209 research outputs found
Polarization of Multi-Agent Gradient Flows Over Manifolds With Application to Opinion Dynamics
peer reviewedMulti-agent systems are known to exhibit stable emergent behaviors, including polarization, over or highly symmetric nonlinear spaces. In this article, we eschew linearity and symmetry of the underlying spaces, and study the stability of polarized equilibria of multi-agent gradient flows evolving on general hypermanifolds. The agents attract or repel each other according to the partition of the communication graph that is connected but otherwise arbitrary. The manifolds are outfitted with geometric features styled “dimples” and “pimples” that characterize the absence of flatness. The signs of inter-agent couplings together with these geometric features give rise to stable polarization under various sufficient conditions. We propose tangible interpretation of the system in the context of opinion dynamics, and highlight throughout the text its versatility in modeling diverse aspects of the polarization phenomenon
Probing center vortices and deconfinement in lattice gauge theory with persistent homology
We investigate the use of persistent homology, a tool from topological data
analysis, as a means to detect and quantitatively describe center vortices in
lattice gauge theory in a gauge-invariant manner. We provide
evidence for the sensitivity of our method to vortices by detecting a vortex
explicitly inserted using twisted boundary conditions in the deconfined phase.
This inspires the definition of a new phase indicator for the deconfinement
phase transition. We also construct a phase indicator without reference to
twisted boundary conditions using a simple -nearest neighbours classifier.
Finite-size scaling analyses of both persistence-based indicators yield
accurate estimates of the critical and critical exponent of correlation
length of the deconfinement phase transition.Comment: 18 pages, 19 figures, accepted versio
Spin waves in curved magnetic shells
This thesis aims to theoretically explore the geometrical effects on spin waves, the fundamental low-energy excitations of ferromagnets, propagating in curved magnetic shells. Supported by an efficient numerical technique developed for this thesis, several aspects of curvilinear spin-wave dynamics involving magnetic pseudo-charges, the topology of curved magnets, symmetry-breaking effects, and dynamics of spin textures are studied. In recent years, geometrical and curvature effects on mesoscale ferromagnets have attracted the attention of fundamental and applied research. Exciting curvature-induced phenomena include chiral symmetry breaking, the stabilization of magnetic skyrmions on Gaussian bumps, or topologically induced domain walls in Möbius ribbons. Spin waves in vortex-state magnetic nanotubes exhibit a curvature-induced dispersion asymmetry due to geometric contributions to the magnetic volume pseudo-charges. However, previous theoretical studies were limited to simple and thin curved shells due to the complexity of analytical models and the time-consuming nature of existing numerical techniques. For a systematic study of spin-wave propagation in curved shells, the first of five thematic parts of this thesis deals with developing a numerical method to calculate spin-wave spectra in waveguides with arbitrarily shaped cross-sections efficiently. For this, a finite-element/boundary-element method to calculate dynamic dipolar fields, the Fredkin-Koehler method, was extended for propagating waves. The technique is implemented in the micromagnetic modeling package TetraX developed and made available as open source to the scientific community. Equipped with this method, the second part of the thesis studies the influence of geometric contributions to the magnetic charges leading to nonlocal chiral symmetry breaking. Introducing the toroidal moment to spin-wave dynamics allows us to predict whether this symmetry breaking is present even in complicated systems with spatially inhomogeneous equilibria or shells with gradient curvatures. The theoretical study of curvilinear magnetism is extended to thick shells, uncovering a curvature-induced nonreciprocity in the spatial mode profiles of the spin waves. Consequently, nonreciprocal dipole-dipole hybridization between different modes leads to asymmetric level gaps enabling spin-wave diode behavior. Besides unidirectional transport, curvature modifies the weakly nonlinear spin-wave interactions. The third part of this thesis focuses on topological effects. A topological Berry phase of spin waves in helical-state nanotubes is studied and connected to a local curvature-induced chiral interaction of exchange origin. The topology of more complicated systems, such as magnetic Möbius ribbons, is shown to impose selection rules on the spectrum of possible spin waves and split it into modes with half and full-integer indices. To understand the effects of achiral symmetry breaking, the fourth part of this thesis focuses on the deformation of symmetric shells, here, cylindrical nanotubes, to polygonal and elliptical shapes. Lowering rotational symmetry leads to splitting spin-wave dispersions into singlet and doublets branches, which is explained using a simple group theory approach and is analogous to the electron band structure in crystals. Apart from mode splitting, this symmetry breaking allows hybridization between different spin-wave modes and modifies their microwave absorption. While this hybridization appears discretely in polygonal tubes, tuning the eccentricity of elliptical tubes allows controlling the level gaps appearing from hybridization. Finally, the last part focuses on the dynamics of spin waves in the vicinity of spin textures in curvilinear systems. The dynamics of topological meron strings are shown to exhibit dipole-induced chiral symmetry breaking like spin waves in curved shells. Moreover, modulational instability is predicted from the softening of their gyrotropic modes, similar to the formation of stripe domains in flat systems. This stripe domain formation can also be observed in curved shells but leads to tilted or helix domains. Overall, this thesis contributes to the fundamental understanding of spin-wave dynamics on the mesoscale but also advertises these for possible magnonic applications.:Abstract
Acknowledgements
Contents
1 Introduction
Theoretical Foundations
2 Micromagnetic continuum theory
3 Spin waves
Numerical methods in micromagnetism
4 Overview
5 Finite-element dynamic-matrix method for propagating spin waves
6 Numerical reverse-engineering of spin-wave dispersions
7 TetraX: A micromagnetic modeling package
Aspects of curvilinear magnetization dynamics
8 Magnetic charges
9 Topology
10 Achiral symmetry breaking
11 Spin textures
Closing remarks
12 Summary and outlook
13 Publications and conference contributions
Appendix
A Extended derivations and proofs
B Supplementary data and discussion
List of Figures
List of Tables
Bibliography
Alphabetical IndexZiel dieser Arbeit ist es, die geometrischen Effekte auf Spinwellen (Magnonen), die fundamentalen niederenergetischen Anregungen von Ferromagneten, die sich in gekrümmten magnetischen Schalen ausbreiten, theoretisch zu untersuchen. Unterstützt durch ein effizientes numerisches Verfahren, das für diese Arbeit entwickelt wurde, werden verschiedene Aspekte der krummlinigen Spinwellen-Dynamik untersucht: magnetische Pseudoladungen, die Topologie gekrümmter Magnete, Symmetriebrechungseffekte und die Dynamik von Spin-Texturen. In den letzten Jahren haben Geometrie- und Krümmungseffekte auf mesoskaligen Ferromagneten die Aufmerksamkeit der Grundlagen- und angewandten Forschung auf sich gezogen. Zu den spannenden krümmungsinduzierten Phänomenen gehören chirale Symmetriebrechung, die Stabilisierung magnetischer Skyrmionen auf Gaußschen Unebenheiten oder topologisch induzierte Domänenwände in Möbiusbändern. Spinwellen in magnetischen Nanoröhren im Vortex-Zustand zeigen eine krümmungsinduzierte Dispersionsasymmetrie aufgrund geometrischer Beiträge zu den magnetischen Volumen-Pseudoladungen. Bisherige theoretische Studien beschränkten sich jedoch auf einfache und dünne gekrümmte Schalen, da die analytischen Modelle zu komplex und die bestehenden numerischen Verfahren zu zeitaufwändig waren. Für eine systematische Untersuchung der Spinwellenausbreitung in gekrümmten Schalen befasst sich der erste von fünf thematischen Teilen dieser Arbeit mit der Entwicklung einer numerischen Methode zur effizienten Berechnung von Spinwellenspektren in Wellenleitern mit beliebig geformten Querschnitten. Dazu wurde eine Finite-Elemente/Grenzelement-Methode zur Berechnung dynamischer Dipolfelder, die Fredkin-Köhler-Methode, für propagierende Wellen erweitert. Die Technik ist in dem mikromagnetischen Modellierungspaket TetraX implementiert, das während dieser Arbeit entwickelt und der wissenschaftlichen Gemeinschaft als Open Source zur Verfügung gestellt wurde. Ausgestattet mit dieser Methode untersucht der zweite Teil der Arbeit den Einfluss von geometrischen Beiträgen zu den magnetischen Ladungen, die zu nichtlokaler chiraler Symmetriebrechung führen. Durch die Einführung des toroidalen Moments in die Spin-Wellen-Dynamik lässt sich vorhersagen, ob diese Symmetriebrechung auch in komplizierten Systemen mit räumlich inhomogenen Gleichgewichtszuständen oder magnetischen Schalen mit Gradientenkrümmungen vorhanden ist. Die theoretische Untersuchung des krummlinigen Magnetismus wird auf dicke Schalen ausgedehnt, für die eine krümmungsbedingte Nichtreziprozität in den räumlichen Modenprofilen der Spinwellen gefunden wird. Als Konsequenz führt nicht-reziproke Dipol-Dipol-Hybridisierung zwischen verschiedenen Moden zu asymmetrischen Niveaulücken, die die Konstruktion von Spinwellen-Dioden ermöglichen. Neben unidirektionalem Transport modifiziert die Krümmung auch die schwach nichtlinearen Spin-Wellen-Wechselwirkungen. Der dritte Teil dieser Arbeit befasst sich mit topologischen Effekten. So wird eine topologische Berry-Phase von Spinwellen in Nanoröhren im Helix-Zustand untersucht, die mit einer lokalen krümmungsinduzierten chiralen Wechselwirkung in Verbindung gebracht wird. Es wird gezeigt, dass die Topologie komplizierterer Systeme, wie z.B. magnetischer Möbiusbänder, dem Spektrum möglicher Spinwellen Auswahlsregeln auferlegt, das damit in Moden mit halb- und ganzzahligen Indizes aufspaltet. Um die Auswirkungen der achiralen Symmetriebrechung zu verstehen, konzentriert sich der vierte Teil dieser Arbeit auf die Verformung symmetrischer Schalen, hier zylindrischer Nanoröhren, zu polygonalen und elliptischen Formen. Die Verringerung der Rotationssymmetrie führt zu einer Aufspaltung der Spin-Wellen-Dispersionen in Singlets Dublets, was mit einem einfachen gruppentheoretischen Ansatz erklärt wird und analog zur Elektronenbandstruktur in Kristallen ist. Abgesehen von der Modenaufspaltung ermöglicht diese Symmetriebrechung eine Hybridisierung zwischen verschiedenen Spin-Wellen-Moden und verändert zudem deren Mikrowellenabsorption. Während diese Hybridisierung in polygonalen Röhren diskret auftritt, kann die Exzentrizität elliptischer Röhren genutzt werden um die durch Hybridisierung entstehenden Niveaulücken kontinuierlich einzustellen. Schließlich konzentriert sich der letzte Teil auf die Dynamik von Spinwellen in der Umgebung von Spinstrukturen in krummlinigen Systemen. Es wird gezeigt, dass die Dynamik topologischer Meron-Strings dipol-induzierte chirale Symmetriebrechungen wie Spinwellen in gekrümmten Schalen aufweist. Darüber hinaus wird eine Instabilität der gyrotropen Mode vorhergesagt, ähnlich der Bildung von Streifendomänen in flachen Systemen. Diese Bildung von Streifendomänen kann auch in gekrümmten Schalen beobachtet werden, führt aber zu gekippten oder spiralförmigen Domänen. Insgesamt trägt diese Arbeit zum grundlegenden Verständnis der Spinnwellen-Dynamik auf der Mesoskala bei, aber diskutiert auch mögliche magnonische Anwendungen.:Abstract
Acknowledgements
Contents
1 Introduction
Theoretical Foundations
2 Micromagnetic continuum theory
3 Spin waves
Numerical methods in micromagnetism
4 Overview
5 Finite-element dynamic-matrix method for propagating spin waves
6 Numerical reverse-engineering of spin-wave dispersions
7 TetraX: A micromagnetic modeling package
Aspects of curvilinear magnetization dynamics
8 Magnetic charges
9 Topology
10 Achiral symmetry breaking
11 Spin textures
Closing remarks
12 Summary and outlook
13 Publications and conference contributions
Appendix
A Extended derivations and proofs
B Supplementary data and discussion
List of Figures
List of Tables
Bibliography
Alphabetical Inde
Cosmic topology. Part II. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
If the Universe has non-trivial spatial topology, observables depend on both
the parameters of the spatial manifold and the position and orientation of the
observer. In infinite Euclidean space, most cosmological observables arise from
the amplitudes of Fourier modes of primordial scalar curvature perturbations.
Topological boundary conditions replace the full set of Fourier modes with
specific linear combinations of selected Fourier modes as the eigenmodes of the
scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean
manifolds with the topologies - , , , , and
that encompass the full range of manifold parameters and observer
positions, generalizing previous treatments. Under the assumption that the
amplitudes of primordial scalar curvature eigenmodes are independent random
variables, for each topology we obtain the correlation matrices of Fourier-mode
amplitudes (of scalar fields linearly related to the scalar curvature) and the
correlation matrices of spherical-harmonic coefficients of such fields sampled
on a sphere, such as the temperature of the cosmic microwave background (CMB).
We evaluate the detectability of these correlations given the cosmic variance
of the observed CMB sky. We find that topologies where the distance to our
nearest clone is less than about 1.2 times the diameter of the last scattering
surface of the CMB give a correlation signal that is larger than cosmic
variance noise in the CMB. This implies that if cosmic topology is the
explanation of large-angle anomalies in the CMB, then the distance to our
nearest clone is not much larger than the diameter of the last scattering
surface. We argue that the topological information is likely to be better
preserved in three-dimensional data, such as will eventually be available from
large-scale structure surveys.Comment: 79 pages, 9 figure
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
The Polytope Formalism: isomerism and associated unimolecular isomerisation
This thesis concerns the ontology of isomerism, this encompassing the conceptual frameworks and relationships that comprise the subject matter; the necessary formal definitions, nomenclature, and representations that have impacts reaching into unexpected areas such as drug registration and patent specifications; the requisite controlled and precise vocabulary that facilitates nuanced communication; and the digital/computational formalisms that underpin the chemistry software and database tools that empower chemists to perform much of their work.
Using conceptual tools taken from Combinatorics, and Graph Theory, means are presented to provide a unified description of isomerism and associated unimolecular isomerisation spanning both constitutional isomerism and stereoisomerism called the Polytope Formalism. This includes unification of the varying approaches historically taken to describe and understand stereoisomerism in organic and inorganic compounds.
Work for this Thesis began with the synthesis, isolation, and characterisation of compounds not adequately describable using existing IUPAC recommendations. Generalisation of the polytopal-rearrangements model of stereoisomerisation used for inorganic chemistry led to the prescriptions that could deal with the synthesised compounds, revealing an unrecognised fundamental form of isomerism called akamptisomerism.
Following on, this Thesis describes how in attempting to place akamptisomerism within the context of existing stereoisomerism reveals significant systematic deficiencies in the IUPAC recommendations. These shortcomings have limited the conceptualisation of broad classes of compounds and hindered development of molecules for medicinal and technological applications.
It is shown how the Polytope Formalism can be applied to the description of constitutional isomerism in a practical manner. Finally, a radically different medicinal chemistry design strategy with broad application, based upon the principles, is describe
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