Topological Field Research Articles

A novel approach to study soft preopen sets inspired by classical topologies

Our target in the present work, is presenting the idea of weakly soft preopen (ws-preopen) subsets and studying some of its characterizations. With the assistance of some elucidative examples, the interrelationships between ws-preopen sets and some extensions of soft open sets are studied. Under some conditions such as extended and hyperconnected soft topologies, several motivating results and relationships are acquired. The interior and closure operators that built through ws-preopen and ws-preclosed subsets are introduced. Their main features that construe the relations among them are established. Soft continuity with respect to theses classes of soft subsets are studied and their substantial characteristics are investigated. Generally, the systematic relations and outcomes that are lost through the scope of this study are discussed. The proposed line in the current study will present new ways to discover novel concepts in the field of soft topology.

Star-disk interactions in the strongly accreting T Tauri star S CrA N

Context. Classical T Tauri stars are thought to accrete material from their surrounding protoplanetary disks through funnel flows along their magnetic field lines. The classical T Tauri stars with high accretion rates (∼10−7 M⊙ yr−1) are ideal targets for testing this magnetospheric accretion scenario in a sustained regime. Aims. We constrained the accretion-ejection phenomena around the strongly accreting northern component of the S CrA young binary system (S CrA N) by deriving its magnetic field topology and its magnetospheric properties, and by detecting ejection signatures, if any. Methods. We led a two-week observing campaign on S CrA N with the ESPaDOnS optical spectropolarimeter at the Canada-France-Hawaii Telescope. We recorded 12 Stokes I and V spectra over 14 nights. We computed the corresponding least-squares deconvolution (LSD) profiles of the photospheric lines and performed Zeeman-Doppler imaging (ZDI). We analyzed the kinematics of noticeable emission lines, namely He I λ5876 and the first four lines of the Balmer series, which are known to trace the accretion process. Results. We found that S CrA N is a low-mass (0.8 M⊙) young (∼1 Myr) and fully convective object exhibiting strong and variable veiling (with a mean value of 7 ± 2), which suggests that the star is in a strong accretion regime. These findings could indicate a stellar evolutionary stage between Class I and Class II for S CrA N. We reconstructed an axisymmetric large-scale magnetic field (∼70% of the total energy) that is primarily located in the dipolar component, but has significant higher poloidal orders. From the narrow emission component radial velocity curve of He I λ5876, we derived a stellar rotation period of P* = 7.3 ± 0.2 days. We found a magnetic truncation radius of ∼2 R* which is significantly closer to the star than the corotation radius of ∼6 R*, suggesting that S CrA N is in an unstable accretion regime. That the truncation radius is quite smaller than the size of the Brγ line emitting region, as measured with the GRAVITY interferometer (∼8 R*), supports the presence of outflows, which is nicely corroborated by the line profiles presented in this work. Conclusions. The findings from spectropolarimetry are complementary to those provided by optical long-baseline interferometry, allowing us to construct a coherent view of the innermost regions of a young, strongly accreting star. The strong and complex magnetic field reconstructed for S CrA N is inconsistent with the observed magnetic signatures of the emission lines associated with the postshock region, however. We recommend a multitechnique synchronized campaign of several days to place more constrains on a system that varies on a timescale of about one day.

Fast Beam Driven Neutron Yield in Thermonuclear Neutron Source Plasmas

The thermonuclear fusion between fast (super-thermal) particles injected in plasma as a neutral beam and the ions of the background plasma is expected to be the main source of fusion neutrons in FNS (fusion neutron source) design based on tokamak. Neutral beam contribution in fusion reactivity and in the total neutron yield depends on the high-energy ion fraction in the integral energy distribution. NESTOR code [1] calculates nuclear fusion rates in the FNS plasma volume, taking into account an external source of high-energy fast ions. Neutral beam model reproduces in detail the actual beam structure in phase space at the injection port plane; while the fast ion distributions in magnetically confined plasma are calculated using a combination of slowing-down classical formulae and magnetic field topology in the tokamak chamber. Here we discuss the issues relevant to the overall neutron production and the contribution of fast ions to the neutron output in plasma.

The local properties in topological groups and related concepts and questions

The next general question is considered below: when certain open subspaces of topological groups are homeomorphic to some topological group? A version of this question has been posed in [4] (open problem 1.4.1). In it, the complements to the elements in any zero-dimensional topological group were considered. A result below in this direction is Theorem 3.1 saying that if G is a σ-compact topological group and F is a nonempty compact subspace of G such that the complement G∖F is homeomorphic to some topological group, then F is a Gδ-subset of G (and therefore, by a remarkable theorem of M.M. Choban [6], F is a dyadic compactum). Another conclusion in this theorem says that if, moreover, the tightness of F is countable (in particular, if F is first countable), or if F is topologically linearly orderable, then G has a countable network. Lemma 4.1 says that if X is a Lindelöf homogeneous space with countable Souslin number and X is puncturable at some point a, then a is a Gδ-point in X, the subspace Y=X∖{a} is Lindelöf, and X is submetrizable. It follows from this that every Lindelöf topological field with countable Souslin number is submetrizable (its topology contains a metrizable topology). A natural Abelian topological group with few open subspaces that are homeomorphic to topological groups is identified in Example 3.2.

Deep-learning accelerating topology optimization of three-dimensional coolant channels for flow and heat transfer in a proton exchange membrane fuel cell

To quickly optimize the cooling performance of three-dimensional coolant channels in a proton exchange membrane fuel (PEMFC) cell, a generative adversarial network (GAN) model that adopts small-scale sample data to predict the coolant channel topology structure is constructed. The coordinate information of the topological pseudo-density field is directionally input into the neural network to improve prediction accuracy. The results show that more microtopologies in the coolant channels can be predicted with the GAN model than with traditional thermal–fluid–structural topology optimization. The topological configuration with a maximum temperature of 0.15 K, lower than the training dataset, is achieved. The well-trained GAN model can generate topological structures for the optimization objective, that is, thermal performance superior to the training set. The proposed model can also generate topological structures with better fluid and structural performance, which is 20.44% and 9.25% superior to that of the training dataset, respectively. The computation time required by the GAN model is <1 s, while the computation time for the same case is 30.2 h using the traditional thermal–fluid–structural topology optimization. These findings can aid in designing coolant channels in PEMFCs.

Customization and Information Encoding of Longitudinally Polarized Light Fields

The tightly focused structured light field displays a non‐negligible component of the electric field in the direction of propagation, i.e., the longitudinal light field. The longitudinal light field results in various novel optical phenomena, such as transverse spin angular momentum and 3D topological light fields. However, it remains a challenge to generate customized longitudinal light fields. Here, based on inverse design theory, the longitudinal light field can be customized on demand under the tightly focusing condition, which allows to generate the longitudinal light field with controllable structured distribution for propagating waves or manipulate the complex structures for all the three components of the electric field. In experiment, an experimental system is built integrating the generation, customization, and detection of structured longitudinal light field, and the customization of the longitudinal light fields with various patterns is experimentally realized. The customized longitudinal light field structures may find applications such as information encoding, long‐distance light manipulation, and novel light–matter interactions. As an example, information encoding is realized by the structured longitudinal light fields.

Highlights of recent SPIDER results and improvements

Three years of experiments on SPIDER allowed characterization of the main features of the source plasma and of the negative ion beam, in the original design configuration. For the large dimensions of the source chamber, and of the extraction area, the investigation of the single-beamlet currents and of the source plasma uniformity had to be carried out to extend the knowledge gained in smaller prototype sources. The configuration of the multiple RF drivers and filter field topologies were found to cause a peculiar behavior in the plasma confinement in the drivers, creating left-right asymmetries which were also visible in the extracted negative ion currents, even after the early implementation of a new scheme of plasma-grid current send and return busbars that greatly improved performance at high filter fields. The plasma properties in the driver and expansion region as well as the positive ion energy at the extraction region were studied in different experimental conditions, and interpreted also with the support of numerical models, suggesting that an improved plasma confinement could contribute to the increase of the plasma density, and to a certain extent to a lowering of the plasma potential profile; both effects shall contribute to increase the presence of cold negative ions for the formation of low-divergence beamlets. Early results related to unwanted RF discharges on the back of the plasma source and the gas conductance of the beam source suggested the reduction of the vessel pressure as mitigation, leading to the definition of a new pumping system. The difficulties related to the simultaneous operation, stable control and high-power operation of multiple RF self-oscillating vacuum tube based RF generators were an unambiguous obstruction to the experimentation, calling for the implementation of RF solid-state amplifiers. The initial tests related to caesium management, the non-uniform plasma properties at different locations across the plasma grid, and the challenges in the measurement of the current and divergence of the accelerated beamlet, unambiguously resulted in the need of new diagnostic systems to investigate with better resolution the spatial uniformities. This contribution summarises how the main experimental findings in the previous experimental campaigns are driving modifications to the SPIDER experiment, during the present shut down, in view of future operations.

Formation of an observed eruptive flux rope above the torus instability threshold through tether-cutting magnetic reconnection

Context. Erupting magnetic flux ropes (MFRs) are believed to play a crucial role in producing solar flares. However, the formation of erupting MFRs in complex coronal magnetic configurations and the role of their subsequent evolution in the flaring events are not fully understood. Aims. We perform a magnetohydrodynamic (MHD) simulation of active region NOAA 12241 to understand the formation of a rising magnetic flux rope during the onset of an M6.9 flare on 2014 December 18 around 21:41 UT (SOL2014-12- 18T21:41M6.9), which was followed by the appearance of parallel flare ribbons. Methods. The MHD simulation was initialised with an extrapolated non-force-free magnetic field generated from the photospheric vector magnetogram of the active region taken a few minutes before the flare. Results. The initial magnetic field topology displays a pre-existing sheared arcade enveloping the polarity inversion line. The simulated dynamics exhibit the movement of the oppositely directed legs of the sheared arcade field lines towards each other due to the converging Lorentz force, resulting in the onset of tether-cutting magnetic reconnection that produces an underlying flare arcade and flare ribbons. Concurrently, a magnetic flux rope above the flare arcade develops inside the sheared arcade and shows a rising motion. The flux rope is found to be formed in a torus-unstable region, thereby explaining its eruptive nature. Interestingly, the location and rise of the rope are in good agreement with the corresponding observations seen in extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Furthermore, the foot points of the simulation’s flare arcade match well with the location of the observed parallel ribbons of the flare. Conclusions. The presented simulation supports the development of the MFR by the tether-cutting magnetic reconnection inside the sheared coronal arcade during flare onset. The MFR is then found to extend along the polarity inversion line (PIL) through slip-running reconnection. The MFR’s eruptive nature is ascribed both to its formation in the torus-unstable region and also to the runaway tether-cutting reconnection.

Effects of Topological Defects and AB Fields on the Thermal Properties, Persistent Currents and Energy Spectra with an Exponential-Type Pseudoharmonic Potential

Effects of Topological Defects and AB Fields on the Thermal Properties, Persistent Currents and Energy Spectra with an Exponential-Type Pseudoharmonic Potential

Pathways towards truly brain-like computing primitives

Taking inspiration from biological information processing in neural assemblies, deep learning and artificial intelligence made solutions to complex problems more feasible. While at first realized by silicon-based hardware, memristive devices for vector-matrix multiplication are attracting huge focus due to their potential integration in large, parallel cross-bar arrays, mimicking the aspect of highly parallel processing (and in-memory processing) in biological neural networks. In real neuron assemblies, however, the connections are not strictly formed in a rigid 2D crossbar array, but form and degrade dynamically in a 3D environment with features of hierarchy, modularity and reconfigurability. To fully explore the capabilities of truly brain-like hardware computing, the transition towards a platform with dynamically reconfigurable connections is mandatory. This work showcases different approaches to address this biological motivation, covering the fields of Topology & Structure as well as Dynamics of biological systems, and classifies them with respect to seven fundamental principles of brain-like computing. The approaches are ranging from highly interconnected nanogranular networks with dynamically reconfigurable connections over liquid-solid composites rearranging connections via dielectrophoresis and guided redox-wiring to the mimicking of neural action potentials by relaxation-type oscillators that are used as input stimuli.

Influence of applied magnetic field in an air-breathing microwave plasma cathode

The air-breathing electric propulsion concept refers to a spacecraft in very-low Earth orbit (VLEO) ingesting upper atmospheric air as propellant for an electric thruster. This compensates atmospheric drag and allows the spacecraft to maintain its orbital altitude, removing the need for on-board propellant storage and allowing an extended mission duration which is not limited by propellant exhaustion. There is a need for development of a robust, high current density and long life cathode (or neutralizer) for air-breathing electrostatic thrusters as conventional thermionic hollow cathodes are susceptible to oxygen poisoning. An Air-breathing Microwave Plasma CAThode is proposed to overcome this issue through the use of a microwave plasma discharge, producing an extracted current in the order of 1 A with 0.1 mg s−1 of air. In this paper, the effect of varying magnetic-field strength and topology is investigated by using an electromagnet coil, which reveals a significantly different behaviour for air compared to xenon. The extracted current with xenon increases by 3.9 times from the zero-field value up to a peak around 150 mT magnetic-field strength at the antenna, whereas an applied field does not increase the extracted current with air at nominal conditions. A non-zero magnetic-field with air is however beneficial for current extraction at reduced neutral densities. A distinct increase in extracted current is identified at low bias voltages with air for a field strength of around 50 mT at the internal microwave antenna, consistent across varying field topologies. The effect of a lowered magnetic-field strength in the orifice region is investigated through the use of a secondary coil, resulting in an extracted current increase of 25% for a relaxation from 6 mT to 1 mT, and demonstrating the beneficial impact of a locally reduced field strength on electron extraction.

Decorated TQFTs and their Hilbert spaces

We discuss topological quantum field theories that compute topological invariants which depend on additional structures (or decorations) on three-manifolds. The q-series invariant Ẑ(q) proposed by Gukov, Pei, Putrov, and Vafa is an example of such an invariant. We describe how to obtain these decorated invariants by cutting and gluing and make a proposal for Hilbert spaces that are assigned to two-dimensional surfaces in the Ẑ-TQFT.

X-ray emission from pre-main sequence stars with multipolar magnetic fields

ABSTRACT The large-scale magnetic fields of several pre-main sequence (PMS) stars have been observed to be simple and axisymmetric, dominated by tilted dipole and octupole components. The magnetic fields of other PMS stars are highly multipolar and dominantly non-axisymmetric. Observations suggest that the magnetic field complexity increases as PMS stars evolve from Hayashi to Henyey tracks in the Hertzsprung–Russell diagram. Independent observations have revealed that X-ray luminosity decreases with age during PMS evolution, with Henyey track PMS stars having lower fractional X-ray luminosities (LX/L*) compared to Hayashi track stars. We investigate how changes in the large-scale magnetic field topology of PMS stars influences coronal X-ray emission. We construct coronal models assuming pure axisymmetric multipole magnetic fields, and magnetic fields consisting of a dipole plus an octupole component only. We determine the closed coronal emitting volume, over which X-ray-emitting plasma is confined, using a pressure balance argument. From the coronal volumes, we determine X-ray luminosities. We find that LX decreases as the degree ℓ of the multipole field increases. For dipole plus octupole magnetic fields, we find that LX tends to decrease as the octupole component becomes more dominant. By fixing the stellar parameters at values appropriate for a solar mass PMS star, varying the magnetic field topology results in two orders of magnitude variation in LX. Our results support the idea that the decrease in LX as PMS stars age can be driven by an increase in the complexity of the large-scale magnetic field.

Don't forget the boundary problem! How EM field topology can address the overlooked cousin to the binding problem for consciousness.

The boundary problem is related to the binding problem, part of a family of puzzles and phenomenal experiences that theories of consciousness (ToC) must either explain or eliminate. By comparison with the phenomenal binding problem, the boundary problem has received very little scholarly attention since first framed in detail by Rosengard in 1998, despite discussion by Chalmers in his widely cited 2016 work on the combination problem. However, any ToC that addresses the binding problem must also address the boundary problem. The binding problem asks how a unified first person perspective (1PP) can bind experiences across multiple physically distinct activities, whether billions of individual neurons firing or some other underlying phenomenon. To a first approximation, the boundary problem asks why we experience hard boundaries around those unified 1PPs and why the boundaries operate at their apparent spatiotemporal scale. We review recent discussion of the boundary problem, identifying several promising avenues but none that yet address all aspects of the problem. We set out five specific boundary problems to aid precision in future efforts. We also examine electromagnetic (EM) field theories in detail, given their previous success with the binding problem, and introduce a feature with the necessary characteristics to address the boundary problem at a conceptual level. Topological segmentation can, in principle, create exactly the hard boundaries desired, enclosing holistic, frame-invariant units capable of effecting downward causality. The conclusion outlines a programme for testing this concept, describing how it might also differentiate between competing EM ToCs.

Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields

Context. Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. Aims. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. Methods. We used the powerful analytical Racah-Wigner algebra used in quantum mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various realistically plausible topologies of fossil magnetic fields. We also computed the induced perturbation of their frequencies. Results. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to the unraveling of the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Conclusions. Asymmetries of dipolar mixed modes provide a key bit of information on the geometrical topology of deep fossil magnetic fields, but this is insufficient on its own. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries.

Coupled quantum vortex kinematics and Berry curvature in real space

The Berry curvature provides a powerful tool to unify several branches of science through their geometrical aspect: topology, energy bands, spin and vector fields. While quantum defects–phase vortices and skyrmions–have been in the spotlight, as rotational entities in condensates, superfluids and optics, their dynamics in multi-component fields remain little explored. Here we use two-component microcavity polaritons to imprint a dynamical pseudospin texture in the form of a double full Bloch beam, a conformal continuous vortex beyond unitary skyrmions. The Berry curvature plays a key role to link various quantum spaces available to describe such textures. It explains for instance the ultrafast spiraling in real space of two singular vortex cores, providing in particular a simple expression–also involving the complex Rabi frequency–for their intricate velocity. Such Berry connections open new perspectives for understanding and controlling highly-structured quantum objects, including strongly asymmetric cases or even higher multi-component fields.

Damping of coronal oscillations in self-consistent 3D radiative magnetohydrodynamics simulations of the solar atmosphere

Context. Oscillations are abundant in the solar corona. Coronal loop oscillations are typically studied using highly idealised models of magnetic flux tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of a realistic magnetic field topology and the density structuring. Aims. We analyse the damping of coronal oscillations using a self-consistent 3D radiation-magnetohydrodynamics simulation of the solar atmosphere spanning from the convection zone into the corona, the associated oscillation dissipation and heating, and finally, the physical processes that cause the damping and dissipation. The simulated corona that forms in this model does not depend on any prior assumptions about the shape of the coronal loops. Methods. We analysed the evolution of a bundle of magnetic loops by tracing the magnetic field. Results. We find that the bundle of magnetic loops shows damped transverse oscillations in response to perturbations in two separate instances, with oscillation periods of 177 s and 191 s, velocity amplitudes of 10 km s−1 and 16 km s−1, and damping times of 176 s and 198 s. The coronal oscillations lead to the development of velocity shear in the simulated corona, which results in the formation of vortices seen in the velocity field that are caused by the Kelvin-Helmholtz instability. This contributes to the damping and dissipation of the transverse oscillations. Conclusions. The oscillation parameters and evolution we observed are in line with the values that are typically seen in observations of coronal loop oscillations. The dynamic evolution of the coronal loop bundle suggests that the models of monolithic and static coronal loops with constant lengths might need to be re-evaluated by relaxing the assumption of highly idealised wave guides.

Properties of the Turbulence and Topology in a Turbulent Magnetic Reconnection

Magnetic reconnection is a crucial process responsible for energy conversion and particle acceleration in space, astrophysical, and laboratory plasmas. Turbulence and magnetic reconnection can be mutually driven, but the underlying nature of energy dissipation, intrinsic turbulence waves, and magnetic field topologies in turbulent magnetic reconnection is still poorly understood. Here, using advanced multi-spacecraft mission and innovative methods, we provide a few new perspectives to investigate the properties of the turbulence and topology in a turbulent magnetic reconnection in the magnetotail. Our results reveal that in turbulent magnetic reconnection: (1) cyclotron resonance, an important mechanism of energy dissipation, is more effective in the core region of the reconnection than in the outflow regions; (2) energy is deposited in the form of kinetic Alfvén waves (KAWs) and fast/slow waves, with KAWs corresponding to low-frequency (ion cyclotron scale) and fast/slow waves corresponding to high-frequency (low-hybrid scale); and (3) the number of spiral nulls (O-lines) were about 3.6 times more than radial ones (X-lines), and three-dimensional structures were about 8 times more prevalent than two-dimensional ones. These findings should help us better unravel the dynamics of turbulent magnetic reconnection.

Locally Meshable Frame Fields

The main robustness issue of state-of-the-art frame field based hexahedral mesh generation algorithms originates from non-meshable topological configurations, which do not admit the construction of an integer-grid map but frequently occur in smooth frame fields. In this article, we investigate the topology of frame fields and derive conditions on their meshability, which are the basis for a novel algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 58%, when compared on the challenging HexMe dataset [Beaufort et al. 2022]. The source code of our implementation and the data of our experiments are available at https://lib.algohex.eu.

Minimal nondegenerate extensions

We prove that every slightly degenerate braided fusion category admits a minimal nondegenerate extension, and hence that every pseudo-unitary super modular tensor category admits a minimal modular extension. This completes the program of characterizing minimal nondegenerate extensions of braided fusion categories. Our proof relies on the new subject of fusion 2 2 -categories. We study in detail the Drinfel’d centre Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) of the fusion 2 2 -category M o d - B {_{}\mathrm {Mod}\text {-}\mathcal {B}} of module categories of a braided fusion 1 1 -category B \mathcal {B} . We show that minimal nondegenerate extensions of B \mathcal {B} correspond to certain trivializations of Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) . In the slightly degenerate case, such trivializations are obstructed by a class in H 5 ( K ( Z 2 , 2 ) ; k × ) H^5(K(\mathbb {Z}_2, 2); \mathbb {k}^\times ) and we use a numerical invariant—defined by evaluating a certain two-dimensional topological field theory on a Klein bottle—to prove that this obstruction always vanishes. Along the way, we develop techniques to explicitly compute in braided fusion 2 2 -categories which we expect will be of independent interest. In addition to the model of Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) in terms of braided B \mathcal {B} -module categories, we develop a computationally useful model in terms of certain algebra objects in B \mathcal {B} . We construct an S S -matrix pairing for any braided fusion 2 2 -category, and show that it is nondegenerate for Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) . As a corollary, we identify components of Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) with blocks in the annular category of B \mathcal {B} and with the homomorphisms from the Grothendieck ring of the Müger centre of B \mathcal {B} to the ground field.