max; Gauger, Nicolas R.
2017-01-01
and is demonstrated on two separate, previously published types of problems in topology optimization. Two separate software packages for automatic differentiation, CoDiPack and Tapenade are considered, and their performance and usability trade-offs are discussed and compared to a hand coded adjoint gradient...
Analytic solutions of topologically disjoint systems
DEFF Research Database (Denmark)
Armstrong, J. R.; Volosniev, A. G.; Fedorov, D. V.
2015-01-01
We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All other interactions are approximated by harmonic oscillator ...
Topological String Theory and Enumerative Geometry
Energy Technology Data Exchange (ETDEWEB)
Song, Y. S
2003-05-19
In this thesis we investigate several problems which have their roots in both topological string theory and enumerative geometry. In the former case, underlying theories are topological field theories, whereas the latter case is concerned with intersection theories on moduli spaces. A permeating theme in this thesis is to examine the close interplay between these two complementary fields of study. The main problems addressed are as follows: In considering the Hurwitz enumeration problem of branched covers of compact connected Riemann surfaces, we completely solve the problem in the case of simple Hurwitz numbers. In addition, utilizing the connection between Hurwitz numbers and Hodge integrals, we derive a generating function for the latter on the moduli space {bar M}{sub g,2} of 2-pointed, genus-g Deligne-Mumford stable curves. We also investigate Givental's recent conjecture regarding semisimple Frobenius structures and Gromov-Witten invariants, both of which are closely related to topological field theories; we consider the case of a complex projective line P{sup 1} as a specific example and verify his conjecture at low genera. In the last chapter, we demonstrate that certain topological open string amplitudes can be computed via relative stable morphisms in the algebraic category.
Modern methods in topological vector spaces
Wilansky, Albert
2013-01-01
Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect
Orbifolds, quantum cosmology, and nontrivial topology
International Nuclear Information System (INIS)
Fagundes, Helio V.; Vargas, Teofilo
2006-01-01
In order to include nontrivial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We consider in detail the case of a 4-spherical orbifold with a cone-point singularity. This allows for the inclusion of a nontrivial topology into the semiclassical path integral approach to quantum cosmology, in the context of a Robertson-Walker minisuperspace. (author)
Topology optimization theory, methods, and applications
Bendsøe, Martin P
2004-01-01
The topology optimization method solves the basic engineering problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also MEMS and materials.
Electromagnetic topology: Characterization of internal electromagnetic coupling
Parmantier, J. P.; Aparicio, J. P.; Faure, F.
1991-01-01
The main principles are presented of a method dealing with the resolution of electromagnetic internal problems: Electromagnetic Topology. A very interesting way is to generalize the multiconductor transmission line network theory to the basic equation of the Electromagnetic Topology: the BLT equation. This generalization is illustrated by the treatment of an aperture as a four port junction. Analytical and experimental derivations of the scattering parameters are presented. These concepts are used to study the electromagnetic coupling in a scale model of an aircraft, and can be seen as a convenient means to test internal electromagnetic interference.
Topology optimization of laminated plates with prestress
DEFF Research Database (Denmark)
Pedersen, Niels Leergaard
2002-01-01
Laminated plates with different prestress in the layers are topology optimized. The objectives are to minimize the deflection due to the prestress or to minimize ordinary compliance. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress...... stiffness matrix to the structural stiffness. The calculations of sensitivities are complicated not only by the prestress but also because we are dealing with laminates. The topology optimization problem is solved using a new penalization scheme as an alternative to the SIMP (power law) approach...
On topology optimization of plates with prestress
DEFF Research Database (Denmark)
Pedersen, Niels Leergaard
2001-01-01
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...... 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...
The geometric topology of 3-manifolds
Bing, R H
1983-01-01
This book belongs in both graduate and undergraduate libraries as a useful reference for students and researchers in topology. It is directed toward mathematicians interested in geometry who have had at least a beginning course in topology. It should provide the reader with a better understanding of the physical properties of Euclidean 3-space-the space in which we presume we live. The reader should learn of some unsolved problems that continue to baffle reseachers. The most profound result in the volume is the side approximation theorem. However, some of the preliminary results and some of th
A note on the comparison of topologies
Directory of Open Access Journals (Sweden)
Martin M. Kovár
2001-01-01
Full Text Available A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom τS2σ which is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly (1977 regarding the comparison of topologies.
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.
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.
Pearsall, Thomas P
2017-01-01
This textbook employs a pedagogical approach that facilitates access to the fundamentals of Quantum Photonics. It contains an introductory description of the quantum properties of photons through the second quantization of the electromagnetic field, introducing stimulated and spontaneous emission of photons at the quantum level. Schrödinger’s equation is used to describe the behavior of electrons in a one-dimensional potential. Tunneling through a barrier is used to introduce the concept of nonlocality of an electron at the quantum level, which is closely-related to quantum confinement tunneling, resonant tunneling, and the origin of energy bands in both periodic (crystalline) and aperiodic (non-crystalline) materials. Introducing the concepts of reciprocal space, Brillouin zones, and Bloch’s theorem, the determination of electronic band structure using the pseudopotential method is presented, allowing direct computation of the band structures of most group IV, group III-V, and group II-VI semiconducto...
Length scale and manufacturability in density-based topology optimization
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Wang, Fengwen; Sigmund, Ole
2016-01-01
Since its original introduction in structural design, density-based topology optimization has been applied to a number of other fields such as microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can...... performance and in many cases can completely destroy the optimality of the solution. Therefore, the goal of this paper is to review recent advancements in obtaining manufacturable topology-optimized designs. The focus is on methods for imposing minimum and maximum length scales, and ensuring manufacturable...
Initial data sets and the topology of closed three-manifolds in general relativity
Carfora, M.
1983-10-01
The interaction between the matter content of a closed physical space associated with a generic gravitational configuration and the topology of the underlying closed three-manifold is discussed. Within the context of the conformal approach to the initial value problem, it is shown that the presence of enough matter and radiation favors the three-sphere topology or the worm-hole topology. It is argued that such topologies leave more room for possible gravitational initial data sets for the field equations.
International Nuclear Information System (INIS)
Quan, Frederic
2012-01-01
Photonics, the broad merger of electronics with the optical sciences, encompasses such a wide swath of technology that its impact is almost universal in our everyday lives. This is a broad overview of some aspects of the industry and their contribution to the ‘green’ or environmental movement. The rationale for energy conservation is briefly discussed and the impact of photonics on our everyday lives and certain industries is described. Some opinions from industry are presented along with market estimates. References are provided to some of the most recent research in these areas. (review article)
Deo, Satya
2018-01-01
This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...
Topology optimized microbioreactors
DEFF Research Database (Denmark)
Schäpper, Daniel; Lencastre Fernandes, Rita; Eliasson Lantz, Anna
2011-01-01
This article presents the fusion of two hitherto unrelated fields—microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein....... Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement...... in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced....
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...... of today, but – perhaps most importantly – also creating and producing architecture that is contemporaneous and reacts to the radical changes of the physical world which surrounds us in the increasingly artificial measures of new materialities and understandings thereof. The contributions range from...... the intricate issues of the imagination and the moving ratio in the topological culture, over urban topology, diagrammatisation, mediality and dynamics of transduction in the contemporary artificial environment....
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
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.
Ring-array processor distribution topology for optical interconnects
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.
Effects of finite element formulation on optimal plate and shell structural topologies
CSIR Research Space (South Africa)
Long, CS
2009-09-01
Full Text Available quantitatively to avoid simply comparing topologies visually. Special attention is paid to plate and shell problems and it is therefore appro- priate to give some background on structural topology optimization of plate and shell problems at this point... to automatically generate not only good, but optimal designs, topology optimization has been receiving unprecedented attention of late. However, we believe that an aspect of the problem which has not received sufficient attention is the effect of the the actual...
Differential topology first steps
Wallace, Andrew H
1968-01-01
Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of d
Topological approximations of multisets
Directory of Open Access Journals (Sweden)
El-Sayed A. Abo-Tabl
2013-07-01
Full Text Available Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset base of multiset topology induced by a multiset relation. Moreover, the relationships between generalized rough msets and mset topologies are given. In addition, an illustrative example is given to illustrate the relationships between different types of generalized definitions of rough multiset approximations.
Monastyrsky, M I
2006-01-01
This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.
DEFF Research Database (Denmark)
Schjøth, Lars; Frisvad, Jeppe Revall; Erleben, Kenny
2007-01-01
illumination features. This is often not desirable as these may lose clarity or vanish altogether. We present an accurate method for reconstruction of indirect illumination with photon mapping. Instead of reconstructing illumination using classic density estimation on finite points, we use the correlation...
Indian Academy of Sciences (India)
Volume 2 Issue 5 May 1997 pp 69-72 Feature Article. Molecule of the Month Molecular–Chameleon: Solvatochromism at its Iridescent Best! Photon Rao · More Details Fulltext PDF. Volume 16 Issue 12 December 2011 pp 1303-1306. Molecule of the Month - Molecular-Chameleon: Solvatochromism at its Iridescent Best!
Linear topologies and sequential compactness in topological modules
African Journals Online (AJOL)
We prove that an absolute semi-valued ring is rst-countable if the set of invertibles is separable and its closure contains 0. We also show that every linearly topologized topological module over an absolute semi-valued ring whose invertibles approach 0 has the trivial topology. We also show that every sequentially compact ...
Topological field theories and duality
International Nuclear Information System (INIS)
Stephany, J.; Universidad Simon Bolivar, Caracas
1996-05-01
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs
Topology optimization of viscoelastic rectifiers
DEFF Research Database (Denmark)
Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin
2012-01-01
An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...
Topological inflation with graceful exit
Energy Technology Data Exchange (ETDEWEB)
Marunović, Anja; Prokopec, Tomislav, E-mail: a.marunovic@uu.nl, E-mail: t.prokopec@uu.nl [Institute for Theoretical Physics, Spinoza Institute and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Postbus 80.195, 3508 TD Utrecht (Netherlands)
2016-04-01
We investigate a class of models of topological inflation in which a super-Hubble-sized global monopole seeds inflation. These models are attractive since inflation starts from rather generic initial conditions, but their not so attractive feature is that, unless symmetry is again restored, inflation never ends. In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation. While the monopole core grows during inflation, the growth stops after inflation, such that the monopole eventually enters the Hubble radius, and shrinks to its Minkowski space size, rendering it immaterial for the subsequent Universe's dynamics. Furthermore, we find that our model can produce cosmological perturbations that source CMB temperature fluctuations and seed large scale structure statistically consistent (within one standard deviation) with all available data. In particular, for small and (in our convention) negative nonminimal couplings, the scalar spectral index can be as large as n {sub s} ≅ 0.955, which is about one standard deviation lower than the central value quoted by the most recent Planck Collaboration.
Topological inflation with graceful exit
International Nuclear Information System (INIS)
Marunović, Anja; Prokopec, Tomislav
2016-01-01
We investigate a class of models of topological inflation in which a super-Hubble-sized global monopole seeds inflation. These models are attractive since inflation starts from rather generic initial conditions, but their not so attractive feature is that, unless symmetry is again restored, inflation never ends. In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation. While the monopole core grows during inflation, the growth stops after inflation, such that the monopole eventually enters the Hubble radius, and shrinks to its Minkowski space size, rendering it immaterial for the subsequent Universe's dynamics. Furthermore, we find that our model can produce cosmological perturbations that source CMB temperature fluctuations and seed large scale structure statistically consistent (within one standard deviation) with all available data. In particular, for small and (in our convention) negative nonminimal couplings, the scalar spectral index can be as large as n s ≅ 0.955, which is about one standard deviation lower than the central value quoted by the most recent Planck Collaboration.
Coherence Multiplex System Topologies
Meijerink, Arjan; Taniman, R.O.; Heideman, G.H.L.M.; van Etten, Wim
2007-01-01
Coherence multiplexing is a potentially inexpensive form of optical code-division multiple access, which is particularly suitable for short-range applications with moderate bandwidth requirements, such as access networks, LANs, or interconnects. Various topologies are known for constructing an
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...
Towards topological quantum computer
Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.
2018-01-01
Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
LHCb Topological Trigger Reoptimization
INSPIRE-00400931; Ilten, Philip; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Williams, Michael
2015-12-23
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. ...
Towards topological quantum computer
Directory of Open Access Journals (Sweden)
D. Melnikov
2018-01-01
Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
Topological Trigger Developments
Likhomanenko, Tatiana
2015-01-01
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger utilized a custom boosted decision tree algorithm, selected an almost 100% pure sample of b-hadrons with a typical efficiency of 60-70%, and its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and uBoost. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. These inclu...
Rendering the Topological Spines
Energy Technology Data Exchange (ETDEWEB)
Nieves-Rivera, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
Topology of Document Retrieval Systems.
Everett, Daniel M.; Cater, Steven C.
1992-01-01
Explains the use of a topological structure to examine the closeness between documents in retrieval systems and analyzes the topological structure of a vector-space model, a fuzzy-set model, an extended Boolean model, a probabilistic model, and a TIRS (Topological Information Retrieval System) model. Proofs for the results are appended. (17…
Noncommuting Momenta of Topological Solitons
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
Topological Properties of Superconducting Junctions
Pikulin, D.I.; Nazarov, Y.V.
Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of s-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the s-matrix is always topologically
Widespread spin polarization effects in photoemission from topological insulators
Energy Technology Data Exchange (ETDEWEB)
Jozwiak, C.; Chen, Y. L.; Fedorov, A. V.; Analytis, J. G.; Rotundu, C. R.; Schmid, A. K.; Denlinger, J. D.; Chuang, Y.-D.; Lee, D.-H.; Fisher, I. R.; Birgeneau, R. J.; Shen, Z.-X.; Hussain, Z.; Lanzara, A.
2011-06-22
High-resolution spin- and angle-resolved photoemission spectroscopy (spin-ARPES) was performed on the three-dimensional topological insulator Bi{sub 2}Se{sub 3} using a recently developed high-efficiency spectrometer. The topological surface state's helical spin structure is observed, in agreement with theoretical prediction. Spin textures of both chiralities, at energies above and below the Dirac point, are observed, and the spin structure is found to persist at room temperature. The measurements reveal additional unexpected spin polarization effects, which also originate from the spin-orbit interaction, but are well differentiated from topological physics by contrasting momentum and photon energy and polarization dependencies. These observations demonstrate significant deviations of photoelectron and quasiparticle spin polarizations. Our findings illustrate the inherent complexity of spin-resolved ARPES and demonstrate key considerations for interpreting experimental results.
Update on photon-photon collisions
International Nuclear Information System (INIS)
Arteaga-Romero, N.; Cochard, G.; Ong, S.; Amiens Univ., 80; Carimalo, C.; Kessler, P.; Nicolaidis, A.; Parisi, J.; Courau, A.
1980-03-01
This report is the continuation of the 'Update' of last year (L.P.C. 79-03, March 1979, in French). In Part I, the structure functions of the photon in QCD are examined. It is shown that, while large psub(T) hadron production is similar to some extent in γγ collisions and in hadron-hadron collisions, the point-like nature of the photon introduces new terms which are entirely calculable, providing new means to test the dynamics of strong interactions. In Part II, problems of analysis in γγ experiments are discussed. The pros and cons of various options with regard to the measurement of outgoing electrons (non-tagging, finite-angle tagging, tagging at 0 0 ) are compared. It is shown that (a) non-tagging may be applied to the study of a limited number of processes only; (b) finite-angle tagging counters allow for various possibilities (double-tagging, single-tagging, double anti-tagging), but none of them is entirely satisfactory; (c) the ideal measurement is double tagging at 0 0 , provided the problem of bremsstrahlung saturation of the tagging counters can be solved
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...
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Undergraduate topology a working textbook
McCluskey, Aisling
2014-01-01
This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp i
Multi-material topology design of laminates with strength criteria
DEFF Research Database (Denmark)
Lund, Erik
2012-01-01
The objective of this paper is to present a novel approach for multi-material topology optimization of laminated composite structures where strength constraints are taken into account together with other global structural performance measures. The topology design problem considered contains very...... many design variables, and when strength criteria are included in the problem, a very large number of criteria functions must be considered in the optimization problem to be solved. Thus, block aggregation methods are introduced, such that global strength measures are obtained. These formulations...... are illustrated for multi-material laminated design problems where the maximum failure index is minimized while compliance and mass constraints are taken into account....
Games for Topological Fixpoint Logic
Directory of Open Access Journals (Sweden)
Nick Bezhanishvili
2016-09-01
Full Text Available Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we introduce games characterising clopen fixpoints of monotone operators on Stone spaces. These fixpoint games allow us to characterise the semantics for our topological fixpoint logic using a two-player graph game. Adequacy of this game is the main result of our paper. Finally, we define bisimulations for the topological structures under consideration and use our game semantics to prove that the truth of a formula of our topological fixpoint logic is bisimulation-invariant.
Floquet topological insulators for sound
Fleury, Romain; Khanikaev, Alexander B.; Alù, Andrea
2016-06-01
The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential of topological acoustics. Here we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. We show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.
Modeling of Photonic Band Gap Crystals and Applications
Energy Technology Data Exchange (ETDEWEB)
El-Kady, Ihab Fathy [Iowa State Univ., Ames, IA (United States)
2002-01-01
In this work, the authors have undertaken a theoretical approach to the complex problem of modeling the flow of electromagnetic waves in photonic crystals. The focus is to address the feasibility of using the exciting phenomena of photonic gaps (PBG) in actual applications. The authors start by providing analytical derivations of the computational electromagnetic methods used in their work. They also present a detailed explanation of the physics underlying each approach, as well as a comparative study of the strengths and weaknesses of each method. The Plane Wave expansion, Transfer Matrix, and Finite Difference time Domain Methods are addressed. They also introduce a new theoretical approach, the Modal Expansion Method. They then shift the attention to actual applications. They begin with a discussion of 2D photonic crystal wave guides. The structure addressed consists of a 2D hexagonal structure of air cylinders in a layered dielectric background. Comparison with the performance of a conventional guide is made, as well as suggestions for enhancing it. The studies provide an upper theoretical limit on the performance of such guides, as they assumed no crystal imperfections and non-absorbing media. Next, they study 3D metallic PBG materials at near infrared and optical wavelengths. The main objective is to study the importance of absorption in the metal and the suitability of observing photonic band gaps in such structures. They study simple cubic structures where the metallic scatters are either cubes or interconnected metallic rods. Several metals are studied (aluminum, gold, copper, and silver). The effect of topology is addressed and isolated metallic cubes are found to be less lossy than the connected rod structures. The results reveal that the best performance is obtained by choosing metals with a large negative real part of the dielectric function, together with a relatively small imaginary part. Finally, they point out a new direction in photonic crystal
DEFF Research Database (Denmark)
Ekman, Ulrik
2015-01-01
This article discusses the issue of approaching the design of the ubiquitous city as a matter of topology. The general context here is the design of contemporary global urbanity in the form of u-cities, smart cities, or intelligent cities emerging with the second phase of network societies...... that increasingly develop mixed reality environments with context-aware out-of-the-box computing as well as the soci-ocultural and experiental horizon of a virtually and physically mobile citizenry. Design here must meet an ongoing and exceedingly complex interactivity among environmental, technical, social...... and personal multiplicities of urban nodes on the move. This chapter focuses on the design of a busy traffic intersection in the South Korean u-city Songdo. Hence, the discussion whether and how Songdo may be approached via design as topology primarily considers the situation, event, and experience in which...
Quist, Daniel A [Los Alamos, NM; Gavrilov, Eugene M [Los Alamos, NM; Fisk, Michael E [Jemez, NM
2008-01-15
A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.
Robinson, Michael
2014-01-01
Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
DEFF Research Database (Denmark)
Blok, Anders
2010-01-01
Climate change is quickly becoming a ubiquitous socionatural reality, mediating extremes of sociospatial scale from the bodily to the planetary. Although environmentalism invites us to ‘think globally and act locally', the meaning of these scalar designations remains ambiguous. This paper explores...... the topological presuppositions of social theory in the context of global climate change, asking how carbon emissions ‘translate' into various sociomaterial forms. Staging a meeting between Tim Ingold's phenomenology of globes and spheres and the social topologies of actor-network theory (ANT), the paper advances...... a ‘relational-scalar' analytics of spatial practices, technoscience, and power. As technoscience gradually constructs a networked global climate, this ‘grey box' comes to circulate within fluid social spaces, taking on new shades as it hybridizes knowledges, symbols, and practices. Global climates thus come...
Operator algebras and topology
International Nuclear Information System (INIS)
Schick, T.
2002-01-01
These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)
Topological confinement and superconductivity
Energy Technology Data Exchange (ETDEWEB)
Al-hassanieh, Dhaled A [Los Alamos National Laboratory; Batista, Cristian D [Los Alamos National Laboratory
2008-01-01
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in aID-system.
Technologies for converter topologies
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yan; Zhang, Haiyu
2017-02-28
In some embodiments of the disclosed inverter topologies, an inverter may include a full bridge LLC resonant converter, a first boost converter, and a second boost converter. In such embodiments, the first and second boost converters operate in an interleaved manner. In other disclosed embodiments, the inverter may include a half-bridge inverter circuit, a resonant circuit, a capacitor divider circuit, and a transformer.
Topological 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.
Derived length for arbitrary topological spaces
Directory of Open Access Journals (Sweden)
A. J. Jayanthan
1992-01-01
Full Text Available The notion of derived length is as old as that of ordinal numbers itself. It is also known as the Cantor-Bendixon length. It is defined only for dispersed (that is scattered spaces. In this paper this notion has been extended in a natural way for all topological spaces such that all its pleasing properties are retained. In this process we solve a problem posed by V. Kannan. ([1] Page 158.
International Nuclear Information System (INIS)
Tanaka, J.; Huke, K.; Chikawa, J.
1985-01-01
The Photon Factory (PF) was established on April 1, 1978 at KEK. The PF is a synchrotron radiation facility, which has a 2.5 GeV electron storage ring fully dedicated to the SR usage and a 2.5 GeV electron linac supplying electrons and positrons to the PF ring and the accumulation ring of TRISTAN (30 GeV electron-positron colliding machine). The PF consists of three departments, injector linac, light source, and instrumentation department. The facility is described
Tight Network Topology Dependent Bounds on Rounds of Communication
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...
Persistent topology for cryo-EM data analysis.
Xia, Kelin; Wei, Guo-Wei
2015-08-01
In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal-to-noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows that are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure Electron Microscopy Data (EMD 1129). Three helix models, an alpha-tubulin monomer model, an alpha-tubulin and beta-tubulin model, and an alpha-tubulin and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another, play little role in the traditional density fitting or optimization but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is
Topologically-protected one-way leaky waves in nonreciprocal plasmonic structures
Hassani Gangaraj, S. Ali; Monticone, Francesco
2018-03-01
We investigate topologically-protected unidirectional leaky waves on magnetized plasmonic structures acting as homogeneous photonic topological insulators. Our theoretical analyses and numerical experiments aim at unveiling the general properties of these exotic surface waves, and their nonreciprocal and topological nature. In particular, we study the behavior of topological leaky modes in stratified structures composed of a magnetized plasma at the interface with isotropic conventional media, and we show how to engineer their propagation and radiation properties, leading to topologically-protected backscattering-immune wave propagation, and highly directive and tunable radiation. Taking advantage of the non-trivial topological properties of these leaky modes, we also theoretically demonstrate advanced functionalities, including arbitrary re-routing of leaky waves on the surface of bodies with complex shapes, as well as the realization of topological leaky-wave (nano)antennas with isolated channels of radiation that are completely independent and separately tunable. Our findings help shedding light on the behavior of topologically-protected modes in open wave-guiding structures, and may open intriguing directions for future antenna generations based on topological structures, at microwaves and optical frequencies.
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
Directory of Open Access Journals (Sweden)
Qinghai Zhao
2015-01-01
Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.
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.
Higgsless superconductivity from topological defects in compact BF terms
Diamantini, M. Cristina; Trugenberger, Carlo A.
2015-02-01
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.
Double gyroid photonic crystal: synthesis and mid-infrared photonic characterization
Peng, Siying; Zhang, Runyu; Khabiboulline, Emil; Barim, Vitoria; Chen, Hongjie; Hon, Philip; Garcia, Juan; Sweatlock, Luke; Braun, Paul; Atwater, Harry
Gyroids are triply symmetric and have surfaces containing no straight lines. Single gyroid (SG) photonic crystals have a large band gap, while double gyroids (DG) with P-breaking symmetry possess Weyl points and topologically non-trivial surface states. These topologically protected states give rise to backscattering immune unidirectional transport. We have synthesized and characterized the first mid-IR gyroid photonic crystals, including both SGs and DGs with Weyl points. Polymer gyroid scaffold was written by DLW, followed by ALD of Al2O3, polymer removal and conformally coating of a-Si. The resulting DGs have Weyl points at 8 μ m and k between 0.3-0.5 π/a. Characterization of SG and DG have been performed by angle resolved mid-IR spectroscopy. The photonic bandstructure is constructed from angle resolved reflectance and transmittance spectra, all the way close to the light line. Constructed bandstructures from SGs exhibit a photonic bandgap. For DGs the bandstructures reveal defect photonic states emerging inside the bandgap. Strategies to observe protected surface states in DGs will be discussed.
Topological imprint for periodic orbits
International Nuclear Information System (INIS)
Martín, Jesús San; Moscoso, Ma José; Gómez, A González
2012-01-01
The more self-crossing points an orbit has the more complex it is. We introduce the topological imprint to characterize crossing points and focus on the period-doubling cascade. The period-doubling cascade topological imprint determines the topological imprint for orbits in chaotic bands. In addition, there is a closer link between this concept and the braids studied by Lettelier et al (2000 J. Phys. A: Math. Gen. 33 1809–25). (paper)
Intuitionistic supra fuzzy topological spaces
International Nuclear Information System (INIS)
Abbas, S.E.
2004-01-01
In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space
Lynch, Mark
2012-01-01
We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…
Chen, Wen-Jie; Xiao, Meng; Chan, C. T.
2016-01-01
Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest type of single Weyl nodes with a topological charge of 1 is difficult, then making a real crystal carrying higher topological charges may seem more challenging. Here we design, and fabricate using planar fabrication technology, a photonic crystal possessing single Weyl points (including type-II nodes) and multiple Weyl points with topological charges of 2 and 3. We characterize this photonic crystal and find nontrivial 2D bulk band gaps for a fixed kz and the associated surface modes. The robustness of these surface states against kz-preserving scattering is experimentally observed for the first time. PMID:27703140
OPTIMAL NETWORK TOPOLOGY DESIGN
Yuen, J. H.
1994-01-01
This program was developed as part of a research study on the topology design and performance analysis for the Space Station Information System (SSIS) network. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. It is intended that this new design technique consider all important performance measures explicitly and take into account the constraints due to various technical feasibilities. In the current program, technical constraints are taken care of by the user properly forming the starting set of candidate components (e.g. nonfeasible links are not included). As subsets are generated, they are tested to see if they form an acceptable network by checking that all requirements are satisfied. Thus the first acceptable subset encountered gives the cost-optimal topology satisfying all given constraints. The user must sort the set of "feasible" link elements in increasing order of their costs. The program prompts the user for the following information for each link: 1) cost, 2) connectivity (number of stations connected by the link), and 3) the stations connected by that link. Unless instructed to stop, the program generates all possible acceptable networks in increasing order of their total costs. The program is written only to generate topologies that are simply connected. Tests on reliability, delay, and other performance measures are discussed in the documentation, but have not been incorporated into the program. This program is written in PASCAL for interactive execution and has been implemented on an IBM PC series computer operating under PC DOS. The disk contains source code only. This program was developed in 1985.
Topologically clean distance fields.
Gyulassy, Attila; Duchaineau, Mark; Natarajan, Vijay; Pascucci, Valerio; Bringa, Eduardo; Higginbotham, Andrew; Hamann, Bernd
2007-01-01
Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the "difference" between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.
Topology Optimization - Engineering Contribution to Architectural Design
Tajs-Zielińska, Katarzyna; Bochenek, Bogdan
2017-10-01
The idea of the topology optimization is to find within a considered design domain the distribution of material that is optimal in some sense. Material, during optimization process, is redistributed and parts that are not necessary from objective point of view are removed. The result is a solid/void structure, for which an objective function is minimized. This paper presents an application of topology optimization to multi-material structures. The design domain defined by shape of a structure is divided into sub-regions, for which different materials are assigned. During design process material is relocated, but only within selected region. The proposed idea has been inspired by architectural designs like multi-material facades of buildings. The effectiveness of topology optimization is determined by proper choice of numerical optimization algorithm. This paper utilises very efficient heuristic method called Cellular Automata. Cellular Automata are mathematical, discrete idealization of a physical systems. Engineering implementation of Cellular Automata requires decomposition of the design domain into a uniform lattice of cells. It is assumed, that the interaction between cells takes place only within the neighbouring cells. The interaction is governed by simple, local update rules, which are based on heuristics or physical laws. The numerical studies show, that this method can be attractive alternative to traditional gradient-based algorithms. The proposed approach is evaluated by selected numerical examples of multi-material bridge structures, for which various material configurations are examined. The numerical studies demonstrated a significant influence the material sub-regions location on the final topologies. The influence of assumed volume fraction on final topologies for multi-material structures is also observed and discussed. The results of numerical calculations show, that this approach produces different results as compared with classical one
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.
Photon collider beam simulation with CAIN
Indian Academy of Sciences (India)
The CAIN simulation program was used to study the outgoing beam profile for the photon collider at ILC. The main aim of the analysis was to verify the feasibility of the photon linear collider running with 20 mrad electron beam crossing angle. The main problem is the distorted electron beam, which has to be removed from ...
Photonic crystal waveguides based on an antiresonant reflecting platform
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Frandsen, Lars Hagedorn; Fage-Pedersen, Jacob
2005-01-01
We apply the antiresonant reflecting layers arrangement to silicon-on-insulator based photonic crystal waveguides. Several layered structures with different combinations of materials (Si-SiO2, Si3N4-SiO2) and layer topology have been analysed. Numerical modelling using 3D Finite-Difference Time...
Isogeometric shape optimization of photonic crystals via Coons patches
DEFF Research Database (Denmark)
Qian, Xiaoping; Sigmund, Ole
2011-01-01
In this paper, we present an approach that extends isogeometric shape optimization from optimization of rectangular-like NURBS patches to the optimization of topologically complex geometries. We have successfully applied this approach in designing photonic crystals where complex geometries have...
Lieb polariton topological insulators
Li, Chunyan; Ye, Fangwei; Chen, Xianfeng; Kartashov, Yaroslav V.; Ferrando, Albert; Torner, Lluis; Skryabin, Dmitry V.
2018-02-01
We predict that the interplay between the spin-orbit coupling, stemming from the transverse electric-transverse magnetic energy splitting, and the Zeeman effect in semiconductor microcavities supporting exciton-polariton quasiparticles, results in the appearance of unidirectional linear topological edge states when the top microcavity mirror is patterned to form a truncated dislocated Lieb lattice of cylindrical pillars. Periodic nonlinear edge states are found to emerge from the linear ones. They are strongly localized across the interface and they are remarkably robust in comparison to their counterparts in honeycomb lattices. Such robustness makes possible the existence of nested unidirectional dark solitons that move steadily along the lattice edge.
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
Meldgaard, Morten
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...... of today, but – perhaps most importantly – also creating and producing architecture that is contemporaneous and reacts to the radical changes of the physical world which surrounds us in the increasingly artificial measures of new materialities and understandings thereof. The contributions range from...
Introduction to generalized topological spaces
Directory of Open Access Journals (Sweden)
Irina Zvina
2011-04-01
Full Text Available We introduce the notion of generalized topological space (gt-space. Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants in terms of generalized spaces.
Large-area metallic photonic lattices for military applications.
Energy Technology Data Exchange (ETDEWEB)
Luk, Ting Shan
2007-11-01
In this project we developed photonic crystal modeling capability and fabrication technology that is scaleable to large area. An intelligent optimization code was developed to find the optimal structure for the desired spectral response. In terms of fabrication, an exhaustive survey of fabrication techniques that would meet the large area requirement was reduced to Deep X-ray Lithography (DXRL) and nano-imprint. Using DXRL, we fabricated a gold logpile photonic crystal in the <100> plane. For the nano-imprint technique, we fabricated a cubic array of gold squares. These two examples also represent two classes of metallic photonic crystal topologies, the connected network and cermet arrangement.
The Causes and Consequences of Topological Stress during DNA Replication.
Keszthelyi, Andrea; Minchell, Nicola E; Baxter, Jonathan
2016-12-21
The faithful replication of sister chromatids is essential for genomic integrity in every cell division. The replication machinery must overcome numerous difficulties in every round of replication, including DNA topological stress. Topological stress arises due to the double-stranded helical nature of DNA. When the strands are pulled apart for replication to occur, the intertwining of the double helix must also be resolved or topological stress will arise. This intrinsic problem is exacerbated by specific chromosomal contexts encountered during DNA replication. The convergence of two replicons during termination, the presence of stable protein-DNA complexes and active transcription can all lead to topological stresses being imposed upon DNA replication. Here we describe how replication forks respond to topological stress by replication fork rotation and fork reversal. We also discuss the genomic contexts where topological stress is likely to occur in eukaryotes, focusing on the contribution of transcription. Finally, we describe how topological stress, and the ways forks respond to it, may contribute to genomic instability in cells.
Extending Topological Abelian Groups by the Unit Circle
Directory of Open Access Journals (Sweden)
Hugo J. Bello
2013-01-01
Full Text Available A twisted sum in the category of topological Abelian groups is a short exact sequence 0→Y→X→Z→0 where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to 0→Y→Y×Z→Z→0. We study the class STG of topological groups G for which every twisted sum 0→→X→G→0 splits. We prove that this class contains Hausdorff locally precompact groups, sequential direct limits of locally compact groups, and topological groups with ℒ∞ topologies. We also prove that it is closed by taking open and dense subgroups, quotients by dually embedded subgroups, and coproducts. As means to find further subclasses of STG, we use the connection between extensions of the form 0→→X→G→0 and quasi-characters on G, as well as three-space problems for topological groups. The subject is inspired on some concepts known in the framework of topological vector spaces such as the notion of -space, which were interpreted for topological groups by Cabello.
Resonance formation in photon-photon collisions
Energy Technology Data Exchange (ETDEWEB)
Gidal, G.
1988-08-01
Recent experimental progress on resonance formation in photon-photon collisions is reviewed with particular emphasis on the pseudoscalar and tensor nonents and on the ..gamma gamma..* production of spin-one resonances. 37 refs., 17 figs., 5 tabs.
Energy Technology Data Exchange (ETDEWEB)
Bauer, W.
2007-03-15
The goal of this diploma thesis is to present an overview of how to reduce the problem of topology change of general spacetimes to the investigation of elementary cobordisms. In the following we investigate the possibility to construct quantum fields on elementary cobordisms, in particular we discuss the trousers topology. Trying to avoid the problems occuring at spacetimes with instant topology change we use a model for simulating topology change. We construct the algebra of observables for a free scalar field with the algebraic approach to quantum field theory. Therefore we determine a fundamental solution of the eld equation. (orig.)
Topology optimization of metallic devices for microwave applications
DEFF Research Database (Denmark)
Aage, Niels; Mortensen, Asger; Sigmund, Ole
2010-01-01
is the skin depth, which calls for highly refined meshing in order to capture the physics. The skin depth problem has therefore prohibited the application of topology optimization to this class of problem. We present a design parameterization that remedies these numerical issues, by the interpolation...
Graph theory data for topological quantum chemistry
Vergniory, M. G.; Elcoro, L.; Wang, Zhijun; Cano, Jennifer; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei; Bradlyn, Barry
2017-08-01
Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.
Tunable Multiband Microwave Photonic Filters
Directory of Open Access Journals (Sweden)
Mable P. Fok
2017-11-01
Full Text Available The increasing demand for multifunctional devices, the use of cognitive wireless technology to solve the frequency resource shortage problem, as well as the capabilities and operational flexibility necessary to meet ever-changing environment result in an urgent need of multiband wireless communications. Spectral filter is an essential part of any communication systems, and in the case of multiband wireless communications, tunable multiband RF filters are required for channel selection, noise/interference removal, and RF signal processing. Unfortunately, it is difficult for RF electronics to achieve both tunable and multiband spectral filtering. Recent advancements of microwave photonics have proven itself to be a promising candidate to solve various challenges in RF electronics including spectral filtering, however, the development of multiband microwave photonic filtering still faces lots of difficulties, due to the limited scalability and tunability of existing microwave photonic schemes. In this review paper, we first discuss the challenges that were facing by multiband microwave photonic filter, then we review recent techniques that have been developed to tackle the challenge and lead to promising developments of tunable microwave photonic multiband filters. The successful design and implementation of tunable microwave photonic multiband filter facilitate the vision of dynamic multiband wireless communications and radio frequency signal processing for commercial, defense, and civilian applications.
1997-01-01
The origins of this volume can be traced back to a conference on "Ethics, Economic and Business" organized by Columbia Busi ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana. Preliminary versions of several of the papers were presented at that meeting. In July 1994 the Fields Institute of Mathematical Sciences sponsored a workshop on "Geometry, Topology and Markets": additional papers and more refined versions of the original papers were presented there. They were published in their present versions in Social Choice and Wel fare, volume 14, number 2, 1997. The common aim of these workshops and this volume is to crystallize research in an area which has emerged rapidly in the last fifteen years, the area of topological approaches to social choice and the theory of games. The area is attracting increasing interest from social choice theorists, game theorists, mathematical econ omists and mathematicians, yet there is no authoritative collection of papers in the a...
Topology with applications topological spaces via near and far
Naimpally, Somashekhar A
2013-01-01
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces. This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising. It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and...
Directory of Open Access Journals (Sweden)
L. Baulieu
2016-11-01
Full Text Available We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al. and condensed matter properties (Kane et al., where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Complexity of generic biochemical circuits: topology versus strength of interactions
Tikhonov, Mikhail; Bialek, William
2016-12-01
The historical focus on network topology as a determinant of biological function is still largely maintained today, illustrated by the rise of structure-only approaches to network analysis. However, biochemical circuits and genetic regulatory networks are defined both by their topology and by a multitude of continuously adjustable parameters, such as the strength of interactions between nodes, also recognized as important. Here we present a class of simple perceptron-based Boolean models within which comparing the relative importance of topology versus interaction strengths becomes a quantitatively well-posed problem. We quantify the intuition that for generic networks, optimization of interaction strengths is a crucial ingredient of achieving high complexity, defined here as the number of fixed points the network can accommodate. We propose a new methodology for characterizing the relative role of parameter optimization for topologies of a given class.
Coverings, Networks and Weak Topologies
Czech Academy of Sciences Publication Activity Database
Dow, A.; Junnila, H.; Pelant, Jan
2006-01-01
Roč. 53, č. 2 (2006), s. 287-320 ISSN 0025-5793 R&D Projects: GA ČR GA201/97/0216 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * weak topologies * networks topologies Subject RIV: BA - General Mathematics
A Course on Topological Groups
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 8. A Course on Topological Groups - A Pellucid Little Book on Topological Groups. K Parthasarathy. Book Review Volume 2 Issue 8 August 1997 pp 82-83. Fulltext. Click here to view fulltext PDF. Permanent link:
Topology optimization of turbulent flows
DEFF Research Database (Denmark)
Dilgen, Cetin B.; Dilgen, Sumer B.; Fuhrman, David R.
2018-01-01
The aim of this work is to present a fast and viable approach for taking into account turbulence in topology optimization of complex fluid flow systems, without resorting to any simplifying assumptions in the derivation of discrete adjoints. Topology optimization is an iterative gradient...
Redundancy of multiset topological spaces
Ghareeb, A.
2016-01-01
In this paper, we prove the redundancies of multiset topologies. It is shown that there is a complement preserving isomorphism between $(P^\\star(U),\\sqsubseteq)$ and $(\\mathcal{P}(X\\times\\mathbb{N}),\\subseteq)$. It therefore follows that multiset topologies are superfluous and unnecessary in the theoretical view point.
Topological phases of quantum matter
Indian Academy of Sciences (India)
Although first to mention topological phases, not really the first Nobel prize for topological phases. First - 1982 Nobel to Klaus von Klitzing for `discovery of quantised. Hall effect '. Second - 1998 Nobel to RobertLaughlin, Horst Stormer and. Daniel Tsui for `discovery of a new form of quantum fluid with fractionally charged ...
Cartography – morphology – topology
DEFF Research Database (Denmark)
Dinesen, Cort Ross; Peder Pedersen, Claus
I 2004 a Summer School was established on the Greek island of Hydra. The was to be the basis of research-based morphological and topological studies, which have since taken place for 4 weeks of every year. Starting with Hydra’s topography different ways of considering topology were developed...
On Neutrosophic Soft Topological Space
Directory of Open Access Journals (Sweden)
Tuhin Bera
2018-03-01
Full Text Available In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also. Then, the notion of neutrosophic soft continuous mapping on a neutrosophic soft topological space and it’s properties are developed here.
Topology optimized RF MEMS switches
DEFF Research Database (Denmark)
Philippine, M. A.; Zareie, H.; Sigmund, Ole
2013-01-01
Topology optimization is a rigorous and powerful method that should become a standard MEMS design tool - it can produce unique and non-intuitive designs that meet complex objectives and can dramatically improve the performance and reliability of MEMS devices. We present successful uses of topolog...
Observational modeling of topological spaces
International Nuclear Information System (INIS)
Molaei, M.R.
2009-01-01
In this paper a model for a multi-dimensional observer by using of the fuzzy theory is presented. Relative form of Tychonoff theorem is proved. The notion of topological entropy is extended. The persistence of relative topological entropy under relative conjugate relation is proved.
Huang, Huaqing; Jin, Kyung-Hwan; Zhang, Shunhong; Liu, Feng
2018-02-22
Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y 2 C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y 2 C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y 2 C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences
Directory of Open Access Journals (Sweden)
Lamia Jaafar Belaid
2010-01-01
Full Text Available Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting.
Photon tagging; considerations for an ELFE DESY proposal
International Nuclear Information System (INIS)
Mackenzie, J.A.
1996-01-01
Photon Tagging in the 5-15 GeV region is considered. The advantage of performing exclusive measurements in relation to obtainable photon flux in described. Finally some technical problems in relation to implementing a photon beam in the framework of the ELFE at DESY proposal are discussed. (author)
Combined Shape and Topology Optimization
DEFF Research Database (Denmark)
Christiansen, Asger Nyman
Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable...... Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface...... representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead...
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....
Topological susceptibility from the overlap
DEFF Research Database (Denmark)
Del Debbio, Luigi; Pica, Claudio
2003-01-01
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge....... Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study...... the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high...
Camara, Pablo G; Marchesano, Fernando
2011-01-01
Type II string compactifications to 4d generically contain massless Ramond-Ramond U(1) gauge symmetries. However there is no massless matter charged under these U(1)'s, which makes a priori difficult to measure any physical consequences of their existence. There is however a window of opportunity if these RR U(1)'s mix with the hypercharge $U(1)_Y$ (hence with the photon). In this paper we study in detail different avenues by which $U(1)_{RR}$ bosons may mix with D-brane U(1)'s. We concentrate on Type IIA orientifolds and their M-theory lift, and provide geometric criteria for the existence of such mixing, which may occur either via standard kinetic mixing or via the mass terms induced by St\\"uckelberg couplings. The latter case is particularly interesting, and appears whenever D-branes wrap torsional $p$-cycles in the compactification manifold. We also show that in the presence of torsional cycles discrete gauge symmetries and Aharanov-Bohm strings and particles appear in the 4d effective action, and that ty...
Transportation Network Topologies
Alexandrov, Natalia (Editor)
2004-01-01
The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.
International Nuclear Information System (INIS)
Gregoire, Thomas; Wacker, Jay G.
2002-01-01
New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking. (author)
Degiorgio, Vittorio
2016-01-01
This extended and revised edition will serve as a concise, self-contained, up-to-date introduction to Photonics for undergraduate students. It can also be used as a primer by researchers and professionals who start working in the field. Blending theory with technical descriptions, the book covers a wide range of topics, including the general mechanism of laser action, continuous and pulsed laser operation, optical propagation in isotropic and anisotropic media, operating principles and structure of passive optical components, electro-optic and acousto-optic modulation, solid-state lasers, semiconductor lasers and LEDs, nonlinear optical phenomena, and optical fiber components and devices. The book concludes with an overview of applications, including optical communications, telemetry and sensing, industrial and biomedical applications, solid-state lighting, displays, and photovoltaics. This second edition includes a set of problems at the end of all but the last chapter. These problems deal with numerical c...
INDIA: Photon multiplicity detector
International Nuclear Information System (INIS)
Anon.
1995-01-01
Full text: The team of Indian scientists from Calcutta's Variable Energy Cyclotron Centre, Bhubaneswar Institute of Physics, Panjab (Chandigarh), Rajasthan (Jaipur) and Jammu in collaboration with GSI Darmstadt have contributed a large and highly granular preshower photon multiplicity detector (PMD) for the WA98 experiment at the CERN SPS proton synchrotron. This experiment studies high energy collisions of lead ions and will measure both charged particle and photon multiplicity in a large overlap region. The motivation for measuring photon multiplicity in ultra-relativistic heavy ion collisions stems from theoretical predictions of changes in the relative production of photons and charged particles in the phase transition of hadronic matter to quarkgluon plasma and its subsequent hadronization. The photon multiplicity detector consists of a matrix of scintillator pads placed in light-tight boxes and mounted behind the lead converter plates. The light from the scintillator pads is transported to the readout system using wavelength shifting (WLS) fibres. Developing on the team's earlier experience with a smaller version for the WA93 experiment (September 1991, page 16), several modifications were incorporated to improve light collection and transport. Use of improved WLS fibres, short WLS pieces to minimize self-absorption, and thermal splicing with long clear fibres were some of the important changes incorporated. Tests showed signficantly improved light collection. The scintillator pads were fabricated at all the five collaborating centres in India and the complicated assembly in the detector box modules carried out at the Variable Energy Cyclotron Centre, Calcutta. More than 400 lead converter plates were machined in Calcutta to rigorous tolerances of 0.2 mm. The assembled detector box modules and lead plates were shipped to CERN in spring 1994 for tests and installation. The WA98 PMD consists of over 50,000 scintillator pads of sizes varying from 15 to
COMPACTNESS IN INTUITIONISTIC FUZZY MULTISET TOPOLOGY
Kunnambath, Shinoj Thekke; John, Sunil Jacob
2017-01-01
– In this paper, we discussVarious properties of Compact and Homeomorphic Intuitionistic Fuzzy Multiset Topological spacesarious properties of Compact and Homeomorphic Intuitionistic Fuzzy Multiset Topological spaces
Zeng, Lunwu; Xu, Jin; Wang, Chengen; Zhang, Jianhua; Zhao, Yuting; Zeng, Jing; Song, Runxia
2017-12-07
When space (time) translation symmetry is spontaneously broken, the space crystal (time crystal) forms; when permittivity and permeability periodically vary with space (time), the photonic crystal (photonic time crystal) forms. We proposed the concept of photonic time crystal and rewritten the Maxwell's equations. Utilizing Finite Difference Time Domain (FDTD) method, we simulated electromagnetic wave propagation in photonic time crystal and photonic space-time crystal, the simulation results show that more intensive scatter fields can obtained in photonic time crystal and photonic space-time crystal.
Mixed methods for viscoelastodynamics and topology optimization
Directory of Open Access Journals (Sweden)
Giacomo Maurelli
2014-07-01
Full Text Available A truly-mixed approach for the analysis of viscoelastic structures and continua is presented. An additive decomposition of the stress state into a viscoelastic part and a purely elastic one is introduced along with an Hellinger-Reissner variational principle wherein the stress represents the main variable of the formulation whereas the kinematic descriptor (that in the case at hand is the velocity field acts as Lagrange multiplier. The resulting problem is a Differential Algebraic Equation (DAE because of the need to introduce static Lagrange multipliers to comply with the Cauchy boundary condition on the stress. The associated eigenvalue problem is known in the literature as constrained eigenvalue problem and poses several difficulties for its solution that are addressed in the paper. The second part of the paper proposes a topology optimization approach for the rationale design of viscoelastic structures and continua. Details concerning density interpolation, compliance problems and eigenvalue-based objectives are given. Worked numerical examples are presented concerning both the dynamic analysis of viscoelastic structures and their topology optimization.
Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens; von Oppen, Felix
2017-07-01
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall-superconductor hybrids.
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.
Quintic quasi-topological gravity
Energy Technology Data Exchange (ETDEWEB)
Cisterna, Adolfo [Vicerrectoría académica, Universidad Central de Chile,Toesca 1783 Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile,Casilla 567, Valdivia (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Física, Universidad de Talca,Casilla 747, Talca (Chile); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla, 160-C, Concepción (Chile)
2017-04-11
We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R{sup 5} terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff’s Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler’s polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in https://arxiv.org/abs/1003.4773, the general geometric structure of these Lagrangians remains an open problem.
An efficient approach for reliability-based topology optimization
Kanakasabai, Pugazhendhi; Dhingra, Anoop K.
2016-01-01
This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15-30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.
Knots, topology and quantum field theories
International Nuclear Information System (INIS)
Lusanna, L.
1989-01-01
The title of the workshop, Knots, Topology and Quantum Field Theory, accurate reflected the topics discussed. There have been important developments in mathematical and quantum field theory in the past few years, which had a large impact on physicist thinking. It is historically unusual and pleasing that these developments are taking place as a result of an intense interaction between mathematical physicists and mathematician. On the one hand, topological concepts and methods are playing an increasingly important lead to novel mathematical concepts: for instance, the study of quantum groups open a new chapter in the deformation theory of Lie algebras. These developments at present will lead to new insights into the theory of elementary particles and their interactions. In essence, the talks dealt with three, broadly defined areas of theoretical physics. One was topological quantum field theories, the other the problem of quantum groups and the third one certain aspects of more traditional field theories, such as, for instance, quantum gravity. These topics, however, are interrelated and the general theme of the workshop defies rigid classification; this was evident from the cross references to be found in almo all the talks
International Nuclear Information System (INIS)
Shaner, J.W.
1979-01-01
Lasers developed for fusion applications now have the capability of creating pressures in excess of 100 Mbar in the laboratory. The capability of these lasers for making high pressure equation of state measurements, progress toward that goal, and the problems which stand in the way are reviewed
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
topological soliton solutions to some time-fractional differential equations. M MIRZAZADEH ... Biswas et al [21,23–27] obtained optical solitons and soliton ..... nonlinear fractional partial differential equations in mathematical and physical sciences.
Metallic photonic band-gap materials
International Nuclear Information System (INIS)
Sigalas, M.M.; Chan, C.T.; Ho, K.M.; Soukoulis, C.M.
1995-01-01
We calculate the transmission and absorption of electromagnetic waves propagating in two-dimensional (2D) and 3D periodic metallic photonic band-gap (PBG) structures. For 2D systems, there is substantial difference between the s- and p-polarized waves. The p-polarized waves exhibit behavior similar to the dielectric PBG's. But, the s-polarized waves have a cutoff frequency below which there are no propagating modes. For 3D systems, the results are qualitatively the same for both polarizations but there are important differences related to the topology of the structure. For 3D structures with isolated metallic scatterers (cermet topology), the behavior is similar to that of the dielectric PBG's, while for 3D structures with the metal forming a continuous network (network topology), there is a cutoff frequency below which there are no propagating modes. The systems with the network topology may have some interesting applications for frequencies less than about 1 THz where the absorption can be neglected. We also study the role of the defects in the metallic structures
Spherical Orbifolds for Cosmic Topology
International Nuclear Information System (INIS)
Kramer, Peter
2012-01-01
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.
Spin Gauge Interactions as a Topological Mechanism of Superconductivity
Dutta Choudhury, Ishita
2017-12-01
We talk about a low energy, effective, topological theory of superconductivity in which a topological mass term is radiatively induced in one loop effective action. In this field theoretic model, an antisymmetric tensor field couples with the vorticity current of charged Dirac fermions in the Lagrangian. The fermion loop generates a coupling between the gauge field and the antisymmetric tensor field below an ultraviolet cut-off. The spin interactions mediated by the antisymmetric tensor field induces a mass for the photon field indicating Meissner effect. The dual antisymmetric tensor field produces a current which satisfies the relativistic version of the London equations of superconductivity. In the non-relativistic limit, the static effective potential shows a linear, always attractive term between two electrons. Thus, the theory can be considered as an alternative, low energy, effective field theory of superconductivity without spontaneous symmetry breaking.
Unconventional quantum Hall effect in Floquet topological insulators
Tahir, M.
2016-07-27
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the lights polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity αyx = 0 at zero Fermi energy, to a Hall insulator state with αyx = e2/2h. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at (±1/2,±3/2,±5/2, ...)e2/h. © 2016 IOP Publishing Ltd Printed in the UK.
Spin Gauge Interactions as a Topological Mechanism of Superconductivity
Directory of Open Access Journals (Sweden)
Dutta Choudhury Ishita
2017-01-01
Full Text Available We talk about a low energy, effective, topological theory of superconductivity in which a topological mass term is radiatively induced in one loop effective action. In this field theoretic model, an antisymmetric tensor field couples with the vorticity current of charged Dirac fermions in the Lagrangian. The fermion loop generates a coupling between the gauge field and the antisymmetric tensor field below an ultraviolet cut-off. The spin interactions mediated by the antisymmetric tensor field induces a mass for the photon field indicating Meissner effect. The dual antisymmetric tensor field produces a current which satisfies the relativistic version of the London equations of superconductivity. In the non-relativistic limit, the static effective potential shows a linear, always attractive term between two electrons. Thus, the theory can be considered as an alternative, low energy, effective field theory of superconductivity without spontaneous symmetry breaking.
Topologically protected states in one-dimensional systems
Fefferman, C L; Weinstein, M I
2017-01-01
The authors study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". They then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
3D Modeling from Photos Given Topological Information.
Kim, Young Min; Cho, Junghyun; Ahn, Sang Chul
2016-09-01
Reconstructing 3D models given a single-view 2D information is inherently an ill-posed problem and requires additional information such as shape prior or user input.We introduce a method to generate multiple 3D models of a particular category given corresponding photographs when the topological information is known. While there is a wide range of shapes for an object of a particular category, the basic topology usually remains constant.In consequence, the topological prior needs to be provided only once for each category and can be easily acquired by consulting an existing database of 3D models or by user input. The input of topological description is only connectivity information between parts; this is in contrast to previous approaches that have required users to interactively mark individual parts. Given the silhouette of an object and the topology, our system automatically finds a skeleton and generates a textured 3D model by jointly fitting multiple parts. The proposed method, therefore, opens the possibility of generating a large number of 3D models by consulting a massive number of photographs. We demonstrate examples of the topological prior and reconstructed 3D models using photos.
PS-Regular Sets in Topology and Generalized Topology
Directory of Open Access Journals (Sweden)
Ankit Gupta
2014-01-01
Full Text Available We define and study a new class of regular sets called PS-regular sets. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided using PS-regular sets. Semiconnectedness is characterized by using PS-regular sets. PS-continuity and almost PS-continuity are introduced and investigated.
Photonic Crystals Towards Nanoscale Photonic Devices
Lourtioz, Jean-Michel; Berger, Vincent; Gérard, Jean-Michel; Maystre, Daniel; Tchelnokov, Alexis
2005-01-01
Just like the periodical crystalline potential in solid-state crystals determines their properties for the conduction of electrons, the periodical structuring of photonic crystals leads to envisioning the possibility of achieving a control of the photon flux in dielectric and metallic materials. The use of photonic crystals as a cage for storing, filtering or guiding light at the wavelength scale thus paves the way to the realisation of optical and optoelectronic devices with ultimate properties and dimensions. This should contribute toward meeting the demands for a greater miniaturisation that the processing of an ever increasing number of data requires. Photonic Crystals intends at providing students and researchers from different fields with the theoretical background needed for modelling photonic crystals and their optical properties, while at the same time presenting the large variety of devices, from optics to microwaves, where photonic crystals have found applications. As such, it aims at building brid...
Photonic Crystals Towards Nanoscale Photonic Devices
Lourtioz, Jean-Michel; Berger, Vincent; Gérard, Jean-Michel; Maystre, Daniel; Tchelnokov, Alexei; Pagnoux, Dominique
2008-01-01
Just like the periodical crystalline potential in solid state crystals determines their properties for the conduction of electrons, the periodical structuring of photonic crystals leads to envisioning the possibility of achieving a control of the photon flux in dielectric and metallic materials. The use of photonic crystals as cages for storing, filtering or guiding light at the wavelength scale paves the way to the realization of optical and optoelectronic devices with ultimate properties and dimensions. This will contribute towards meeting the demands for greater miniaturization imposed by the processing of an ever increasing number of data. Photonic Crystals will provide students and researchers from different fields with the theoretical background required for modelling photonic crystals and their optical properties, while at the same time presenting the large variety of devices, ranging from optics to microwaves, where photonic crystals have found application. As such, it aims at building bridges between...
Habs, D.; Günther, M. M.; Jentschel, M.; Thirolf, P. G.
2012-07-01
With the planned new γ-beam facilities like MEGa-ray at LLNL (USA) or ELI-NP at Bucharest (Romania) with 1013 γ/s and a band width of ΔEγ/Eγ≈10-3, a new era of γ beams with energies up to 20MeV comes into operation, compared to the present world-leading HIγS facility at Duke University (USA) with 108 γ/s and ΔEγ/Eγ≈3ṡ10-2. In the long run even a seeded quantum FEL for γ beams may become possible, with much higher brilliance and spectral flux. At the same time new exciting possibilities open up for focused γ beams. Here we describe a new experiment at the γ beam of the ILL reactor (Grenoble, France), where we observed for the first time that the index of refraction for γ beams is determined by virtual pair creation. Using a combination of refractive and reflective optics, efficient monochromators for γ beams are being developed. Thus, we have to optimize the total system: the γ-beam facility, the γ-beam optics and γ detectors. We can trade γ intensity for band width, going down to ΔEγ/Eγ≈10-6 and address individual nuclear levels. The term "nuclear photonics" stresses the importance of nuclear applications. We can address with γ-beams individual nuclear isotopes and not just elements like with X-ray beams. Compared to X rays, γ beams can penetrate much deeper into big samples like radioactive waste barrels, motors or batteries. We can perform tomography and microscopy studies by focusing down to μm resolution using Nuclear Resonance Fluorescence (NRF) for detection with eV resolution and high spatial resolution at the same time. We discuss the dominating M1 and E1 excitations like the scissors mode, two-phonon quadrupole octupole excitations, pygmy dipole excitations or giant dipole excitations under the new facet of applications. We find many new applications in biomedicine, green energy, radioactive waste management or homeland security. Also more brilliant secondary beams of neutrons and positrons can be produced.
Multiscale topology optimization of solid and fluid structures
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe
This thesis considers the application of the topology optimization method to multiscale problems, specifically the fluid-structure interaction problem. By multiple-scale methods the governing equations, the Navier-Cauchy and the incompressible Navier-Stokes equations are expanded and separated...... leaving a set of micro- and macroscale equations for the interaction modeling. The topology optimization method is applied to the material design in order to optimize the pressure coupling properties of porous materials. Furthermore, by combining both the material design and the macroscopic modeling......, it is shown that the material microstructure can be optimized with respect to application scale properties. A poroelastic actuator consisting of two saturated porous materials is optimized using this approach. Based on the homogenization of a fixed microstructure topology, material design interpolation...
Topological Fulde-Ferrell superfluid in spin-orbit-coupled atomic Fermi gases
Liu, Xia-Ji; Hu, Hui
2013-08-01
We theoretically predict a topological matter—topological inhomogeneous Fulde-Ferrell superfluid—in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near s-wave Feshbach resonances. The realization of such a spin-orbit-coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a nontrivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.
Energy Technology Data Exchange (ETDEWEB)
Swinteck, N., E-mail: swinteck@email.arizona.edu; Matsuo, S.; Runge, K.; Lucas, P.; Deymier, P. A. [Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721 (United States); Vasseur, J. O. [Institut d' Electronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, Cité Scientifique, 59652 Villeneuve d' Ascq Cedex (France)
2015-08-14
Recent progress in electronic and electromagnetic topological insulators has led to the demonstration of one way propagation of electron and photon edge states and the possibility of immunity to backscattering by edge defects. Unfortunately, such topologically protected propagation of waves in the bulk of a material has not been observed. We show, in the case of sound/elastic waves, that bulk waves with unidirectional backscattering-immune topological states can be observed in a time-dependent elastic superlattice. The superlattice is realized via spatial and temporal modulation of the stiffness of an elastic material. Bulk elastic waves in this superlattice are supported by a manifold in momentum space with the topology of a single twist Möbius strip. Our results demonstrate the possibility of attaining one way transport and immunity to scattering of bulk elastic waves.
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
On the usefulness of non-gradient approaches in topology optimization
DEFF Research Database (Denmark)
Sigmund, Ole
2011-01-01
Topology optimization is a highly developed tool for structural design and is by now being extensively used in mechanical, automotive and aerospace industries throughout the world. Gradient-based topology optimization algorithms may efficiently solve fine-resolution problems with thousands and up...