615 research outputs found

    Historical Burdens on Physics

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    When learning physics, one follows a track very similar to the historical path of the evolution of this science: one takes detours, overcomes superfluous obstacles and repeats mistakes, one learns inappropriate concepts and uses outdated methods. In the book, more than 200 articles present and analyze such obsolete concepts methods. All articles have the same structure: 1. subject, 2. deficiencies, 3. origin, 4. disposal. The articles had originally appeared as columns in various magazines. Accordingly, we had tried to write them in an easily understandable way

    Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach

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    Thesis elaborated from 2018 to 2023 at the Instituto de Astrofísica de Andalucía under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI : With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels

    Quantum state engineering by steering in the presence of errors

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    Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed in the past for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against various errors. We study a set of errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of erroneous choice of system-detector coupling, re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the system-detector interaction. We show that the protocol remains fully robust against the erroneous choice of system-detector coupling parameters and presents reasonable robustness against other errors. We employ various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes.Comment: 31 pages of main text + 17 pages of appendices, 13 figure

    Isomonodromic Deformations: Confluence, Reduction and Quantisation

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    First-order perturbation theory of eigenmodes for systems with interfaces

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    We present an exact first-order perturbation theory for eigenmodes in systems with interfaces causing material discontinuities. We show that when interfaces deform, higher-order terms of the perturbation series can contribute to the eigenmode frequencies in first order in the deformation depth. In such cases, the first-order approximation is different from the usual diagonal approximation and its single-mode result. Extracting additional first-order corrections from all higher-order terms enables us to recover the diagonal formalism in a modified form. A general formula for the single-mode first-order correction to electromagnetic eigenmodes in systems with interfaces is derived, capable of treating dispersive, magnetic, and chiral materials of arbitrary shape

    Quantum states in materials with complex topological electronic and magnetic structure

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    Η σύνθετη τοπολογική ηλεκτρονική και μαγνητική δομή των υλικών είναι ένα πεδίο έρευνας που αποκτά όλο και μεγαλύτερη σημασία τα τελευταία χρόνια, λόγω της εφαρμογής του στο πεδίο της σπιντρονικής, με πιθανές προεκτάσεις στην πληροφορία της τεχνολογίας. Στην παρούσα διδακτορική διατριβή, κύριο στόχο αποτελεί η θεωρητική και υπολογιστική μελέτη φαινομένων μεταφοράς του σπιν σε τοπολογικές δομές. Οι προσομοιώσεις μας βασίζονται σε υπολογισμούς υλικών από πρώτες αρχές εφαρμόζοντας τη θεωρία ηλεκτρονικής σκέδασης. Αρχικά, επικεντρωνόμαστε στο φαινόμενο της ροπής στρέψης σπιν σε τοπολογικούς μονωτές εμπλουτισμένους με μαγνητικές προσμίξεις. Μελετούμε τη ροπή στρέψης σπιν που ασκείται στη μαγνητική ροπή σιδηρομαγνητικά συζευγμένων προσμίξεων, και συγκεκριμένα μετάλλων μετάβασης (Cr, Mn, Fe, και Co), στην επιφάνεια του τοπολογικού μονωτή Bi2Te3, ως απόκριση σε ηλεκτρικό ρεύματος στην επιφάνεια. Οι ιδιότητες σκέδασης των επιφανειακών καταστάσεων στις μαγνητικές προσμίξεις υπολογίζονται με τη μέθοδο Korringa-Kohn-Rostoker (KKR) συναρτήσεων Green, ενώ οι υπολογισμοί της ροπής στρέψης σπιν πραγματοποιούνται συνδυάζοντας τα αποτελέσματα της KKR στην επιφάνεια Fermi και το ρυθμό σκέδασης με την ημικλασική γραμμικοποιημένη εξίσωση Boltzmann. Συζητάμε τη συσχέτιση της ροπής στρέψης σπιν με το ρεύμα σπιν, αναλύοντας τη συνεισφορά της ροής σπιν στη ροπή στρέψης σπιν στις προσμίξεις. Επιπλέον, εξετάζουμε πώς σχετίζεται η ροπή στρέψης σπιν με την αντίσταση και την παραγωγή θερμότητας Joule. Σύμφωνα με τα αποτελέσματά μας, τα συστήματα αυτά είναι ευνοϊκά για σπιντρονικές εφαρμογές. Ειδικότερα, προβλέπουμε ότι το σύστημα Mn/Bi2Te3 είναι το πλέον υποσχόμενο μεταξύ των συστημάτων που μελετήσαμε για εφαρμογές της ροπής στρέψης σπιν. Στη συνέχεια, επικεντρωνόμαστε στη μελέτη διδιάστατων μαγνητικών σκυρμιονίων, τα οποία είναι τοπολογικά σολιτόνια σε σιδηρομαγνητικά υμένια και τα οποία συμπεριφέρονται ως σωματίδια που δύνανται να σχηματιστούν, μεταφερθούν και ανιχνευθούν. Για τη μελέτη αυτή, βασιστήκαμε στη μέθοδο KKR και πραγματοποιήσαμε υπολογισμούς θεωρίας συναρτησιακού της μη συγγραμικής πυκνότητας σπιν για το σχηματισμό ευσταθών μαγνητικών σκυρμιονίων σε υπέρλεπτα υμένια Pd/Fe/Ir(111). Κατόπιν, επιλύοντας την αυτοσυνεπή εξίσωση Boltzmann, εξετάζουμε το τοπολογικό φαινόμενο Hall, το οποίο προκαλείται από τη σκέδαση των ηλεκτρονίων σε συστήματα σκυρμιονίων. Η μελέτη του τοπολογικού φαινομένου Hall είναι θεμελιώδους σημασίας σε τέτοιου είδους συστήματα, καθώς το φαινόμενο αυτό αποτελεί μία από τις βασικές μεθόδους για την ανίχνευση μαγνητικών σκυρμιονίων. Παρουσιάζουμε την αντίσταση και τη γωνία Hall του συστήματος, και εξετάζουμε την εξάρτηση του τοπολογικού φαινομένου Hall από το βαθμό αταξίας του δείγματος, εισάγοντάς τον στους υπολογισμούς μας μέσω ενός επιπλέον όρου ηλεκτρονικής σκέδασης. Τα ευρήματά μας προβλέπουν μία ισχυρή εξάρτηση του τοπολογικού φαινομένου Hall από το βαθμό αταξίας του δείγματος.The research on the complex topological electronic and magnetic structure of materials has been gaining importance over the last few years, as it can be applied in the field of spintronics with prospects for implementation in information technology. The main goal of this thesis is the theoretical and computational study of spin-transport phenomena in topological structures. Our simulations are based on ab-initio calculations augmented by electronic scattering theory. Firstly, we focus on the phenomenon of the spin-orbit torque in a special materials class, the topological insulators, doped with magnetic impurities. We investigate the spin-orbit torque exerted on the magnetic moments of ferromagnetically coupled transition-metal defects (Cr, Mn, Fe, and Co) embedded in the surface of the topological insulator Bi2Te3, in response to an electrical current flow in the surface. The scattering properties of surface states off multiple magnetic impurities are calculated within the Korringa-Kohn-Rostoker (KKR) Green function method, while the spin-orbit torque calculations are performed by combining the KKR results on the Fermi surface and scattering rate with the semiclassical linearized Boltzmann equation. We discuss the correlation of the spin-orbit torque to the spin current on the Fermi surface, analyzing the spin flux contribution to the spin-orbit torque on the defects. In addition, we relate the torque to the resistivity and the Joule heat production. We find these systems may be favorable for spintronic applications. In particular, we predict that the Mn/Bi2Te3 is the most promising among the studied systems for applications of the spin-orbit torque effect. Secondly, we focus on magnetic skyrmions in magnetic films, which are two-dimensional topological solitons that behave like particles that can be formed, transported, detected. Based on the KKR method, non-collinear spin-density-functional theory calculations are carried out for the formation of stable magnetic skyrmions in Pd/Fe/Ir(111) ultrathin films. Next, solving selfconsistently the Boltzmann transport equation, we study the topological Hall effect (THE) induced by the electron scattering on skyrmion systems. The investigation of the THE is of pivotal importance in these systems, since it is one of the key methods for electrically detecting magnetic skyrmions. We present the resistivity and the Hall angle of the system, and we examine the dependence of the THE on disorder, modelled by an additional electron scattering term. Our findings predict a strong dependence of the topological Hall angle on the degree of disorder of the sample

    Monotonicity methods for inverse scattering problems

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    We consider two inverse scattering problems in unbounded free space. On the one hand, we investigate an inverse acoustic obstacle scattering problem governed by the time-harmonic Helmholtz equation. On the other hand, we examine an inverse electromagnetic medium scattering problem modeled by the time-harmonic Maxwell equations. In both cases, our goal is to recover the position and the shape of compactly supported scatterers D from far field observations of scattered waves. For the acoustic scattering problem, we assume that the scatterers are impenetrable obstacles that carry mixed Dirichlet and Neumann boundary conditions. For the electromagnetic scattering problem, the media are supposed to be penetrable, non-magnetic and non-absorbing but the electric permittivity may be inhomogeneous inside the scattering objects. We approach both shape identification problems utilizing a monotonicity-based reconstruction ansatz. First, we establish monotonicity relations for the eigenvalues of the far field operators which map superpositions of plane wave incident fields to the far field patterns of the corresponding scattered fields. In addition, we discuss the existence of localized wave functions that have arbitrarily large energy in some prescribed region while at the same time having arbitrarily small energy in some other prescribed region. Combining the monotonicity relations and the localized wave functions leads to rigorous characterizations of the support of the scattering objects. More precisely, we develop criteria that allow us to evaluate whether certain probing domains B are contained inside the unknown scatterer D or not and vice versa. Therefore, we introduce probing operators corresponding to the probing domains B and show that the number of positive or negative eigenvalues of suitable linear combinations of the far field operator corresponding to D and these probing operators is finite if and only if B is contained within D or if and only if B contains D. Finally, we complement our theoretical findings with numerical reconstruction algorithms and give some examples to illustrate the reconstruction procedure

    50 Years of quantum chromodynamics – Introduction and Review

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    Spin waves in curved magnetic shells

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    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

    Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature

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    The so-called Darboux III oscillator is an exactly solvable N-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable deformation of the usual N-dimensional harmonic oscillator in terms of a non-negative parameter λ which is directly related to the curvature of the underlying space. In this paper, a detailed study of the Shannon information entropy for the quantum version of the Darboux III oscillator is presented, and the interplay between entropy and curvature is analysed. In particular, analytical results for the Shannon entropy in the position space can be found in the N-dimensional case, and the known results for the quantum states of the N-dimensional harmonic oscillator are recovered in the limit of vanishing curvature λ → 0. However, the Fourier transform of the Darboux III wave functions cannot be computed in exact form, thus preventing the analytical study of the information entropy in momentum space. Nevertheless, we have computed the latter numerically both in the one and three-dimensional cases and we have found that by increasing the absolute value of the negative curvature (through a larger λ parameter) the information entropy in position space increases, while in momentum space it becomes smaller. This result is indeed consistent with the spreading properties of the wave functions of this quantum nonlinear oscillator, which are explicitly shown. The sum of the entropies in position and momentum spaces has been also analysed in terms of the curvature: for all excited states such total entropy decreases with λ, but for the ground state the total entropy is minimized when λ vanishes, and the corresponding uncertainty relation is always fulfilled.This work has been partially supported by Agencia Estatal de Investigación (Spain) under grant PID2019-106802GB-I00/AEI/ 10.13039/501100011033, by the Regional Government of Castilla y León (Junta de Castilla y León, Spain) and by the Spanish Ministry of Science and Innovation MICIN and the European Union NextGenerationEU/PRTR, as well as the contribution of the European Cooperation in Science and Technology through the COST Action CA18108. The authors acknowledge A. Najafizade for useful discussions at the early stages of this work, and also the Referee for several relevant comments and suggestions
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