Topology of generalized spinors and chiral anomaly
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Joint Topology Identification and State Estimation in Unobservable Distribution Grids
Many distribution system operations (e.g., state estimation, control, fault detection/localization) rely on the assumption that the underlying topology is accurately defined. In general, topology identification is a challenging problem in distribution systems as these systems are unobservable with a very limited number of available measurements. In this paper, we tackle this problem by designing a compressive sensing framework that jointly estimates the systems states and network topology via an integrated mixed integer nonlinear program (MINLP) formulation. Here, two reformulations of the original MINLP problems are investigated. Firstly, in order to remove the nonlinearity in the MINLP formulation, a mixed integer linear programming (MILP) problem that employs auxiliary variables is derived. Furthermore, to achieve a faster solution, convex relaxation of the original formulation is derived. Finally, using a Markovian model for topology changes, prior information about system topology is used to improve topology identification particularly when a limited amount of measurements is available. Simulation results on IEEE 37-bus test feeder and IEEE 123-bus test feeder illustrate the efficiency and scalability of the proposed approaches from both state estimation and topology identification point of view (even with 30% of available data).
42 ENGINEERING↗
Proliferation transitions from a topological phase in 2+1 dimensions
We consider phase transitions out of a general topological phase in 2+1 dimensions. We assume that the transition is triggered by a single Abelian anyon, which becomes light near the transition and whose worldlines proliferate after the transition. (This proliferation is often referred to as “condensation.”) We describe the transition using a continuum field theory obtained by coupling the corresponding topological quantum field theory (TQFT) to a single complex scalar field associated with this anyon. With these assumptions, we find the most general relativistic field theory for such a transition. Even though for a given TQFT and a choice of anyon, there are infinitely many such field theories, the transition theory depends on only a single additional integer parameter. We analyze all these theories, their global symmetries, and their phases. In generic cases, the theory after the transition can be related to the original one via an Abelian hierarchy construction. In special cases, the theory after the transition is gapless, and with a particular deformation, it is related to the original TQFT by gauging an anomaly-free one-form global symmetry. We also explore the enrichment of this setup by a global U(1) symmetry. In some cases, enriching the original TQFT is incompatible with the full transition theory. Lastly, we demonstrate our construction with many specific examples.
Anyons↗
Recursive dynamics for flexible multibody systems using spatial operators
Due to their structural flexibility, spacecraft and space manipulators are multibody systems with complex dynamics and possess a large number of degrees of freedom. Here the spatial operator algebra methodology is used to develop a new dynamics formulation and spatially recursive algorithms for such flexible multibody systems. A key feature of the formulation is that the operator description of the flexible system dynamics is identical in form to the corresponding operator description of the dynamics of rigid multibody systems. A significant advantage of this unifying approach is that it allows ideas and techniques for rigid multibody systems to be easily applied to flexible multibody systems. The algorithms use standard finite-element and assumed modes models for the individual body deformation. A Newton-Euler Operator Factorization of the mass matrix of the multibody system is first developed. It forms the basis for recursive algorithms such as for the inverse dynamics, the computation of the mass matrix, and the composite body forward dynamics for the system. Subsequently, an alternative Innovations Operator Factorization of the mass matrix, each of whose factors is invertible, is developed. It leads to an operator expression for the inverse of the mass matrix, and forms the basis for the recursive articulated body forward dynamics algorithm for the flexible multibody system. For simplicity, most of the development here focuses on serial chain multibody systems. However, extensions of the algorithms to general topology flexible multibody systems are described. While the computational cost of the algorithms depends on factors such as the topology and the amount of flexibility in the multibody system, in general, it appears that in contrast to the rigid multibody case, the articulated body forward dynamics algorithm is the more efficient algorithm for flexible multibody systems containing even a small number of flexible bodies. The variety of algorithms described here permits a user to choose the algorithm which is optimal for the multibody system at hand. The availability of a number of algorithms is even more important for real-time applications, where implementation on parallel processors or custom computing hardware is often necessary to maximize speed.
Jain, A.↗
The Branes Behind Generalized Symmetry Operators
The modern approach to m-form global symmetries in a d-dimensional quantum field theory (QFT) entails specifying dimension d–m–1 topological generalized symmetry operators which non-trivially link with m-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry X, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary ∂X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in ∂X. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Formal mathematical solutions of the force-free equations, spontaneous discontinuities, and dissipation in large-scale magnetic fields
Direct integration of the force-free field equation del x B = alpha B, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active X-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the X-ray corona.
Parker, E. N.↗
Increased localization of Majorana modes in antiferromagnetic chains on superconductors
Magnet-superconductor hybrid (MSH) systems are a key platform for custom-designed topological superconductors. Ideally, the ends of a one-dimensional MSH structure will host Majorana zero-modes (MZMs), the fundamental unit of topological quantum computing. However, some experiments with ferromagnetic (FM) chains show a more complicated picture. Due to tiny gap sizes and hence long coherence lengths, MZMs might hybridize and lose their topological protection. Recent experiments on a niobium surface have shown that both FM and antiferromagnetic (AFM) chains may be engineered, with the magnetic order depending on the crystallographic direction of the chain. While FM chains are well understood, AFM chains are less so. Here, we study two models inspired by the niobium surface: A minimal model to elucidate the general topological properties of AFM chains and an extended model to more closely simulate a real system by mimicking the proximity effect. Here, we find that, in general, for AFM chains, the topological gap is larger than for FM ones, and thus, coherence lengths are shorter for AFM chains, yielding more pronounced localization of MZMs in these chains. While for some parameters AFM chains may be topologically trivial, we find in these cases that adding an adjacent chain can result in a nontrivial system, with a single MZM at each chain end.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Topological confinement in Skyrme holography
Abstract We study phase transitions in five-dimensional Einstein gravity with a negative cosmological constant, coupled to a Skyrme matter field. These transitions are topological generalizations of the Hawking–Page transition between thermal anti de Sitter (AdS) spacetime and an AdS black hole. Phases are characterized by a topological number associated with the Skyrme field configuration. Depending on that topological number and on the Skyrme coupling strength, there occur transitions between those phases at two, one, or no value(s) of the temperature. Through the holographic (AdS/CFT) correspondence, these solutions are dual to topologically non-trivial states in a conformal field theory with an SU (2)-symmetry, which support either confined or deconfined (quasi-)particles at strong coupling. We compare to similar known phase transitions, and discuss potential applications to confinement in topological phases of condensed matter and the quark–gluon plasma.
Astronomy & Astrophysics↗
Open-closed string duality, branes, and topological recursion
We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.
2D Gravity↗
Modeling Chemical Reactions in Classical Molecular Dynamics Simulations
An algorithm capable of incorporating multi-step reaction mechanisms into atomistic molecular dynamics (MD) simulations using traditional fixed valence force fields is proposed and implemented within the framework of LAMMPS (Large-scale Atomic Molecular Massively Parallel Simulator). This extension, referred to as fix bond/react, enables bonding topology modifications during a running MD simulation using pre- and post-reaction bonding templates to carry out a pre-specified reaction. Candidate reactants are first identified by interatomic separation, followed by the application of a generalized topology matching algorithm to confirm they match the pre-reaction template. This is followed by a topology conversion to match the post-reaction template and a dynamic relaxation to minimize high energy configurations. Two case studies, the condensation polymerization of nylon 6,6 and the formation of a highly-crosslinked epoxy, are simulated to demonstrate the robustness, stability, and speed of the algorithm. Improvements which could increase its utility are discussed.
Jacob R Gissinger↗
Ka-band, multibeam, contiguous coverage satellite antenna for the USA
The behavior of a multibeam antenna is determined by three major characteristics: beam topology, realizable radiation characteristics, and realizable beamforming network architecture. Eight canonical topology plans have been developed and analyzed: angular separation between identical frequency cells, angular separation between orthogonally polarized identical frequency cells, number and configuration of cells forming coverage areas, and crossover level between nonidentical frequency band cells. A general topology plan is developed for the continental United States for 100-deg W synchronous satellite longitude.
Foldes, P.↗
Homotopy characterization of non-Hermitian Hamiltonians
We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called “point-gap” and “line-gap” schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from $\mathbb{Z}$ winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups $\mathbb{Z}_n$ (rather than $\mathbb{Z}$ Chern number). Finally, we interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The evolution of voids in the adhesion approximation
We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 128(exp 3) particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H(sub 50) = 1 scals approximately as bar D(z) = bar D(sub zero)/(1+2)(exp 1/2), where bar D(sub zero) approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordialpotential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is strongly epoch dependent, with void topologies generally simplifying with time. This means that as voids grow older they become progressively more empty and have less structure within them. We evaluate the genus measure both for individual voids as well as for the entire ensemble of voids predicted by CDM model. As a result we find that the topology of voids when taken together with the void spectrum is a very useful statistical indicator of the evolution of the structure of the universe on large scales.
Sahni, Varun↗
Structural Studies of Fucosylated N-Glycans by Ion Mobility Mass Spectrometry and Collision-Induced Fragmentation of Negative Ions
There is considerable potential for the use of ion mobility mass spectrometry in structural glycobiology due in large part to the gas-phase separation attributes not typically observed by orthogonal methods. Here, we evaluate the capability of traveling wave ion mobility combined with negative ion collision-induced dissociation to provide structural information on N-linked glycans containing multiple fucose residues forming the Lewis{sup x} and Lewis{sup y} epitopes. These epitopes are involved in processes such as cell-cell recognition and are important as cancer biomarkers. Specific information that could be obtained from the intact N-glycans by negative ion CID included the general topology of the glycan such as the presence or absence of a bisecting GlcNAc residue and the branching pattern of the triantennary glycans. Information on the location of the fucose residues was also readily obtainable from ions specific to each antenna. Some isobaric fragment ions produced prior to ion mobility could subsequently be separated and, in some cases, provided additional valuable structural information that was missing from the CID spectra alone. .
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Periodic motion in a class of nth-order autonomous differential equations
Sufficient conditions are obtained for the existence of periodic motion in a class of autonomous nonlinear differential equations of order greater than two. The approach is based on the decomposition of an equation into a linear and a nonlinear part. The analysis relies on some basic ideas from linear analysis and geometry. Sufficient conditions for a periodic solution are derived by means of a general topological principle referred to as the torus principle. The existence of a periodic solution is concluded by an appropriate use of the Brouwer fixed-point theorem.
Williamson, D.↗
On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields
The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.
Lerche, I.↗
On equilibrium states of heated self-gravitating gas clouds cooling by conduction in an external gravitational field
Exact analytic solutions are presented for equilibrium states of a self-gravitating one-dimensional cloud of gas, embedded in an external gravitational field due to a plane of 'stars' being heated at a rate proportional to the local gas density, and cooling by thermal conduction. It is found that the general topology of the solutions is such that the gas density has a minimum on the plane of 'stars', rising to an infinite but integrable peak away from the plane so that the total mass of gas in the cloud is finite. The results may be of interest in investigations of interstellar molecular clouds and of filamentary structures in supernova remnants as well as in the modeling of gas distributions around 'cocoon' protostars.
Lerche, I.↗
Recursive flexible multibody system dynamics using spatial operators
This paper uses spatial operators to develop new spatially recursive dynamics algorithms for flexible multibody systems. The operator description of the dynamics is identical to that for rigid multibody systems. Assumed-mode models are used for the deformation of each individual body. The algorithms are based on two spatial operator factorizations of the system mass matrix. The first (Newton-Euler) factorization of the mass matrix leads to recursive algorithms for the inverse dynamics, mass matrix evaluation, and composite-body forward dynamics for the systems. The second (innovations) factorization of the mass matrix, leads to an operator expression for the mass matrix inverse and to a recursive articulated-body forward dynamics algorithm. The primary focus is on serial chains, but extensions to general topologies are also described. A comparison of computational costs shows that the articulated-body, forward dynamics algorithm is much more efficient than the composite-body algorithm for most flexible multibody systems.
Jain, A.↗