Topological Field Research Articles

Evolution of a long-duration transpolar arc during very quiet period

In this study, we explore the evolution of long-duration transpolar arcs observed during an exceptionally quiet period by the Fengyun-3D and Defense Meteorological Satellite Program satellites on 17 January 2019. Leveraging the extensive field of view of WAI, we captured the complete structure and evolution of the TPA over a very quiet period exceeding 7 h, with AE<30 nT. The TPA initially manifested at the poleward boundary of the auroral oval in the dawn sector, gradually migrating towards the dusk as the y-component of the interplanetary magnetic field (IMF BY) transitioned from negative to positive. Throughout this phase, the TPA underwent a distortion, transforming from a straight line to an “l-shape”. Following a reversal in interplanetary magnetic field BY to negative, the TPA retraced its path towards dawn and ultimately dissipated when the IMF turned southward. Of particular interest is the observation that when the TPA approached the noon-midnight line, small-scale spiral structures became apparent within the TPA. This suggests the presence of intricate small-scale magnetic field topologies or plasma instabilities/shears in the source region. These observations highlight the likelihood of complex field and particle dynamics in the high-latitude reconnection region and the twisted tail plasma sheet.

Nanoparticles synthesis in microwave plasmas: peculiarities and comprehensive insight

Low-pressure plasma processes are routinely used to grow, functionalize or etch materials, and thanks to some of its unique attributes, plasma has become a major player for some applications such as microelectronics. Plasma processes are however still at a research level when it comes to the synthesis and functionalization of nanoparticles. Yet plasma processes can offer a particularly suitable solution to produce nanoparticles having very peculiar features since they enable to: (i) reach particle with a variety of chemical compositions, (ii) tune the size and density of the particle cloud by acting on the transport dynamics of neutral or charged particles through a convenient setting of the thermal gradients or the electric field topology in the reactor chamber and (iii) manipulate nanoparticles and deposit them directly onto a substrate, or codeposit them along with a continuous film to produce nanocomposites or (iv) use them as a template to produce 1D materials. In this article, we present an experimental investigation of nanoparticles synthesis and dynamics in low-pressure microwave plasmas by combining time-resolved and in-situ laser extinction and scattering diagnostics, QCL absorption spectroscopy, mass spectrometry, optical emission spectroscopy and SEM along with a particle transport model. We showed for the first time the thermophoresis-driven dynamic of particle cloud in electrodless microwave plasmas. We showed that this effect is linked to particular fluctuations in the plasma composition and results in the formation of a void region in the bulk of the plasma surrounded by a particle cloud in the peripherical post-discharge. We also reveals and analyze the kinetics of precursor dissociation and molecular growth that result in the observed nanoparticle nucleation.

Advancing Solar Magnetic Field Extrapolations through Multiheight Magnetic Field Measurements

Nonlinear force-free extrapolations are a common approach to estimate the 3D topology of coronal magnetic fields based on photospheric vector magnetograms. The force-free assumption is a valid approximation at coronal heights, but for the dense plasma conditions in the lower atmosphere, this assumption is not satisfied. In this study, we utilize multiheight magnetic field measurements in combination with physics-informed neural networks to advance solar magnetic field extrapolations. We include a flexible height-mapping, which allows us to account for the different formation heights of the observed magnetic field measurements. The comparison to analytical and simulated magnetic fields demonstrates that including chromospheric magnetic field measurements leads to a significant improvement of our magnetic field extrapolations. We also apply our method to chromospheric line-of-sight magnetograms from the Vector Spectromagnetograph (VSM) on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) observatory, in combination with photospheric vector magnetograms from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). The comparison to observations in extreme-ultraviolet wavelengths shows that the additional chromospheric information leads to a better agreement with the observed coronal structures. In addition, our method intrinsically provides an estimate of the corrugation of the observed magnetograms. With this new approach, we make efficient use of multiheight magnetic field measurements and advance the realism of coronal magnetic field simulations.

Nucleosynthesis in magnetorotational supernovae: impact of the magnetic field configuration

ABSTRACT The production of heavy elements is one of the main by-products of the explosive end of massive stars. A long sought goal is finding differentiated patterns in the nucleosynthesis yields, which could permit identifying a number of properties of the explosive core. Among them, the traces of the magnetic field topology are particularly important for extreme supernova (SN) explosions, most likely hosted by magnetorotational effects. We investigate the nucleosynthesis of five state-of-the-art magnetohydrodynamic models with fast rotation that have been previously calculated in full 3D and that involve an accurate neutrino transport (M1). One of the models does not contain any magnetic field and synthesizes elements around the iron group, in agreement with other CC-SNe models in literature. All other models host a strong magnetic field of the same intensity, but with different topology. For the first time, we investigate the nucleosynthesis of MR-SNe models with a quadrupolar magnetic field and a 90° tilted dipole. We obtain a large variety of ejecta compositions reaching from iron nuclei to nuclei up to the third r-process peak. We assess the robustness of our results by considering the impact of different nuclear physics uncertainties such as different nuclear masses, β−-decays and β−-delayed neutron emission probabilities, neutrino reactions, fission, and a feedback of nuclear energy on the temperature. We find that the qualitative results do not change with different nuclear physics input. The properties of the explosion dynamics and the magnetic field configuration are the dominant factors determining the ejecta composition.

Topological entanglement entropy for torus-knot bipartitions and the Verlinde-like formulas

The topological Rényi and entanglement entropies depend on the bipartition of the manifold and the choice of the ground states. However, these entanglement quantities remain invariant under a coordinate transformation when the bipartition also undergoes the identical transformation. In topological quantum field theories (TQFTs), these coordinate transformations reduce to representations of the mapping class group on the manifold of the Hilbert space. We employ this invariant property of the Rényi and entanglement entropies under coordinate transformations for TQFTs in (2 + 1) dimensions on a torus with various bipartitions. By utilizing the replica trick and the surgery method to compute the topological Rényi and entanglement entropies, the invariant property results in Verlinde-like formulas. Furthermore, for the bipartition with interfaces as two non-intersecting torus knots, an SL(2, ℤ) transformation can untwist the torus knots, leading to a simple bipartition with an effective ground state. This invariant property allows us to demonstrate that the topological entanglement entropy has a lower bound −2 ln D, where D is the total quantum dimensions of the system.

Anomaly enforced gaplessness and symmetry fractionalization for SpinG symmetries

Symmetries and their anomalies give strong constraints on renormalization group (RG) flows of quantum field theories. Recently, the identification of a theory’s global symmetries with its topological sector has provided additional constraints on RG flows to symmetry preserving gapped phases due to mathematical results in category and topological quantum field theory. In this paper, we derive constraints on RG flows from ℤ2-valued pure- and mixed-gravitational anomalies that can only be activated on non-spin manifolds. We show that such anomalies cannot be matched by a unitary, symmetry preserving gapped phase without symmetry fractionalization. In particular, we discuss examples that commonly arise in 4d gauge theories with fermions.

Interacting topological quantum chemistry in 2D with many-body real space invariants

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the U(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.

From convective stellar dynamo simulations to Zeeman-Doppler images

Context. Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high-resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, such as poloidality versus toroidality and axisymmetry versus non-axisymmetry, in addition to the field strength. Aims. In this study, we want to test how well these characteristics are preserved when applying the ZDI method to simulated data. We are particularly interested in how accurately the field topology is preserved and to what extent stellar parameters, such as projected rotation velocity and rotation axis inclination, influence the reconstruction. Methods. For these tests, we used published magnetic field vector data from direct numerical magnetohydrodynamic simulations taken near the surface of the simulation domain. These simulations have variable rotation rates and therefore represent different levels of activity of an otherwise Sun-like setup with a convective envelope of solar thickness. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. Results. In general, the ZDI method works as expected. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Conclusions. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the ‘real’ value, as smaller structures with opposite polarities will be blurred in the inversion. This is also seen in the relative distribution of magnetic energy in terms of the angular degree ℓ. Secondly, the axisymmetry is overestimated. The poloidality versus toroidality is better recovered. The reconstruction works better for a stronger field and faster rotation velocity. Still, the ZDI method works surprisingly well even for a weaker field and slow rotation provided the data have a high signal-to-noise ratio and good rotation phase coverage.

Operads, Operadic Categories and the Blob Complex

We will show that the Morrison–Walker blob complex appearing in Topological Quantum Field Theory is an operadic bar resolution of a certain operad composed of fields and local relations. As a by-product we develop the theory of unary operadic categories and study some novel and interesting phenomena arising in this context.

Magnetic Relaxation Seen in a Rapidly Evolving Light Bridge in a Sunspot

We report a magnetic relaxation process inside a sunspot associated with the evolution of a transient light bridge (LB). From high-resolution imaging and spectro-polarimetric data taken by the 1.6 m Goode Solar Telescope installed at Big Bear Solar Observatory, we observe the evolutionary process of a rapidly evolving LB. The LB is formed as a result of the strong intrusion of filamentary structures with relatively horizontal fields into the vertical umbral field region. A strong current density is detected along a localized region where the magnetic field topology changes rapidly in the sunspot, especially in the boundary region between the LB and the umbra, and bright jets are observed intermittently and repeatedly in the chromosphere along this region through magnetic reconnection. In the second half of our observation, the horizontal component of the magnetic field diminishes within the LB, and the typical convection structure within the sunspot, which manifests itself as umbral dots, is restored. Our findings provide a comprehensive perspective not only on the evolution of an LB itself but also on its impacts in the neighboring regions, including the chromospheric activity and the change of magnetic energy of a sunspot.

RF dispersion relations in FRC geometries and HHFW regime

Field reversed configurations (FRC) are characterized by a magnetic field topology, which exhibits the inversion of the external magnetic field through plasma sustained current and the subsequent presence of a null field surface. A monotonical radial decrease in the longitudinal magnetic field leads to the potential presence of harmonics of the ion cyclotron frequency of any order in the region included between the outer wall and the null field surface. What is the effective hot-plasma dispersion relation obtained through the convolution of a large ensemble of high harmonics fast waves (HHFW) confined in a finite radial region represents an open question that we attempt to address here. In particular, we discuss a combination of analytical modeling and numerical treatment, which allows us to retrieve the resulting high harmonic fast wave complex wavevector for any radial location of any FRC radial profile. Moreover, we show how the obtained hot-plasma HHFW wavevector relates to the cold-plasma solution, and how it depends on the plasma parameters.

Lost in the curve: Investigating the disappearing knots in blazar 3C 454.3

One of the most well-known extragalactic sources in the sky, quasar 3C 454.3, shows a curved parsec-scale jet that has been exhaustively monitored with very-long-baseline interferometry (VLBI) over the recent years. In this work, we present a comprehensive analysis of four years of high-frequency VLBI observations at 43 GHz and 86 GHz, between 2013–2017, in total intensity and linear polarization. The images obtained from these observations enabled us to study the jet structure and the magnetic field topology of the source on spatial scales down to 4.6 parsec in projected distance. The kinematic analysis reveals the abrupt vanishing of at least four new superluminal jet features in a characteristic jet region (i.e., region C), which is located at an approximate distance of 0.6 milliarcsec from the VLBI core. Our results support a model in which the jet bends, directing the relativistic plasma flow almost perfectly toward our line of sight, co-spatially with the region where components appear to stop.

Coexistence of electron and phonon topology in conjunction with quantum transport device modeling

The escalating research in the field of topology necessitates an understanding of the underlying rich physics behind the materials possessing unique features of non-trivial topology in both electronic and phononic states. Due to the interaction between electronic quasiparticles and spin degrees of freedom, the realization of magnetic topological materials has opened up a new frontier with unusual topological phases, however, these are rarely reported alongside phononic quasiparticle excitations. In this work, by first-principles calculations and symmetry analysis, the intermetallic ferromagnetic compounds MnGaGe and MnZnSb with the coexistence of exceptional topological features in the electronic and phononic states are proposed. These compounds host nodal surface on ky=π plane in bulk Brillouin zone in the electronic and phononic spectra protected by the combination of time-reversal symmetry and nonsymmorphic two-fold screw-rotation symmetry. In the former case, a spin-polarized nodal surface is present in the majority and minority spin channels and found to be robust to ground-state magnetic polarization. The presence of nodal line features is analyzed in both the quasiparticle spectra, whose non-trivial nature is confirmed by the Berry phase calculation. The incorporation of spin–orbit coupling in the electron spectra introduces distinctive characteristics in the transport properties, facilitating the emergence of anomalous Hall conductivity through Berry curvature in both bulk and monolayer. Furthermore, the monolayer has been proposed as a two-terminal device model to investigate the quantum transport properties using the non-equilibrium Green’s function approach. This superlative combination of observations and modeling sets the path for a greater level of insight into the behavior and aspects of topological materials at the atomic scale.

Studying the Spheromak Rotation in Data-constrained Coronal Mass Ejection Modeling with EUHFORIA and Assessing Its Effect on the B z Prediction

A key challenge in space weather forecasting is accurately predicting the magnetic field topology of interplanetary coronal mass ejections (ICMEs), specifically the north–south magnetic field component (B z ) for Earth-directed CMEs. Heliospheric MHD models typically use spheromaks to represent the magnetic structure of CMEs. However, when inserted into the ambient interplanetary magnetic field, spheromaks can experience a phenomenon reminiscent of the condition known as the “spheromak tilting instability,” causing its magnetic axis to rotate. From the perspective of space weather forecasting, it is crucial to understand the effect of this rotation on predicting B z at 1 au while implementing the spheromak model for realistic event studies. In this work, we study this by modeling a CME event on 2013 April 11 using the European Heliospheric Forecasting Information Asset. Our results show that a significant spheromak rotation up to 90° has occurred by the time it reaches 1 au, while the majority of this rotation occurs below 0.3 au. This total rotation resulted in poor predicted magnetic field topology of the ICME at 1 au. To address this issue, we further investigated the influence of spheromak density on mitigating rotation. The results show that the spheromak rotation is less for higher densities. Importantly, we observe a substantial reduction in the uncertainties associated with predicting B z when there is minimal spheromak rotation. Therefore, we conclude that spheromak rotation adversely affects B z prediction in the analyzed event, emphasizing the need for caution when employing spheromaks in global MHD models for space weather forecasting.

Near-wall bubble migration and wake structure in viscous liquids

The migration and wake structure of a single bubble in a viscous medium near a vertical wall have been experimentally investigated using a two-camera orthogonal shadowing method combined with a particle image velocimetry system. The effects of bubble size, liquid properties, and migration modes on the motion of a near-wall bubble and its wake structure are discussed. It is shown that, unlike migration in pure water, collisions between bubbles and walls are rare in viscous liquids. As viscosity increases, the mobility of the bubble near the wall changes from 3D to 2D and finally exhibits 1D motion with only one degree of freedom. While 1D motion is dominated by viscous forces, 2D migration is influenced by both wall effects and viscous forces, while 3D migration is primarily affected by bubble size. After analyzing the wakes produced by different factors, it was found that the wakes generated by mobile bubbles in three dimensions exhibit similar shedding patterns to Karman vortex streets, while two-dimensional wakes show stronger continuity. The average topological flow field structure of the bubble wake is obtained through periodic phase averaging, and the effect of different factors on the evolution of near-wall bubble wakes is analyzed.

Intermediate defect groups, polarization pairs, and noninvertible duality defects

Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing noninvertible duality defects in theories in 2k spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their (k−1)-form defect groups are concerned, including their (k−1)-form symmetries, global structures (including discrete θ-angle), and local counterterms. Using the associated symmetry topological field theory (TFT), we show that the polarization pair is capable of succinctly describing topological manipulations, e.g., gauging (k−1)-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the (k−1)-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as dualities between absolute QFTs descending from the same relative QFT. Using this formalism, we present a prescription for building noninvertible symmetries of absolute QFTs. A large class of known examples, e.g., noninvertible defects in 4D N=4 super-Yang-Mills, can be reformulated via this prescription. As another class of examples, we identify and investigate in detail a family of noninvertible duality defects in 6D superconformal field theories (SCFTs), including from the perspective of the symmetry TFT derived from type IIB string theory. Published by the American Physical Society 2024

Effective brane field theory with higher-form symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

Exkurs zur Analyse der Korrelat konstruktionen

The main idea that led me to write such research paper within the framework of Germanic linguistics is that I have not found any topic dealing with the term correlate in the German language, except in several articles in linguistic journals as well as one topic in a book describing the use of such a linguistic phenomenon in the language system. The research initially deals with the definition of the correlate at the level of the German language system. Correlate is unity describes specific relation of two sentences and identifies denoted constructs. Correlate is called a placeholder at the syntactic level because it does not occupy its original topological fields in the syntactic structure. The correlate (es) or the prepositional adverbs or adverbs can occur in the matrix clause, it is the second feature. The third categorical feature of the correlate is morphological, in that the correlate is inflexible and the last feature shows that the correlate does not confer case features on its syntactic environment, where the correlate possesses the matrix clause. The correlate can appear as the first part of the complex connector in the subordinate clause or the infinitive construction. The last feature refers to the fact that the correlate construction can be attributive in the complex sentence, whereby the sentence structure, which is the constituent of attributively formed correlate specifiers, is embedded. The research presents the conceptual content of the linguistic expression described by the correlate, functioning as a pro-element in the major premise and considered as a dentate. It is a matter of denotation of the correlate and deictic expressions. Furthermore, the present research sheds light on the obligatory and optional use of the correlate constructions in the German sentence. In German there are correlates when using certain verbs. In addition, certain linguistic constructions or expressions require correlates of both particles and prepositional adverbs. The reasons for this are contextual and communicative aspects. In relation to the contextual-communicative aspects such as verbs affect the connection with the correlate. She signals the connection through the grade particles. Compared to other verbs, the use of the correlate (es) is reduced. The reason for this is the appearance of degree particles as well, even, at most, only, only. This can be the case if the grading of the text passage does not focus on the extreme predicate, but rather on the infinitive construction or the subordinate clause. This was studied at work. Then it was examined how the correlate constructions occur with certain subjunctives by dividing them into two forms, namely attributive correlate constructions and left displacement constructions. If the correlate occurs before the subjunctive phrase, it is called an attributive correlate construction. This form is also called a correlate specifier. The subjunctive phrase has the function of being an attribute for the correlate. They can be directly followed by the correlate, whereby it is possible that the correlate alone carries the main clause after deducting the so-called phrase.

μ-L-Closed Subsets of Noetherian Generalized Topological Spaces

In the final years of the 20th century, the notion of generalized topological spaces was introduced, marking a significant shift in the field of topology. This paper focuses on a subset of on a non-empty set that is closed under arbitrary unions, defining a generalized topology and subsequently a generalized topological space (GTS) denoted by . Within this framework, we explore the concept of Noetherian generalized topological spaces and delve into the properties of closed subsets within the Noetherian GTS. The investigation reveals that subspaces of a Noetherian GTS , with the induced topology, inherit the Noetherian property and exhibit finitely many non-empty irreducible components. Furthermore, the study extends to the analysis of hereditary properties, regular , , irreducible closed subsets, and the product properties of closed subsets under continuous functions. We also establish the closure property of finite unions in Noetherian GTS and clarify the homeomorphic nature of Noetherian GTS to itself.

Wave transformations near a coronal magnetic null point

Context. Null points are often invoked in studies of quasi-periodic coronal jets and in connection with periodic signals preceding actual reconnection events. Although the periodicity of these events spans a wide range of periods, most show a 2- to 5-min periodicity compatible with the global p-modes. Aims We investigate whether magnetohydrodynamics (MHD) waves, in particular, acoustic p-modes, can cause strong current accumulation at the null points. This can in turn drive localized periodic heating in the solar corona. Methods. To do this, we began with a three-dimensional numerical setup incorporating a gravitationally stratified solar atmosphere and an axially symmetric magnetic field including a coronal magnetic null point. To excite waves, we employed wave drivers mimicking global p-modes. Using our recently developed wave-mode decomposition technique, we investigated the process of mode conversion, mode transmission, and wave reflection at various important layers of the solar atmosphere, such as the Alfvén acoustic equipartition layer and transition region. We examined the energy flux distribution in various MHD modes or in acoustic and magnetic components, as the waves propagate and interact with a magnetic field of null topology. We also examined current accumulation in the surroundings of the null point. Results. We found that most of the vertical velocity is transmitted through the Alfvén acoustic equipartition layer and maintains an acoustic nature, while a small fraction generates fast waves via the mode conversion process. The fast waves undergo almost total reflection in the transition region due to sharp gradients in density and Alfvén speed. There are only weak signatures of Alfvén wave generation near the transition region through the fast-to-Alfvén mode conversion. Because the slow waves propagate with the local sound speed, they are not much affected by the density gradients in the transition region and undergo secondary mode conversion and transmission at the Alfvén-acoustic equipartition layer surrounding the null point. This leads to fast-wave focusing at the null point. These fast waves have associated perturbations in current density and show oscillatory signatures that are compatible with the second harmonic of the driving frequency. This might result in resistive heating and in an enhanced intensity in the presence of finite resistivity. Conclusions. We conclude that MHD waves are a potential source for oscillatory current dissipation around the magnetic null point. We conjecture that in addition to oscillatory magnetic reconnection, global p-modes could lead to the formation of various quasi-periodic energetic events.