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The eXTP mission is a major project of the Chinese Academy of Sciences (CAS), with a large involvement of Europe. Its scientific payload includes four instruments: SFA, PFA, LAD and WFM. They offer an unprecedented simultaneous wide-band Xray timing and polarimetry sensitivity. A large European consortium is contributing to the eXTP study, both for the science and the instrumentation. Europe is expected to provide two of the four instruments: LAD and WFM; the LAD is led by Italy and the WFM by Spain. The WFM for eXTP is based on the design originally proposed for the LOFT ESA M3 mission, that underwent a Phase A feasibility study. It will be a wide field of view X-ray monitor instrument working in the 2-50 keV energy range, achieved with large-area Silicon Drift Detectors (SDDs), similar to the ones used for the LAD but with better spatial resolution. The WFM will consist of 3 pairs of coded mask cameras with a total combined field of view (FoV) of 90x180 degrees at zero response and a source localisation accuracy of ~1 arc min. The main goal of the WFM is to provide triggers for the target of opportunity observations of the SFA, PFA and LAD, in order to perform the core science programme, dedicated to the study of matter under extreme conditions of density, gravity and magnetism. In addition, the unprecedented combination of large field of view and imaging capability, down to 2 keV, of the WFM will allow eXTP to make important discoveries of the variable and transient X-ray sky, and provide X-ray coverage of a broad range of astrophysical objects covered under 'observatory science', such as gamma-ray bursts, fast radio bursts, gravitational wave electromagnetic counterparts. In this paper we provide an overview of the WFM instrument, explaining its design, configuration, and anticipated performance., Comment: 15 pages, 13 figures, Proceedings of SPIE 13093, Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray; Proceedings Volume 13093, Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray; 130931Y (2024); doi: 10.1117/12.3020020

The Wide Field Monitor (WFM) is one of the three instruments on the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X) mission, which was proposed in response to the NASA 2023 call for a probe class mission. The WFM is a coded-mask camera system that would be the most scientifically capable wide-angle monitor ever flown. The field of view covers one third of the sky, to 50 percent mask coding, and the energy sensitivity is 2 to 50 keV. The WFM is designed to identify new X-ray transients and to capture spectral and timing changes in known sources with data of unprecedented quality. Science applications cover diverse classes, in including X-ray bursts that coincide with gravitational wave detections, gamma ray bursts and their transition from prompt emission to afterglow, subluminous GRBs that may signal shock breakout in supernovae, state transitions in accreting compact objects and their jets, bright flares in fast X-ray transients, accretion onset in transitional pulsars, and coronal flares from many types of active stars., Comment: 19 pages, 5 figures, accepted for publication in JATIS

We study the evolution of populations of binary stars within massive cluster-forming regions. We simulate the formation of young massive star clusters within giant molecular clouds with masses ranging from 2 x 10$^{4}$ to 3.2 x 10$^{5}$ M$_{\odot}$. We use Torch, which couples stellar dynamics, magnetohydrodynamics, star and binary formation, stellar evolution, and stellar feedback through the AMUSE framework. We find that the binary fraction decreases during cluster formation at all molecular cloud masses. The binaries' orbital properties also change, with stronger and quicker changes in denser, more massive clouds. Most of the changes we see can be attributed to the disruption of binaries wider than 100 au, although the close binary fraction also decreases in the densest cluster-forming region. The binary fraction for O stars remains above 90%, but exchanges and dynamical hardening are ubiquitous, indicating that O stars undergo frequent few-body interactions early during the cluster formation process. Changes to the populations of binaries are a by-product of hierarchical cluster assembly: most changes to the binary population take place when the star formation rate is high and there are frequent mergers between sub-clusters in the cluster-forming region. A universal primordial binary distribution based on observed inner companions in the Galactic field is consistent with the binary populations of young clusters with resolved stellar populations, and the scatter between clusters of similar masses could be explained by differences in their formation history., Comment: 15 pages, 8 figures, 3 tables. Submitted to ApJ

Massive stars are predominantly born in stellar associations or clusters. Their radiation fields, stellar winds, and supernovae strongly impact their local environment. In the first few million years of a cluster's life, massive stars are dynamically ejected running away from the cluster at high speed. However, the production rate of dynamically ejected runaways is poorly constrained. Here we report on a sample of 55 massive runaway stars ejected from the young cluster R136 in the Large Magellanic Cloud. Astrometric analysis with Gaia reveals two channels of dynamically ejected runaways. The first channel ejects massive stars in all directions and is consistent with dynamical interactions during and after the birth of R136. The second channel launches stars in a preferred direction and may be related to a cluster interaction. We find that 23-33% of the most luminous stars initially born in R136 are runaways. Model predictions have significantly underestimated the dynamical escape fraction of massive stars. Consequently, their role in shaping and heating the interstellar and galactic medium, along with their role in driving galactic outflows, is far more important than previously thought., Comment: Published in Nature on 2024 October 09. 39 pages, 17 figures

Gaia astrometry of nearby stars is precise enough to detect the tiny displacements induced by substellar companions, but radial velocity data are needed for definitive confirmation. Here we present radial velocity follow-up observations of 28 M and K stars with candidate astrometric substellar companions, which led to the confirmation of two systems, Gaia-4b and Gaia-5b, and the refutation of 21 systems as stellar binaries. Gaia-4b is a massive planet ($M = 11.8 \pm 0.7 \:\mathrm{M_J}$) in a $P = 571.3 \pm 1.4\:\mathrm{day}$ orbit with a projected semi-major axis $a_0=0.312 \pm 0.040\:\mathrm{mas}$ orbiting a $0.644 \pm 0.02 \:\mathrm{M_\odot}$ star. Gaia-5b is a brown dwarf ($M = 20.9 \pm 0.5\:\mathrm{M_J}$) in a $P = 358.58 \pm 0.19\:\mathrm{days}$ eccentric $e=0.6412 \pm 0.0027$ orbit with a projected angular semi-major axis of $a_0 = 0.947 \pm 0.038\:\mathrm{mas}$ around a $0.34 \pm 0.03 \mathrm{M_\odot}$ star. Gaia-4b is one of the first exoplanets discovered via the astrometric technique, and is one of the most massive planets known to orbit a low-mass star., Comment: Submitted to AAS journals. 26 pages, 12 figures, 4 tables

Protoplanetary disks surrounding young stars are the birth places of planets. Among them, transition disks with inner dust cavities of tens of au are sometimes suggested to host massive companions. Yet, such companions are often not detected. Some transition disks exhibit a large amount of gas inside the dust cavity and relatively high stellar accretion rates, which contradicts typical models of gas-giant-hosting systems. Therefore, we investigate whether a sequence of low-mass planets can produce cavities in the dust disk. We evolve the disks with low-mass accreting embryos in combination with 1D dust transport and 3D pebble accretion, to investigate the reduction of the pebble flux at the embryos' orbits. We vary the planet and disk properties. We find that multiple pebble-accreting planets can efficiently decrease the dust surface density, resulting in dust cavities consistent with transition disks. The number of low-mass planets necessary to sweep up all pebbles decreases with decreasing turbulent strength and is preferred when the dust Stokes number is $10^{-2}-10^{-4}$. Compared to dust rings caused by pressure bumps, those by efficient pebble accretion exhibit more extended outer edges. We also highlight the observational reflections: the transition disks with rings featuring extended outer edges tend to have a large gas content in the dust cavities and rather high stellar accretion rates. We propose that planet-hosting transition disks consist of two groups. In Group A disks, planets have evolved into gas giants, opening deep gaps in the gas disk. Pebbles concentrate in pressure maxima, forming dust rings. In Group B, multiple Neptunes (unable to open deep gas gaps) accrete incoming pebbles, causing the appearance of inner dust cavities. The morphological discrepancy of these rings may aid in distinguishing between the two groups using high-resolution ALMA observations., Comment: 12 pages, 9 figures. Accepted for publication in A&A

The Milky way Galaxy is brimming with free-floating objects, including stars, planets and planetesimals. For the purpose of this chapter, we define a free-floating object as a solid body that is not orbited by a considerably more massive body. A planet then is considered free floating if it is not orbiting a star but it may be orbiting another planet. A binary planet, or planet-moon pair that is not orbiting a star, is then considered free floating. Most free-floating objects are not born as such because most objects form in some sort of coordinated environmental effort, such as a star forming region or a circum-stellar disk. Free-floating stars then originate from dissolved clusters. Free floating planets are ejected from their parent star in an internal dynamical encounter with another planet or stripped from the star by other means such as a supernova or a nearby passing star. Free floating (interstellar) planetesimals probably form in a similar fashion as free-floating planets. The number of free-floating objects in the Galaxy can be large. With billions of stars and planets, and trillions of interstellar planetesimals. Although free-floating planets appear to be quite common (a few hundred have been observed), only two interstellar planetesimals have been discovered so far. The expectation, however, is that they outnumber the stars in the Galaxy by a considerable margin. We expect them to be found more frequently once large new instruments come online, such as the Vera Cooper Rubin Observatory., Comment: Preprint of a chapter for the 'Encyclopedia of Astrophysics' (Editor-in-Chief Ilya Mandel, Section Editor Dimitri Veras) to be published by Elsevier as a Reference Module

We simulate mergers between star clusters embedded within their natal giant molecular cloud. We extract initial conditions from cloud-scale simulations of cluster formation and introduce different prescriptions for primordial binaries. We find that simulations that do not include primordial binaries result in a larger fraction of unbound stars than simulations which include a prescription for binaries based on observations. We also find a preferred direction of motion for stars that become unbound during the merger. Sub-cluster mergers within realistic gas environments promote binary disruption while mergers between idealized, gas-rich spherical clusters do not produce the same disruption. Binary systems with smaller semi-major axes are disrupted in simulations of sub-cluster mergers within their natal environment compared to simulations that do not include the realistic gas environment. We conclude that binary disruption and the production of an anisotropic distribution of unbound stars are the natural consequences of sub-cluster mergers during star cluster assembly., Comment: 13 pages, 8 figures. Re-submitted to ApJ following favourable referee report

We use the stellar evolution code BPASS and the gravitational wave simulation code LEGWORK to simulate populations of compact binaries that may be detected by the in-development space-based gravitational wave (GW) detector LISA. Specifically, we simulate the Magellanic Clouds and binary populations mimicking several globular clusters, neglecting dynamical effects. We find that the Magellanic Clouds would have a handful of detectable sources each, but for globular clusters the amount of detectable sources would be less than one. We compare our results to earlier research and find that our predicted numbers are several tens of times lower than calculations using the stellar evolution code BSE that take dynamical effects into account, but also calculations using the stellar evolution code SeBa for the Magellanic Clouds. This correlates with earlier research which compared BPASS models for GW sources in the Galactic disk with BSE models and found a similarly sized discrepancy. We analyse and explain this discrepancy as being caused by differences between the stellar evolution codes, particularly in the treatment of mass transfer and common-envelope events in binaries, where in BPASS mass transfer is more likely to be stable and tends to lead to less orbital shrinkage in the common-envelope phase than in other codes. This difference results in fewer compact binaries with periods short enough to be detected by LISA existing in the BPASS population. For globular clusters, we conclude that the impact of dynamical effects is uncertain from the literature, but the differences in stellar evolution have an effect of a factor of a few tens., Comment: 11 pages, 2 figures, 4 tables. Submitted to A&A

Unlike the Solar System planets, thousands of smaller bodies beyond Neptune orbit the Sun on eccentric ($e >$ 0.1) and ($i>$ 3$^\circ$) orbits. While migration of the giant planets during the early stages of Solar System evolution can induce substantial scattering of trans-Neptunian objects (TNO), this process cannot account for the small number of distant TNOs ($r_p >$ 60 au) outside the planets' reach. The alternative scenario of the close flyby of another star can instead produce all these TNO features simultaneously, but the possible parameter space for such an encounter is vast. Here, we compare observed TNO properties with thousands of flyby simulations to determine the specific properties of a flyby that reproduces all the different dynamical TNO populations, their location and their relative abundance and find that a 0.8$^{+0.1}_{-0.1}$ $M_{\odot}$ star passing at a distance of $ r_p =$ 110 $\mathbf{\pm}$ 10 au, inclined by $i$ = 70$^\circ$ $^{+5}_{-10}$ gives a near-perfect match. This flyby also replicates the retrograde TNO population, which has proved difficult to explain. Such a flyby is reasonably frequent; at least 140 million solar-type stars in the Milky Way are likely to have experienced a similar one. In light of these results, we predict that the upcoming Vera Rubin telescope will reveal that distant and retrograde TNOs are relatively common., Comment: 15 pages, 3 figures Open access version of original Nature Astronomy available under 10.1038/s41550-024-02349-x

Mass segregation is seen in many star clusters, but whether massive stars form in the center of a cluster or migrate there dynamically is still debated. N-body simulations have shown that early dynamical mass segregation is possible when sub-clusters merge to form a dense core with a small crossing time. However, the effect of gas dynamics on both the formation and dynamics of the stars could inhibit the formation of the dense core. We aim to study the dynamical mass segregation of star cluster models that include gas dynamics and self-consistently form stars from the dense substructure in the gas. Our models use the Torch framework, which is based on AMUSE and includes stellar and magnetized gas dynamics, as well as stellar evolution and feedback from radiation, stellar winds, and supernovae. Our models consist of three star clusters forming from initial turbulent spherical clouds of mass $10^{4,5,6}\rm~M_\odot$ and radius $11.7\rm~pc$ that have final stellar masses of $3.6\times10^3\rm~M_\odot$, $6.5\times10^4\rm~M_\odot$, and $8.9\times10^5\rm~M_\odot$, respectively. There is no primordial mass segregation in the model by construction. All three clusters become dynamically mass segregated at early times via collapse confirming that this mechanism occurs within sub-clusters forming directly out of the dense substructure in the gas. The dynamics of the embedded gas and stellar feedback do not inhibit the collapse of the cluster. We find that each model cluster becomes mass segregated within $2~$Myr of the onset of star formation, reaching the levels observed in young clusters in the Milky Way. However, we note that the exact values are highly time-variable during these early phases of evolution. Massive stars that segregate to the center during core collapse are likely to be dynamically ejected, a process that can decrease the overall level of mass segregation again., Comment: Submitted to A&A. 8 pages, 4 figures

Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is well-known that it is challenging to extend these applications to languages with recursion and computational effects such as probabilistic choice, because these features are not easily represented in constructive type theory. We show how to define and reason about a programming language with probabilistic choice and recursive types, in guarded type theory. We use higher inductive types to represent finite distributions and guarded recursion to model recursion. We define both operational and denotational semantics, as well as a relation between the two. The relation can be used to prove adequacy, but we also show how to use it to reason about programs up to contextual equivalence., Comment: 61 pages

We present {\sc Venice}, an operator splitting algorithm to integrate a numerical model on a hierarchy of timescales. {\sc Venice} allows a wide variety of different physical processes operating a different scales to be coupled on individual and adaptive time-steps. It therewith mediates the development of complex multi-scale and multi-physics simulation environments with a wide variety of independent components. The coupling between various physical models and scales is dynamic, and realized through (Strang) operators splitting using adaptive time steps. We demonstrate the functionality and performance of this algorithm using astrophysical models of a stellar cluster, first coupling gravitational dynamics and stellar evolution, then coupling internal gravitational dynamics with dynamics within a galactic background potential, and finally combining these models while also introducing dwarf galaxy-like perturbers. These tests show numerical convergence for decreasing coupling timescales, demonstrate how {\sc Venice} can improve the performance of a simulation by shortening coupling timescales when appropriate, and provide a case study of how {\sc Venice} can be used to gradually build up and tune a complex multi-physics model. Although the examples couple complete numerical models, {\sc Venice} can also be used to efficiently solve systems of stiff differential equations., Comment: Accepted for publication by A&A

Context: Current exoplanet formation studies tend to overlook the birth environment of stars in clustered environments. The effect of this environment on the planet-formation process, however, is important, especially in the earliest stage. Aims: We investigate the differences in planet populations forming in star-cluster environments through pebble accretion and compare these results with the planet formation around isolated stars. We try to provide potential signatures on the young planetary systems to guide future observation. Methods: We design and present a new planet population synthesis code for clustered environments. The planet formation model is based on pebble accretion and includes migration in the circumstellar disk. The disk's gas and dust are evolved in 1D simulations considering the effects of photo-evaporation of the nearby stars. Results: Planetary systems in a clustered environment are different than those born in isolation; the environmental effects are important for a wide range of observable parameters and the eventual architecture of the planetary systems. Planetary systems born in a clustered environment lack cold Jupiters compared to isolated planetary systems. This effect is more pronounced for low-mass stars ($\lesssim$0.2 $M_\odot$). On the other hand, planetary systems born in clusters show an excess of cold Neptune around these low-mass stars. Conclusions: In future observations, finding an excess of cold Neptunes and a lack of cold Jupiters could be used to constrain the birth environments of these planetary systems. Exploring the dependence of cold Jupiter's intrinsic occurrence rate on stellar mass provides insights into the birth environment of their proto-embryos., Comment: 13 pages 10 figures. Accepted for publication in A&A

We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviations and extreme-value theory, we show how the optimal value scales as the prescribed bound on the violation probability becomes small and how convex programs emerge in the limit. We also use our results to show that the popular CVaR approximation is asymptotically optimal under light-tail assumptions, but it is sub-optimal in a heavy-tailed setting. Then, we apply point process techniques and random set theory to study the suboptimality gap in the Monte Carlo based scenario approach., Comment: 17 pages

In scientific imaging, deep learning has become a pivotal tool for image analytics. However, handling large volumetric datasets, which often exceed the memory capacity of standard GPUs, require special attention when subjected to deep learning efforts. This paper introduces qlty, a toolkit designed to address these challenges through tensor management techniques. qlty offers robust methods for subsampling, cleaning, and stitching of large-scale spatial data, enabling effective training and inference even in resource-limited environments.

We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large-deviation principle with logarithmic speed: the rare event that the largest component contains linearly more vertices than expected is caused by the presence of constantly many vertices with linear degree. Conditionally on this rare event, we prove distributional limits of the weight distribution and component-size distribution., Comment: 36 pages

DC networks play an important role within the ongoing energy transition. In this context, simulations of designed and existing networks and their corresponding assets are a core tool to get insights and form a support to decision-making. Hereby, these simulations of DC networks are executed in the time domain. Due to the involved high frequencies and the used controllers, the equations that model these DC networks are stiff and highly oscillatory differential equations. By exploiting sparsity, we show that conventional adaptive time stepping schemes can be used efficiently for the time domain simulation of very large DC networks and that this scales linearly in the computational cost as the size of the networks increase., Comment: 17 pages, 5 figures, 3 tables. First version, all comments are welcome

Dynamical interactions in star clusters are an efficient mechanism to produce the coalescing binary black holes (BBHs) that have been detected with gravitational waves (GWs). We want to understand how BBH coalescence can occur during - or after - binary-single interactions with different mass ratios. We perform gravitational scattering experiments of binary-single interactions using different mass ratios of the binary components ($q_2\equiv m_2/m_1\le1$) and the incoming single ($q_3\equiv m_3/m_1$). We extract cross sections and rates for (i) GW capture during resonant interactions; (ii) GW inspiral in between resonant interactions and apply the results to different globular cluster conditions. We find that GW capture during resonant interactions is most efficient if $q_2\simeq q_3$ and that the mass-ratio distribution of BBH coalescence due to inspirals is $\propto m_1^{-1}q^{2.9+\alpha}$, where $\alpha$ is the exponent of the BH mass function. The total rate of GW captures and inspirals depends mostly on $m_1$ and is relatively insensitive to $q_2$ and $q_3$. We show that eccentricity increase by non-resonant encounters approximately doubles the rate of BBH inspiral in between resonant encounters. For a given GC mass and radius, the BBH merger rate in metal-rich GCs is approximately double that of metal-poor GCs, because of their (on average) lower BH masses ($m_1$) and steeper BH mass function, yielding binaries with lower $q$. Our results enable the translating from the mass-ratio distribution of dynamically formed BBH mergers to the underlying BH mass function. The additional mechanism that leads to a doubling of the inspirals provides an explanation for the reported high fraction of in-cluster inspirals in $N$-body models of clusters., Comment: 14 pages, 7 figures

Two main mechanisms have classically been proposed for the formation of runaway stars. In the binary supernova scenario (BSS), a massive star in a binary explodes as a supernova, ejecting its companion. In the dynamical ejection scenario, a star is ejected during a strong dynamical encounter between multiple stars. We propose a third mechanism for the formation of runaway stars: the subcluster ejection scenario (SCES), where a subset of stars from an infalling subcluster is ejected out of the cluster via a tidal interaction with the contracting gravitational potential of the assembling cluster. We demonstrate the SCES in a star-by-star simulation of the formation of a young massive cluster from a $10^6\rm~M_\odot$ gas cloud using the Torch framework. This star cluster forms hierarchically through a sequence of subcluster mergers determined by the initial turbulent, spherical conditions of the gas. We find that these mergers drive the formation of runaway stars in our model. Late-forming subclusters fall into the central potential, where they are tidally disrupted, forming tidal tails of runaway stars that are distributed highly anisotropically. Runaways formed in the same SCES have similar ages, velocities, and ejection directions. Surveying observations, we identify several SCES candidate groups with anisotropic ejection directions. The SCES is capable of producing runaway binaries: two wide dynamical binaries in infalling subclusters were tightened through ejection. This allows for another velocity kick via subsequent via a subsequent BSS ejection. An SCES-BSS ejection is a possible avenue for the creation of hypervelocity stars unbound to the Galaxy. We expect nonspherical initial gas distributions to increase the number of calculated runaway stars. The observation of groups of runaway stars formed via the SCES can thus reveal the assembly history of their natal clusters., Comment: 11 pages, 10 figures. Accepted for publication in A&A. Abstract abridged for arXiv

Control design for linear, time-invariant mechanical systems typically requires an accurate low-order approximation in the low frequency range. For example a series expansion of the transfer function around zero consisting of a mass, velocity, and compliance term. Because computing such a series expansion of the transfer function can be cumbersome, a new method to compute low-order approximations of mechanical systems is developed in this paper. The method does not require an explicit expression for the transfer function, which is not always available for infinite-dimensional systems. The advantages of the proposed method is demonstrated in three examples., Comment: 32 pages, 7 figures

Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term rewriting methods, we also describe when a minimal set of equations axiomatises the composite theory.

We develop explicit bounds for the tail of the distribution for the all-time supremum of a random walk with negative drift, where the increments have a truncated heavy-tailed distribution. As an application, we consider a ruin problem in the presence of re-insurance.

The three-body problem (3BP) poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3BP. This study probes the presence of regular (i.e. non chaotic) trajectories within the 3BP and assesses their impact on statistical escape theories. Using numerical simulations, we establish criteria for identifying regular trajectories and analyse their impact on statistical outcomes. Our analysis reveals that regular trajectories occupy up to 32% of the phase space, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. Integration errors manifest as numerical chaos, artificially enhancing the mixing of the phase space and affecting the reliability of individual simulations, yet preserving the statistical correctness of an ensemble of realizations. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity., Comment: 15 pages, 13 figures, accepted for publication in Astronomy & Astrophysics

As a direct continuation of K. Zwart, arXiv:2304.02648, which is built on the work of M. M\"uger and L. Tuset, we reduce the Mathieu conjecture, formulated by O. Mathieu in 1997, for $Sp(N)$ and $G_2$ to a conjecture involving functions over $\mathbb{R}^n\times (S^1)^m$ with $n,m\in\mathbb{N}_0$. The proofs rely on Euler-style parametrizations of these groups, a specific version of the $KAK$ decomposition, which we discuss and prove., Comment: 30 pages, no figures

A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics to be a Riesz-spectral operator. In that case, its spectrum is computed explicitly, together with the corresponding eigenfunctions, which constitutes the main result of our note. In particular, this enables to characterize easily many different concepts, such as stability. We apply our results to characterize exponential stability of a co-current heat exchanger.

Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this manuscript consist in converting the infinite-dimensional continuous-time systems into infinite-dimensional discrete-time systems for which the operators dynamics are matrices, in solving the LQ-optimal control problem in discrete-time and then in interpreting the solution in the continuous-time variables, giving rise to the optimal boundary control input. The results are applied to two examples, a small network of three vibrating strings and a co-current heat-exchanger, for which boundary sensors and actuators are considered.

Within the magnetospheric radius, the geometry of accretion flow in X-ray pulsars is shaped by a strong magnetic field of a neutron star. Starting at the magnetospheric radius, accretion flow follows field lines and reaches the stellar surface in small regions located close to the magnetic poles of a star. At low mass accretion rates, the dynamic of the flow is determined by gravitational attraction and rotation of the magnetosphere due to the centrifugal force. At the luminosity range close to the Eddington limit and above it, the flow is additionally affected by the radiative force. We construct a model simulating accretion flow dynamics over the magnetosphere, assuming that the flow strictly follows field lines and is affected by gravity, radiative and centrifugal forces only. The magnetic field of a NS is taken to be dominated by the dipole component of arbitrary inclination with respect to the accretion disc plane. We show that accretion flow becomes unstable at high mass accretion rates and tends to fluctuate quasi-periodically with a typical period comparable to the free-fall time from the inner disc radius. The inclination of a magnetic dipole with respect to the disc plane and strong anisotropy of X-ray radiation stabilise the mass accretion rate at the poles of a star, but the surface density of material covering the magnetosphere fluctuates even in this case., Comment: 14 pages, 13 figures, submitted to MNRAS

Located at the core of the Galactic Centre, the S-star cluster serves as a remarkable illustration of chaos in dynamical systems. The long-term chaotic behaviour of this system can be studied with gravitational $N$-body simulations. By applying a small perturbation to the initial position of star S5, we can compare the evolution of this system to its unperturbed evolution. This results in the two solutions diverging exponentially, defined by the separation in position space $\delta_{r}$, with an average Lyapunov timescale of $\sim$420 yr, corresponding to the largest positive Lyapunov exponent. Even though the general trend of the chaotic evolution is governed in part by the supermassive black hole Sagittarius $\rm A^{*}$ (Sgr $\rm A^{*}$), individual differences between the stars can be noted in the behaviour of their phase-space curves. We present an analysis of the individual behaviour of the stars in this Newtonian chaotic dynamical system. The individuality of their behaviour is evident from offsets in the position space separation curves of the S-stars and the black hole. We propose that the offsets originate from the initial orbital elements of the S-stars, where Sgr $\rm A^{*}$ is considered in one of the focal points of the Keplerian orbits. Methods were considered to find a relationship between these elements and the separation in position space. Symbolic regression turns out to provide the clearest diagnostics for finding an interpretable expression for the problem. Our symbolic regression model indicates that $\left\langle\delta_r\right\rangle \propto e^{2.3}$, implying that the time-averaged individual separation in position space increases rapidly with the initial eccentricity of the S-stars., Comment: Accepted for publication in A&A

The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the Torch framework, which uses AMUSE to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgrade Torch by implementing the N-body code PeTar, thereby enabling Torch to handle massive clusters forming from $10^6\rm\, M_\odot$ clouds with $\ge10^5$ individual stars. We present results from Torch simulations of star clusters forming from $10^4, 10^5$, and $10^6\rm M_\odot$ turbulent, spherical gas clouds (named M4, M5, M6) of radius $R=11.7$ pc. We find that star formation is highly efficient and becomes more so at higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities $2.325\times 10^{1,2,3}\rm\, M_\odot\, pc^{-2}$, after a free-fall time of $t_{ff}=6.7,2.1,0.67$ Myr, we find that $\sim30\%$, 40%, and 60% of the cloud mass has formed into stars, respectively. The final integrated star formation efficiency is $32\%,\, 65\%$, and 85\% for M4, M5, and M6. Observations of nearby clusters similar to M4 have similar integrated star formation efficiencies of $\leq30\%$. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense ($\ge 10^2 \rm\,M_\odot\,pc^{-2}$) and massive ($\ge10^5\rm\, M_\odot$). In such environments, the dynamical time of the cloud becomes short enough that stellar feedback cannot act quickly enough to slow star formation., Comment: Submitted to A&A

Aims: Investigate properties of a cluster of intermediate-mass black holes surrounding a supermassive black hole. Methods: We simulate clusters of equal-mass intermediate-mass black holes ($m_{\rm{IMBH}} = 10^{3}$ ${\rm{M_\odot}}$) initialised in a shell between $0.15\leq r$ [pc] $\leq 0.25$ centered about a supermassive black hole. We explore the influence of the cluster population and supermassive black hole mass on the merger rate, the ejection rate and the escape velocity. For $M_{\text{SMBH}} = 4\times10^{6}$ ${\rm {M}_\odot}$, we use both a Newtonian and post-Newtonian formalism, going up to the 2.5th order and including cross-terms. For the other two SMBH masses ($M_{\rm{SMBH}} = 4\times10^{5}$ ${\rm{M_\odot}}$ and $M_{\rm{SMBH}} = 4\times10^{7}$ $\rm{M_\odot}$), we model the system only taking into account relativistic effects. The simulations end once a black hole escapes the cluster, a merger occurs, or the system has evolved till $100$ Myr. Results: The post-Newtonian formalism accelerates the loss rate of intermediate-mass black holes. Ejections occur more often for lower supermassive black hole masses while more massive ones increase the rate of mergers. Although relativistic effects allow for circularisation, all merging binaries have $e \gtrsim 0.97$. Strong gravitational wave signals are suppressed during our Newtonian calculations. Weaker and more frequent signals are expected from gravitational wave radiation emitted in a fly-by. In our post-Newtonian calculations, $30/406$ of the gravitational wave events capable of being observed with LISA and $\mu$Ares are detected as gravitational wave capture binaries with the remaining being in-cluster mergers. Throughout our investigation, no IMBH-IMBH binaries were detected., Comment: 18 pages, 18 figures

The recently observed population of 540 free-floating Jupiter-mass objects, including 40 dynamically soft pairs in the Trapezium cluster have raised interesting questions on their formation and evolution. We test various scenarios for the origin and survivability of these free floating Jupiter-mass objects and Jupiter-mass Binary Objects (JuMBOs) in the Trapezium cluster. The numerical calculations are performed by direct N-body integration of the stars and planets in the Trapezium cluster starting with a wide variety of planets in various configurations. We discuss four models: SPP, in which selected stars have two outer orbiting Jupiter-mass planets; SPM, where selected stars are orbited by Jupiter-mass planet-moon pairs; ISF in which JuMBOs form in situ with the stars, and FFC, where we introduce a population of free-floating single Jupiter-mass objects, but no initialized binaries. Models FFC and SPP fail to produce enough JuMBOs. Models SPM can produce sufficient JuMBOs, but requires unusually wide orbits for the planet-moon system around the star. The observed JuMBOs and free-floating Jupiter-mass objects in the Trapezium cluster are best reproduced if they formed in pairs and as free-floaters together with the other stars in a smooth (Plummer) density profile with a virial radius of 0.5pc. A fractal stellar distribution also works, but requires relatively recent formations (>0.2Myr after the other stars formed) or a high (50%) initial binary fraction. This would make the primordial binary fraction of JuMBOs even higher than the already large observation fraction of 8%. The fraction of JuMBOs will continue to drop with time, and the lack of JuMBOs in Upper Scorpius could then result in its higher age, causing more JuMBOs to be ionized. We then also predict that the interstellar density of Jupiter-mass objects (mostly singles with 2% lucky surviving binaries) is 0.05/pc$^{3}$., Comment: Accepted for publiation in golden open-access journal SciPost Astronomy, see https://scipost.org/submission/scipost_202312_00003v1/ Software available at: https://github.com/spzwart/JuMBOs.git Simulation data available at: https://zenodo.org/records/10149241

The optimal power flow (OPF) problem is one of the most fundamental problems in power system operations. The non-linear alternating current (AC) power flow equations that model different physical laws (together with operational constraints) lay the foundation for the feasibility region of the OPF problem. While significant research has focused on convex relaxations, which are approaches to solve an OPF problem by enlarging the true feasibility region, the opposite approach of convex restrictions offers valuable insights as well. Convex restrictions, including polyhedral restrictions, reduce the true feasible region to a convex region, ensuring that it contains only feasible points. In this work, we develop a sequential optimization method that offers a scalable way to obtain (bounds on) solutions to OPF problems for distribution networks. To do so, we first develop sufficient conditions for the existence of feasible power flow solutions in the neighborhood of a specific (feasible) operating point in distribution networks, and second, based on these conditions, we construct a polyhedral restriction of the feasibility region. Our numerical results demonstrate the efficacy of the sequential optimization method as an alternative to existing approaches to obtain (bounds on) solutions to OPF problems for distribution networks. By construction, the optimization problems can be solved in polynomial time and are guaranteed to have feasible solutions., Comment: 12 pages, 4 figures

The delay monad provides a way to introduce general recursion in type theory. To write programs that use a wide range of computational effects directly in type theory, we need to combine the delay monad with the monads of these effects. Here we present a first systematic study of such combinations. We study both the coinductive delay monad and its guarded recursive cousin, giving concrete examples of combining these with well-known computational effects. We also provide general theorems stating which algebraic effects distribute over the delay monad, and which do not. Lastly, we salvage some of the impossible cases by considering distributive laws up to weak bisimilarity., Comment: This version (v2) is to appear in the journal LMCS, as an extended version of the conference paper "What Monads Can and Cannot Do with a Bit of Extra Time", which was published at CSL 2024. A preprint of the conference paper is also available here as (v1)

Decision problems encountered in practice often possess a highly dynamic and uncertain nature. In particular fast changing forecasts for parameters (e.g., photovoltaic generation forecasts in the context of energy management) pose large challenges for the classical rolling horizon framework. Within this work, we propose an online scheduling algorithm for a rolling horizon framework, which directly uses short-term forecasts and observations of the uncertainty. The online scheduling algorithm is based on insights and results from combinatorial online optimization problems and makes use of key properties of robust optimization. Applied within a robust energy management approach, we show that the online scheduling algorithm is able to reduce the total electricity costs within a local microgrid by more than 85% compared to a classical rolling horizon framework and by more than 50% compared to a tailor-made dynamic, yet still offline rolling horizon framework. A detailed analysis provides insights into the working of the online scheduling algorithm under different underlying forecast error distributions., Comment: 40 pages, 14 figures

Due to the energy transition, lots of research has been conducted within the last decade on the topics of energy management systems or local energy trading approaches, often on the day-ahead or intraday level. A large majority of these approaches focuses on 15 or 60-minute time intervals for their operation, however, the question of how the planned solutions are realized within these time intervals is often left unanswered. Within this work, we aim to close this gap and propose a real-time balancing and control approach for a set of microgrids, which implements the day-ahead solutions. The approach is based on a three-step framework, in which the first step consists of ensuring the feasibility of devices within the microgrids. The second step focuses on the grid constraints of the connecting medium voltage grid using the DC power flow formulation due to the running time requirements of a real-time approach. The last step is to propagate the solution into the individual microgrids, where the allocated power needs to be distributed among the devices and households. Within a case study, we show that the proposed real-time control approach works as intended and is comparable to an optimal offline algorithm under some mild assumptions., Comment: 35 pages, 6 figures, 2 tables