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The azimuthal self-magnetic field of the ideal Z pinch contains a central magnetic null. Trajectories around this null govern transport in the core. Particles follow cyclotron orbits when the guiding-center approximation holds. Approaching the field null, where the ordinary guiding-center regime breaks down, particles exhibit trajectories called, in some historical contexts, betatron orbits. We quantify transitional magnetization between cyclotron and betatron orbits by a magnetization parameter that decomposes phase space into these orbit regimes. Considering the distribution of all orbits, this phase-space decomposition reveals a transitional magnetization region wherein both populations coexist. Classical magnetized transport theory fails within this region, where the diamagnetic drift reverses. The drift flux is instead supported by the flux of betatron orbits. Kinematic diffusivity remains approximately constant rather than diverging at the null. These transport modifications are governed solely by the number density per unit length in the ideal pinch.

We investigate the correspondence between the geometry of a smooth compact Lie group action on a manifold $\mathrm{M}$ and the intrinsic smooth structure of the orbit space $\mathrm{M}/\mathrm{G}$. While the action on $\mathrm{M}$ is classically organized by the orbit-type stratification, we show this structure fails to predict the intrinsic $Klein\ stratif\!ication$ of the quotient, which partitions the space into the orbits of local diffeomorphisms, thereby classifying the space by its intrinsic singularity types. The correct correspondence, we prove, is governed by a finer partition on $\mathrm{M}$: the $isostabilizer\ decomposition$. We establish a surjective map from the components of this partition to the Klein strata of $\mathrm{M}/\mathrm{G}$. As a corollary, we obtain by pullback a new canonical stratification on $\mathrm{M}$, the $Inverse\ Klein\ Stratif\!ication$, and clarify its relationship with classical structures.

The third Gaia data release (DR3) contains $\sim$170\,000 astrometric orbit solutions of two-body systems located within $\sim$500 pc of the Sun. Determining component masses in these systems, in particular of stars hosting exoplanets, usually hinges on incorporating complementary observations in addition to the astrometry, e.g. spectroscopy and radial velocities. Several Gaia DR3 two-body systems with exoplanet, brown-dwarf, stellar, and black-hole components have been confirmed in this way. We developed an alternative machine learning approach that uses only the Gaia DR3 orbital solutions with the aim of identifying the best candidates for exoplanets and brown-dwarf companions. Based on confirmed substellar companions in the literature, we use semi-supervised anomaly detection methods in combination with extreme gradient boosting and random forest classifiers to determine likely low-mass outliers in the population of non-single sources. We employ and study feature importance to investigate the method's plausibility and produced a list of 20 best candidates of which two are exoplanet candidates and another five are either very-massive brown dwarfs or very-low mass stars. Three can

Orbital parameters, such as eccentricity and maximum vertical excursion, of stars in the Milky Way are an important tool for understanding its dynamics and evolution, but calculation of such parameters usually relies on computationally-expensive numerical orbit integration. We present and test a fast method for estimating these parameters using an application of the Stäckel fudge, used previously for the estimation of action-angle variables. We show that the method is highly accurate, to a level of $<1\%$ in eccentricity, over a large range of relevant orbits and in different Milky Way-like potentials, and demonstrate its validity by estimating the eccentricity distribution of the RAVE-TGAS data set and comparing it to that from orbit integration. Using the method, the orbital characteristics of the $\sim 7$ million $\textit{Gaia}$ DR2 stars with radial velocity measurements are computed with Monte Carlo sampled errors in $\sim 116$ hours of parallelised cpu time, at a speed that we estimate to be $\sim 3$ to $4$ orders of magnitude faster than using numerical orbit integration. We demonstrate using this catalogue that $\textit{Gaia}$ DR2 samples a large range of orbits in the s

This article is a brief review of Zeeman spin-orbit coupling, arising in a low-carrier commensurate Néel antiferromagnet subject to magnetic field. The field tends to lift the degeneracy of the electron spectrum. However, a hidden symmetry protects double degeneracy of Bloch eigenstates at special momenta in the Brillouin zone. The effective transverse $g$-factor vanishes at such points, thus acquiring a substantial momentum dependence, which turns a textbook Zeeman term into a spin-orbit coupling. After describing the symmetry underpinnings of the Zeeman spin-orbit coupling, I compare it with its intrinsic counterparts such as Rashba coupling, and then show how Zeeman spin-orbit coupling may survive in the presence of intrinsic spin-orbit coupling. Finally, I outline some of the likely experimental manifestations of Zeeman spin-orbit coupling, and compare it with similar phenomena in other settings such as semiconducting quantum wells.

Since the discovery of the figure-8 orbit for the three-body problem [Moore 1993] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have appeared in the literature are either planar or are obtained from perturbations of planar orbits. Here we exhibit a number of new three-dimensional periodic n-body orbits with equal masses and cubic symmetry. We found these orbits numerically by minimizing the action as a function of the trajectories' Fourier coefficients. We also give numerical evidence that a planar 3-body orbit first found in [Hénon, 1976], rediscovered by [Moore 1993], and found to exist for different masses by [Nauenberg 2001], is dynamically stable. It is a pleasure to dedicate this paper to Philip Holmes.

We characterize the actions of compact tori on smooth manifolds for which the orbit space is a topological manifold (either closed or with boundary). For closed manifolds the result was originally proved by Styrt in 2009. We give a new proof for closed manifolds which is also applicable to manifolds with boundary. In our arguments we use the result of Provan and Billera who characterized matroid complexes which are pseudomanifolds. We study the combinatorial structure of torus actions whose orbit spaces are manifolds. In two appendix sections we give an overview of two theories related to our work. The first one is the combinatorial theory of Leontief substitution systems from mathematical economics. The second one is the topological Kaluza--Klein model of Dirac's monopole studied by Atiyah. The aim of these sections is to draw some bridges between disciplines and motivate further studies in toric topology.

In the nineteenth century, the Netherlands quickly adopted the time ball -- a British innovation for maritime chronometer calibration -- in its main naval ports (Nieuwediep/Den Helder, Vlissingen, Hellevoetsluis) and commercial centres (Amsterdam, Rotterdam). A large sphere dropped from a mast at a fixed time, the device enabled ships to verify their chronometers against a standard, essential for accurate longitude determination and safe navigation. Its ready acceptance was eased by indigenous Dutch traditions. Rural communities had long used visual time signals like the sjouw on Terschelling island, a wicker ball raised on a mast to mark the lunch hour and milking time for farmers, and the lawei, a basket or sack used in the peat bogs of Friesland to regulate labourers' hours. The Dutch time-signal system was distinguished by its strong institutional backing from the country's Royal Navy, its Hydrographic Service and by professional astronomers. Among the latter, Frederik Kaiser was a pivotal figure, vehemently defending the system's accuracy and pioneering technical improvements. He successfully advocated for replacing the traditional falling ball with a system of rotating flaps,

Let g be a semisimple Lie algebra with h a Cartan subalgebra. The orbit method attempts to assign representations of g to orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits which should lead to highest weight representations of g. It is known that all unitary highest weight representations can be obtained in this fashion. A hypersurface orbital variety is one which is of codimension 1 in the nilradical of a parabolic. Their classification for g = sl(n) obtains from general results. Recently Benlolo and Sanderson conjectured the form of the (non-linear) element describing such a variety. This paper proves that conjecture and further constructs a simple module with integral highest weight which ``quantizes'' the variety in the precise sense that the regular functions of its closure is given a g module structure compatible (up to shift by the highest weight) with its h module structure.

Large low-Earth orbit (LEO) satellite networks are being built to provide low-latency broadband Internet access to a global subscriber base. In addition to network transmissions, researchers have proposed embedding compute resources in satellites to support LEO edge computing. To make software systems ready for the LEO edge, they need to be adapted for its unique execution environment, e.g., to support handovers in face of satellite mobility. So far, research around LEO edge software systems has focused on the predictable behavior of satellite networks, such as orbital movements. Additionally, we must also consider failure patterns, e.g., effects of radiation on compute hardware in space. In this paper, we present a taxonomy of failures that may occur in LEO edge computing and how they could affect software systems. From there, we derive considerations for LEO edge software systems and lay out avenues for future work.

When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the altitude of the satellite becomes high, which is the case around the apocentre of this type of orbit. For several reasons, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and therefore limited to quasi-circular orbits [17, 25]. On the other hand, the time-dependency due to the motion of the third-body is often neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the disturbing function into a finite polynomial using Fourier expansions of elliptic motion functions in multiple of the satellite's eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, we show how to perform a normalization of the expanded Hamiltonian by means of a time-dependent Lie transformation which aims to eliminate peri

Accurate measurements of osculating orbital elements are essential in order to understand and model the complex dynamic behavior of Near Earth Asteroids (NEAs). ESA's Gaia mission promises to have great potential in this respect. In this article we investigate the prospects of constraining orbits of newly discovered and known NEAs using nearly simultaneous observations from the Earth and Gaia. We find that observations performed simultaneously from two sites can effectively constrain preliminary orbits derived via statistical ranging. By linking discoveries stored in the Minor Planet Center databases to Gaia astrometric alerts one can identify nearly simultaneous observations of Near Earth Objects and benefit from improved initial orbit solutions at no additional observational cost.

Let a compact torus $T=T^{n-1}$ act on an orientable smooth compact manifold $X=X^{2n}$ effectively, with nonempty finite set of fixed points, and suppose that stabilizers of all points are connected. If $H^{odd}(X)=0$ and the weights of tangent representation at each fixed point are in general position, we prove that the orbit space $Q=X/T$ is a homology $(n+1)$-sphere. If, in addition, $π_1(X)=0$, then $Q$ is homeomorphic to $S^{n+1}$. We introduce the notion of $j$-generality of tangent weights of torus action. For any action of $T^k$ on $X^{2n}$ with isolated fixed points and $H^{odd}(X)=0$, we prove that $j$-generality of weights implies $(j+1)$-acyclicity of the orbit space $Q$. This statement generalizes several known results for actions of complexity zero and one. In complexity one, we give a criterion of equivariant formality in terms of the orbit space. In this case, we give a formula expressing Betti numbers of a manifold in terms of certain combinatorial structure that sits in the orbit space.

For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kaehler space. This notion establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces; in particular, in the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The space of representations of the fundamental group of a closed surface in a compact Lie group inherits a (positive) normal (stratified) Kaehler structure, as does the closure of a holomorphic nilpotent orbit in a semisimple Lie algebra of hermitian type. The closure of the principal holomorphic nilpotent orbit arises from a regular semisimple holomorphic orbit by contraction. Symplectic reduction carries a (positive) Kaehler manifold to a (po

We develop a foundation model using 1.2m high resolution satellite images of the Netherlands. By combining a Convolutional Neural Network and a Vision Transformer, the model captures both low- and high-frequency landscape features, such as fine textures, edges, and small objects as well as large terrain structures, elevation patterns, and land-cover distributions. Leveraging temporal data as input, the model learns from broader contextual information across time, allowing the model to exploit the temporal dependencies, such as topographic features, land-cover changes, and seasonal dynamics. These additional constraints reduce feature ambiguity, improve representation learning, and enable better generalization with fewer labeled samples. The foundation model is evaluated on multiple downstream tasks, ranging from use cases within the Netherlands to global benchmarking datasets. On the vegetation monitoring dataset of the Netherlands, the model shows clear performance improvements by incorporating temporal information instead of relying on a single time point. Despite using a smaller model and less pretraining data limited to the Netherlands, it achieves competitive results on global

In this paper, for any positive integer $n$, we study the Maslov-type index theory of $i_{L_0}$, $i_{L_1}$ and $i_{\sqrt{-1}}^{L_0}$ with $L_0=\{0\}\times \R^n\subset \R^{2n}$ and $L_1=\R^n\times \{0\} \subset \R^{2n}$. As applications we study the minimal period problems for brake orbits of nonlinear autonomous reversible Hamiltonian systems. For first order nonlinear autonomous reversible Hamiltonian systems in $\R^{2n}$, which are semipositive, and superquadratic at zero and infinity, we prove that for any $T>0$, the considered Hamiltonian systems possesses a nonconstant $T$ periodic brake orbit $X_T$ with minimal period no less than $\frac{T}{2n+2}$. Furthermore if $\int_0^T H"_{22}(x_T(t))dt$ is positive definite, then the minimal period of $x_T$ belongs to $\{T,\;\frac{T}{2}\}$. Moreover, if the Hamiltonian system is even, we prove that for any $T>0$, the considered even semipositive Hamiltonian systems possesses a nonconstant symmetric brake orbit with minimal period belonging to $\{T,\;\frac{T}{3}\}$

In this paper we first note a result of birational automorphisms with bounded degree of projective varieties related with the Zariski dense orbit conjecture (ZDO) and the Zariski density of periodic points. Next, we give a reduced result of ZDO for automorphisms of projective threefolds, and showed ZDO for automorphisms of projective varieties $X$ with the irregularity $q(X)\ge\dim X-1$.

We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally divergent non-closed orbit is dense for r > 2 and its closure is a finite union of tori orbits for r = 2. Our results confirm an orbit rigidity conjecture of Margulis in all cases except for (i) r = 2 and, (ii) r > 2 and the Hilbert modular space corresponds to a CM-field; in the cases (i) and (ii) our results contradict the conjecture. As an application, we describe the set of values at integral points of collections of non-proportional, split, binary, quadratic forms over number fields.

This paper employs agent-based modelling to explore the factors driving the high rate of tertiary education completion in the Netherlands. We examine the interplay of economic motivations, such as expected wages and financial constraints, alongside sociological and psychological influences, including peer effects, student disposition, personality, and geographic accessibility. Through simulations, we analyse the sustainability of these trends and evaluate the impact of educational policies, such as student grants and loans, on enrollment and borrowing behaviour among students from different socioeconomic backgrounds, further considering implications for the Dutch labour market.