Topological Conditions Research Articles

From incoherent field to coherent reconnection

Context. Magnetic reconnection in the quiet Sun is a phenomenon that is consistently observed, however, its conditions of occurrence are not as well known as for more energetic events. It has recently become feasible to address this issue with 3D numerical simulations of realistically stratified and convection-driven reconnection. Aims. We aim to illustrate ways by which quiet Sun fields may contribute to solar atmospheric heating via magnetic reconnection that is driven by convective motion. We also aim to compare our complex stratified model to earlier idealized coronal models in terms of reconnection drivers and topological conditions. Methods. We analyzed a simulation of the quiet Sun in which a complex coronal magnetic field is self-consistently driven by the underlying convection. We employed a selection of Lagrangian markers to trace the spatiotemporal behavior of specific magnetic features that are relevant to magnetic reconnection and atmospheric heating. Results. A relatively large-scale reconnection-driven heating event occurs in the simulated corona, in a flattened X-shaped feature characterized by a weak field and high current. It is reminiscent of a hyperbolic flux tube (HFT), which is located at the interface between multiple flux systems. One of these is a smooth overlying horizontal field and the two most relevant others are located below the HFT. They consist of an arcade and a horizontal flux rope which eventually reconnect with the overlying field, raising coronal plasma temperatures up to 1.47 MK. Conclusions. We have identified a reconnection-driven coronal heating event in a quiet Sun simulation. We find that our results are in good phenomenological agreement with idealized coronal flare models, which demonstrates that the same general physical concepts are valid. However, we also find that the reconnecting flux rope and arcade are neither formed by any obvious coherent flux emergence, nor by any ordered photospheric motion or flux cancellation. Instead, they seem to develop merely from the self-consistent convective driving of pre-existing tangled field lines. This gradual and smooth ordering suggests an inverse cascade of magnetic helicity via smaller reconnection events, located at or above slowly-moving photospheric flux concentrations. We suggest that this case is representative of many heating events that may be ubiquitous in the real quiet Sun.

Existence of matching priors on compact spaces

Summary A matching prior at level $1-\alpha$ is a prior such that an associated $1-\alpha$ credible region is also a $1-\alpha$ confidence set. We study the existence of matching priors for general families of credible regions. Our main result gives topological conditions under which matching priors for specific families of credible regions exist. Informally, we prove that, on compact parameter spaces, a matching prior exists if the so-called rejection-probability function is jointly continuous when we adopt the Wasserstein metric on priors. In light of this general result, we observe that typical families of credible regions, such as credible balls, highest-posterior density regions, quantiles, etc., fail to meet this topological condition. We show how to design approximate posterior credible balls and highest-posterior density regions that meet these topological conditions, yielding matching priors. Finally, we evaluate a numerical scheme for computing approximately matching priors based on discretization and iteration. The proof of our main theorem uses tools from nonstandard analysis and establishes new results about the nonstandard extension of the Wasserstein metric that may be of independent interest.

The simple type conjecture for mod 2 Seiberg–Witten invariants

We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg–Witten simple type. This result shows that there exists a large class of topological 4-manifolds such that all smooth structures have mod 2 simple type, and yet some have non-vanishing (mod 2) Seiberg–Witten invariants. As corollaries, we obtain adjunction inequalities and show that, under a mild topological condition, every geometrically simply connected closed 4-manifold has the vanishing mod 2 Seiberg–Witten invariant for at least one orientation.

A note on stabilisations of manifolds

In this short note we consider the relationships between two topological tameness condition at infinity of open manifolds in the case of product with a ball.

Hydrocarbon Products Occluded within Zeolite Micropores Impose Transport Barriers that Regulate Brønsted Acid-Catalyzed Propene Oligomerization.

Brønsted acid zeolites catalyze alkene oligomerization to heavier hydrocarbon products of varied size and branching. Propene dimerization rates decrease monotonically with increasing crystallite size for MFI zeolites synthesized with fixed H+-site density, revealing the strong influence of intrazeolite transport limitations on measured rates, which has gone unrecognized in previous studies. Transient changes in dimerization rates upon step-changes in reactant pressure (150-470 kPa C3H6) or temperature (483-523 K) reveal that intrazeolite diffusion limitations become more severe under reaction conditions that favor the formation of heavier products. Together with effectiveness factor formalisms, these data reveal that product and reactant diffusion, and consequently oligomerization rates and selectivity, are governed by the composition of hydrocarbon products that accumulate within zeolitic micropores during alkene oligomerization. This occluded organic phase strongly influences rates and selectivities of alkene oligomerization on medium-pore zeolites (MFI, MEL, TON). Recognizing the coupled influences of kinetic factors and intrazeolite transport limitations imposed by occluded reaction products provides opportunities to competently tailor rates and selectivity in alkene oligomerization and other molecular chain-growth reactions through judicious selection of zeolite topology and reaction conditions.

Cooperative distributed state estimation: resilient topologies against smart spoofers

A network of observers is considered, where through asynchronous (with bounded delay) communications, they cooperatively estimate the states of a linear time-invariant (LTI) system. In such a setting, a new type of adversary might affect the observation process by impersonating the identity of the regular node, which is a violation of communication authenticity. These adversaries also inherit the capabilities of Byzantine nodes, making them more powerful threats called smart spoofers. We show how asynchronous networks are vulnerable to smart spoofing attack. In the estimation scheme considered in this paper, information flows from the sets of source nodes, which can detect a portion of the state variables each, to the other follower nodes. The regular nodes, to avoid being misguided by the threats, distributively filter the extreme values received from the nodes in their neighborhood. Topological conditions based on strong robustness are proposed to guarantee the convergence. Two simulation scenarios are provided to verify the results.

NLS Based Hierarchical Anti-Disturbance Controller for Vehicle Platoons With Time-Varying Parameter Uncertainties

Cooperative adaptive cruise control (CACC) is a promising technology for vehicle platoons to increase roadway capacity. This paper proposes a networked Lagrange system (NLS) based CACC dynamic model based on which a hierarchical anti-disturbance controller is developed to solve the stability problem of CACC in vehicle platoons with time-varying parameter uncertainties, external disturbances, and directional dynamic communication topology. First, a hierarchical anti-disturbance controller for NLS is constructed which comprises three layers, these are, the adaptive smooth estimator-control layer, the distributed classifying amplitude-related layer, and the anti-disturbance control layer, in which the parameter uncertainties are estimated in the adaptive smooth estimator-control layer, the disturbance classification and distribute control are executed in the distributed classifying amplitude-related layer and the anti-disturbance control layer respectively. In addition, the proposed controller is extended to address the stability problem of CACC in vehicle platoons with time-varying parameter uncertainties, external disturbances, and directional dynamic communication topology conditions, which shows the versatility of the controller. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented controllers.

Topological differentiation of the vegetation cover of the Sandomiria Upper Dnister geobotanical district

The article provides distribution patterns of natural vegetation depending on topological conditions and outlines the main directions of its anthropogenic transformation. The boundaries as well as botanical and geographical features of the studied district are specified. The syntaxonomic classification of plant communities is presented. The combinative ecological and coenotic profile was created showing distribution patterns of the main plant communities in relation to changes in the indicator values of ecological factors. Three types of mesocombinations are distinguished: forest, grassland (meadow) and swamp-flood ones. Averaged (relevant) indicator values were calculated based on environmental conditions. It has been established that the forest range is characterized by the indicators close to the background ones, which indicate a high stabilizing role of forest ecosystems. Correlative dependence between changes in indicators of certain factors was found, that enables to predict possible cause-and-effect changes. Under current trends of anthropogenic and climatic changes, a decrease in the humidity regime along with raise in soil pH can be expected in the future, while increase in seasonal changes in moisture will accelerate processes of nitrification and soil mineralization. Some habitats within the district are under significant negative effect of invasive species, e.g. the territory between the Lomnytsia River and Kolomyia town is classified as the one under the highest degree of threats due to huge, probably largest in Ukraine, areas of Heracleum sosnowskyi, Erigeron annuus, Solidago canadensis and Rudbeckia laciniata. In the future, this region may undergo substantial transformation and a special attention is required to protect its biodiversity.

Higher central charges and topological boundaries in 2+1-dimensional TQFTs

A 2+1-dimensional topological quantum field theory (TQFT) may or may not admit topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition for the existence of a topological boundary condition is that the chiral central charge c_-c− has to vanish. In this paper, we consider conditions associated with ``higher" central charges, which have been introduced recently in the math literature. In terms of these new obstructions, we identify necessary and sufficient conditions for the existence of a topological boundary in the case of bosonic, Abelian TQFTs, providing an alternative to the identification of a Lagrangian subgroup. Our proof relies on general aspects of gauging generalized global symmetries. For non-Abelian TQFTs, we give a geometric way of studying topological boundary conditions, and explain certain necessary conditions given again in terms of the higher central charges. Along the way, we find a curious duality in the partition functions of Abelian TQFTs, which begs for an explanation via the 3d-3d correspondence.

Effective magnetic monopole mechanism for localized electron pairing in HTS

The mechanism responsible for spatially localized strong coupling electron pairing characteristic of high-temperature superconductors (HTS) remains elusive and is a subject of hot debate. Here we propose a new HTS pairing mechanism which is the binding of two electrons residing in adjacent conducting planes of layered HTS materials by effective magnetic monopoles forming between these planes. The pairs localized near the monopoles form real-space seeds for superconducting droplets and strong coupling is due to the topological Dirac quantization condition. The pairing occurs well above the superconducting transition temperature Tc. Localized electron pairing around effective monopoles promotes, upon cooling, the formation of superconducting droplets connected by Josephson links. Global superconductivity arises when strongly coupled granules form an infinite cluster, and global superconducting phase coherence sets in. The resulting Tc is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way for tailoring materials with elevated superconducting transition temperatures.

Stoechiometric and dynamical autocatalysis for diluted chemical reaction networks.

Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. (PNAS 117(41):25230-25236, 2020) gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions such that the balance for all autocatalytic species is strictly positive, and investigated minimal autocatalytic networks, called autocatalytic cores. By contrast, spontaneous autocatalysis-namely, exponential amplification of all species internal to a reaction network, starting from a diluted regime, i.e. low concentrations-is a dynamical property. We introduce here a topological condition (Top) for autocatalysis, namely: restricting the reaction network description to highly diluted species, we assume existence of a strongly connected component possessing at least one reaction with multiple products (including multiple copies of a single species). We find this condition to be necessary and sufficient for stoechiometric autocatalysis. When degradation reactions have small enough rates, the topological condition further ensures dynamical autocatalysis, characterized by a strictly positive Lyapunov exponent giving the instantaneous exponential growth rate of the system. The proof is generally based on the study of auxiliary Markov chains. We provide as examples general autocatalytic cores of Type I and Type III in the typology of Blokhuis et al. (PNAS 117(41):25230-25236, 2020) . In a companion article (Unterberger in Dynamical autocatalysis for autocatalytic cores, 2021), Lyapunov exponents and the behavior in the growth regime are studied quantitatively beyond the present diluted regime .

A Real-Time Calibrated Adaptive-ZVS Class-D Power Amplifier for 6.78 MHz Wireless Power Transfer System

This brief presents a class-D power amplifier (PA) with an adaptive zero-voltage switching (A-ZVS) technique for 6.78 MHz resonant wireless power transfer (R-WPT) system. In R-WPT operation, the loading impedance of a PA can be varied by the process tolerance of the LC resonant components or WPT environments, such as the resonant topology, coupling coefficient, and loading condition of the receiver. In particular, the commonly used series-parallel resonant topology suffers from resonant point deviation of primary LC tank, resulting in hard switching of the PA. Consequently, efficiency degradation and electromagnetic interference can occur under multi-MHz operation. The proposed A-ZVS feedback loop calibrates the equivalent resonant capacitance in real-time to achieve ZVS by adjusting the loading impedance to be slightly inductive. The proposed PA was fully integrated except for one switched capacitor used as the tuning element and fabricated in a TSMC 0.18 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> BCD process. The measurement results demonstrated robust ZVS operation with a peak system efficiency of 52.7 % and an enhanced maximum transmitting power of 107 %.

Approximation of discontinuous inverse operators with neural networks

In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a regularizing inverse operator by using a dataset of input–output pairs of the forward model rely on deep learning techniques. In these approaches, a neural network (NN) is trained to predict the value of the sought parameters directly from the data. In this paper, we show that these methods provide suboptimal results when a regularizing inverse operator is discontinuous with respect to the Euclidean topology. Hence, we propose a two-step strategy for approximating it by means of a NN, which works under general topological conditions. First, we embed the parameters into a subspace of a low-dimensional Euclidean space; second, we use a NN to approximate a homeomorphism between the subspace and the image of the parameter space through the forward operator. The parameters are then retrieved by applying the inverse of the embedding to the network predictions. The results are shown for the problem of x-ray imaging of solar flares with data from the Spectrometer/Telescope for Imaging X-rays. In this case, the parameter space is homeomorphic to a Moebius strip. Our simulation studies show that the use of a NN for predicting the parameters directly from the data yields systematic errors due to the non-Euclidean topology of the parameter space. The proposed strategy overcomes the discontinuity issues and furnishes stable and accurate reconstructions.

Topology, Oxidation States, and Charge Transport in Ionic Conductors

AbstractRecent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge‐invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday's picture of ionic transport—whereby each atom carries a well‐defined integer charge—with a rigorous quantum description of the electronic charge‐density distribution, which hardly suggests its partition into well defined atomic contributions. In this paper, these progresses are reviewed; in particular, it is shown how, by relaxing some general topological conditions, charge may be transported in ionic conductors without any net ionic displacements. After reporting numerical experiments which corroborate these findings, a new connection between the topological picture and the well‐known Marcus–Hush theory of electron transfer is introduced in terms of the topology of adiabatic paths drawn by atomic trajectories. As a significant byproduct, the results reviewed here permit to classify different regimes of ionic transport according to the topological properties of the electronic structure of the conducting material. Finally, a few recent applications to energy materials and planetary sciences are reported.

Absolute Continuity of the Harmonic Measure on Low Dimensional Rectifiable Sets

In the past decades, we learnt that uniform rectifiability is often a right candidate to go past Lipschitz boundaries in boundary value problems. If Omega is an open domain in mathbb {R}^n with mild topological conditions, we can even characterize the n-1 dimensional uniformly rectifiability of the boundary partial Omega by the A_infty -absolute continuity of the harmonic measure on partial Omega with respect to the surface measure. In low dimension (d<n-1), David and Mayboroda tackled one direction of the above characterization, i.e. proved that if Gamma is a d-dimensional uniformly rectifiable set, then the harmonic measure (associated to an suitable degenerate elliptic operator) on Gamma is A_infty -absolutely continuous with respect to the d-dimensional Hausdorff measure. In the present article, we use a completely new approach to give an alternative and significantly shorter proof of David and Mayboroda’s result.

Physical limits to human brain B0 shimming with spherical harmonics, engineering implications thereof.

As the MRI main magnetic field rises for improved signal-to-noise ratio, susceptibility-induced B0-inhomogeneity increases proportionally, aggravating related artifacts. Considering only susceptibility disparities between air and biological tissue, we explore the topological conditions for which perfect shimming could be performed in a Region of Interest (ROI) such as the human brain or part thereof. After theoretical considerations for perfect shimming, spherical harmonic (SH) shimming simulations of very high degree are performed, based on a 100-subject database of 1.7-mm-resolved brain fieldmaps acquired at 3T . In addition to the whole brain, shimmed ROIs include slabs targeting the prefrontal cortex, both or single temporal lobes, or spheres in the frontal brain above the nasal sinus. We show "perfect" SH shimming is possible only if the ROI can be contained in a sphere that does not enclose sources of magnetic field inhomogeneity, which are gathered at the air-tissue interface. We establish a [Formula: see text]Hz inhomogeneity hard shim limit at 7T for whole brain SH shimming, that can only be attained at shimming degree higher than 90. On the other hand, under limited power and SH degree resources, 3D region-specific shimming is shown to greatly improve homogeneity in critical zones such as the prefrontal cortex and around ear canals.

The second closed geodesic, the fundamental group, and generic Finsler metrics

For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. We show a bumpy metrics theorem for Finsler metrics and prove that a C^4-generic Finsler metric on a compact and simply-connected manifold carries infinitely many closed geodesics.

Pair-partitioned bulk localized states induced by topological band inversion

Photonic topological insulators have recently received widespread attention mainly due to their ability to provide directions in the development of photonic integration platforms. The proposal for a topological bulk cavity with a single-mode expands upon previous research works on topological cavities; thus, interest in topological edge states and corner states is beginning to shift into analysis on bulk properties and their applications. However, there remains a gap in research on a multi-mode cavity of the topological photonic crystals (PCs). In this Letter, a cavity of the topological PCs is proposed involving pair-partitioned bulk localized states (BLSs) from a two-dimensional inner and outer nested square lattice (2D IONSL), which can enable a multi-mode cavity for the topological PCs. First, the topological characteristics are described in terms of a Zak phase, and band inversions are achieved by changing the size of scatterers in the inner and outer circles that reside within the unit cell. Afterwards, analogous to the tight-binding model for electronic systems, the Hamiltonian and topological phase transition conditions of 2D IONSL PCs are derived. Furthermore, it is proposed that the demonstrated optical field reflection and confinement mechanism induced by topological band inversions due to the opposite parities of wavefunctions may lead to the phenomenon of pair-partitioned BLSs. This research increases the research works of bulk topological effects, creating a route for photonic integration platforms for near-infrared.

Event-Based Tracking Consensus for Multiagent Systems With Volatile Control Gain.

This work investigates the tracking consensus problem of multiagent systems over directed networks, where the control gains follow certain volatile patterns. Some event-based consensus protocols are formulated so as to reduce the redundant execution of control. By using an extended differential inequality with a time-dependent coefficient, criteria for tracking consensus under time- and state-dependent triggering conditions are constructed, respectively. It is proved that the time average of the control gain, together with the agent dynamics, network topology, and triggering conditions, governs the consensus despite the fluctuation of control gain. The derived theorem can be utilized to ensure consensus with intermittent strategies aiming to lessen the burden in communications, including aperiodic on-off control with periodic perturbation and pulse-modulated on-off control. Unlike existing works, the requirement of a positive lower bound of control ratios is removed and, thus, a wide range of control gain patterns is possible, signifying higher flexibility in intermittent policy design. Finally, numerical examples are provided to further illustrate the theoretical results.

S-Transform Based Traveling Wave Directional Pilot Protection for Hybrid LCC-MMC-HVDC Transmission Line

In this paper, the traveling wave protection issue of a hybrid high-voltage direct-current transmission line based on the line-commutated converter and modular multilevel converter is investigated. Generally, traveling wave protection based on voltage variation criterion, voltage variation rate criterion and current variation rate criterion is applied on hybrid high-voltage direct-current transmission lines as primary protection. There are two issues that should be addressed: (i) it has no fault direction identification capability which may cause wrong operation regarding external faults; and (ii) it does not consider the difference between line-commutated converter based rectifier station topology and modular multilevel converter based inverter station topology. Therefore, a novel traveling wave directional pilot protection principle for the hybrid high-voltage direct-current transmission line is proposed based on the S-transform. Firstly, the data processing capability of S-transform is described. Secondly, the typical traveling wave propagation process on a hybrid high-voltage direct-current transmission line is studied. Thirdly, a novel traveling wave fault direction identification principle is proposed. Eventually, based on PSCAD/EMTDC, a typical ±400 kV hybrid high-voltage direct-current transmission system is used for a case study to verify its robustness against fault location, fault resistance and fault type.