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Mixed-frame formulations of radiation-hydrodynamics (RHD), where the radiation quantities are computed in an inertial frame but matter quantities are in a comoving frame, are advantageous because they admit algorithms that conserve energy and momentum to machine precision and combine more naturally with adaptive mesh techniques, since unlike pure comoving-frame methods they do not face the problem that radiation quantities must change frame every time a cell is refined or coarsened. However, implementing multigroup RHD in a mixed-frame formulation presents challenges due to the complexity of handling frequency-dependent interactions and the Doppler shift of radiation boundaries. In this paper, we introduce a novel method for multigroup RHD that integrates a mixed-frame formulation with a piecewise powerlaw approximation for frequency dependence within groups. This approach ensures the exact conservation of total energy and momentum while effectively managing the Lorentz transformation of group boundaries and evaluation of group-averaged opacities. Our method takes advantage of the locality of matter-radiation coupling, allowing the source term for $N_g$ frequency groups to be handled with simple equations with a sparse Jacobian matrix of size $N_g + 1$, which can be inverted with $O(N_g)$ complexity. This results in a computational complexity that scales linearly with $N_g$ and requires no more communication than a pure hydrodynamics update, making it highly efficient for massively parallel and GPU-based systems. We implement our method in the GPU-accelerated RHD code QUOKKA and demonstrate that it passes a wide range of numerical tests. We demonstrate that the piecewise powerlaw method shows significant advantages over traditional opacity averaging methods for handling rapidly variable opacities with modest frequency resolution., Comment: 17 pages, 8 figures, submitted to MNRAS. Comments are welcome. The code described in this article is available at: https://github.com/quokka-astro/quokka

In this paper, we present an approach for guaranteeing the completion of complex tasks with cyber-physical systems (CPS). Specifically, we leverage temporal logic trees constructed using Hamilton-Jacobi reachability analysis to (1) check for the existence of control policies that complete a specified task and (2) develop a computationally-efficient approach to synthesize the full set of control inputs the CPS can implement in real-time to ensure the task is completed. We show that, by checking the approximation directions of each state set in the temporal logic tree, we can check if the temporal logic tree suffers from the "leaking corner issue," where the intersection of reachable sets yields an incorrect approximation. By ensuring a temporal logic tree has no leaking corners, we know the temporal logic tree correctly verifies the existence of control policies that satisfy the specified task. After confirming the existence of control policies, we show that we can leverage the value functions obtained through Hamilton-Jacobi reachability analysis to efficiently compute the set of control inputs the CPS can implement throughout the deployment time horizon to guarantee the completion of the specified task. Finally, we use a newly released Python toolbox to evaluate the presented approach on a simulated driving task.

Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of timescales, and where the relative importance of these processes often varies by orders of magnitude across the computational domain. Here we present a new implicit-explicit (IMEX) method for numerical RHD that has a number of desirable properties that have not previously been combined in a single method. Our scheme is based on moments and allows machine-precision conservation of energy and momentum, making it highly suitable for adaptive mesh refinement applications; it requires no more communication than hydrodynamics and includes no non-local iterative steps, making it highly suitable for massively parallel and GPU-based systems where communication is a bottleneck; and we show that it is asymptotically-accurate in the streaming, static diffusion, and dynamic diffusion limits, including in the so-called asymptotic diffusion regime where the computational grid does not resolve the photon mean free path. We implement our method in the GPU-accelerated RHD code QUOKKA and show that it passes a wide range of numerical tests., Comment: 14 pages, 6 figures, submitted to MNRAS; Code available for download at https://github.com/quokka-astro/quokka

The formation of circumstellar discs is a critical step in the formation of stars and planets. Magnetic fields can strongly affect the evolution of angular momentum during prestellar core collapse, potentially leading to the failure of protostellar disc formation. This phenomenon, known as the magnetic braking catastrophe, has been observed in ideal-MHD simulations. In this work, we present results from ideal-MHD simulations of circumstellar disc formation from realistic initial conditions of strongly magnetised, massive cores with masses between $30 ~{\rm M}_\odot$ and $300 ~{\rm M}_\odot$ resolved by zooming into Giant Molecular Clouds with masses $\sim 10^4 \ {\rm M}_\odot$ and initial mass-to-flux ratios $0.6 \le \mu_0 \le 3$. Due to the large turbulence caused by the non-axisymmetric gravitational collapse of the gas, the dominant vertical support of discs is turbulent motion, while magnetic and turbulent pressures contribute equally in the outer toroid. The magnetic field topology is extremely turbulent and incoherent, reducing the effect of magnetic braking by roughly one order of magnitude and leading to the formation of large Keplerian discs even in magnetically critical or near-critical cores. Only cores in GMCs with $\mu_0 < 1$ fail to form discs. Instead, they collapse into a sheet-like structure and produce numerous low-mass stars. We also discuss a universal $B-\rho$ relation valid over a large range of scales from the GMC to massive cores, irrespective of the GMC magnetisation. This study differs from the vast literature on this topic which typically focus on smaller mass discs with idealised initial and boundary conditions, therefore providing insights into the initial conditions of massive prestellar core collapse and disc formation., Comment: 15 pages, 11 figures, submitted to MNRAS

We present the results of a set of radiation magnetohydrodynamic simulations of turbulent molecular clouds in which we vary the initial strength of the magnetic field within a range ($1 \lesssim \mu \lesssim 5$) consistent with observations of local giant molecular clouds (GMCs). We find that as we increase the strength of the magnetic field, star formation transitions from unimodal (the baseline case, $\mu=5$, with a single burst of star formation and Salpeter IMF) to bimodal. This effect is clearest in the most strongly magnetized GMCs ($\mu=1$): a first burst of star formation with duration, intensity and IMF comparable to the baseline case, is followed by a second star formation episode in which only low-mass stars are formed. Overall, due to the second burst of star formation, the strongly magnetized case results in a longer star formation period and a higher efficiency of star formation. The second burst is produced by gas that is not expelled by radiative feedback, instead remaining trapped in the GMC by the large-scale B-field, producing a nearly one-dimensional flow of gas along the field lines. The trapped gas has a turbulent and magnetic topology that differs from that of the first phase and strongly suppresses gas accretion onto protostellar cores, reducing their masses. We speculate that this star formation bimodality may be an important ingredient to understand the origin of multiple stellar populations observed in massive globular clusters., Comment: 16 Pages, 10 Figures, Published in MNRAS

We simulate the formation and collapse of prestellar cores at few-AU resolution in a set of radiation-magneto-hydrodynamic simulations of giant molecular clouds (GMCs) using the grid-based code RAMSES-RT. We adopt, for the first time to our best knowledge, realistic initial/boundary conditions by zooming-in onto individual massive prestellar cores within the GMC. We identify two distinct modes of fragmentation: "quasi-spherical" and "filamentary". In both modes the fragments eventually become embedded in a quasi-steady accretion disk or toroid with radii ~ 500-5000 AU and opening angles $H/R \sim 0.5-1$. The disks/toroids are Toomre stable but the accreted pre-existing fragments are found orbiting the outer disk, appearing as disk fragmentation. Each core converts nearly 100 percent of the gas mass into a few massive stars forming near the disk center. Large and massive disks around high-mass stars are supported by magnetic pressure in the outer disk, at radii >200-1000 AU, and turbulent pressure in the inner disk. The most massive core accretes several times more mass than its initial mass, forming a (proto)star cluster of 8 massive stars enshrouded by a toroid, suggesting a competitive accretion scenario for ultra-high-mass star formation. We also find that the HII regions produced by a single massive star remain trapped in the dense circumstellar disks for a few hundred kiloyears, while the dynamic motions of massive stars in wide binaries or multiple systems displace the stars from the densest parts of the disk, allowing UV radiation to escape producing steady or pulsating bipolar HII regions., Comment: 20 pages, 13 figures, submitted to MNRAS. Comments welcome. Simulation movie available at https://chongchonghe.github.io/data/#cores

A new array signal reconstruction and signal-channel DOA estimation method based on TMLA by nonuniform period modulation are proposed. By using non-uniform period modulation, the harmonic component produced by different elements could be separated. Therefore, the conventional snapshot could be reconstructed by analyzing the spectrum of the combined signal. Then spatial spectrum estimation method is used to implement DOA estimation. Numerical simulations are provided to verify the feasibility and accuracy of the proposed method. Since the duration of the signal in the frequency domain analysis processed in a single time is very short, this method is also applicable to narrowband signals. Another highlight is that this method can simultaneously measure the number of the elements-1 angle of incident signals.

In this paper, we study an intelligent reflecting surface (IRS)-aided radar-communication (Radcom) system, where the IRS is leveraged to help Radcom base station (BS) transmit the joint of communication signals and radar signals for serving communication users and tracking targets simultaneously. The objective of this paper is to minimize the total transmit power at the Radcom BS by jointly optimizing the active beamformers, including communication beamformers and radar beamformers, at the Radcom BS and the phase shifts at the IRS, subject to the minimum signal-to-interference-plus-noise ratio (SINR) required by communication users, the minimum SINR required by the radar, and the cross-correlation pattern design. In particular, we consider two cases, namely, case I and case II, based on the presence or absence of the radar cross-correlation design and the interference introduced by the IRS on the Radcom BS. For case I where the cross correlation design and the interference are not considered, we prove that the dedicated radar signals are not needed, which significantly reduces implementation complexity and simplifies algorithm design. Then, a penalty-based algorithm is proposed to solve the resulting non-convex optimization problem. Whereas for case II considering the cross-correlation design and the interference, we unveil that the dedicated radar signals are needed in general to enhance the system performance. Since the resulting optimization problem is more challenging to solve as compared with the case I, the semidefinite relaxation (SDR) based alternating optimization (AO) algorithm is proposed. Simulation results demonstrate the effectiveness of proposed algorithms and also show the superiority of the proposed scheme over various benchmark schemes., Comment: This paper answers the fundamental question: whether the dedicated radar signals are needed under two considered scenarios. The manuscript has been submitted to IEEE journal for possible publication

We investigate the fundamental multiple access (MA) scheme in an active intelligent reflecting surface (IRS) aided energy-constrained Internet-of-Things (IoT) system, where an active IRS is deployed to assist the uplink transmission from multiple IoT devices to an access point (AP). Our goal is to maximize the sum throughput by optimizing the IRS beamforming vectors across time and resource allocation. To this end, we first study two typical active IRS aided MA schemes, namely time division multiple access (TDMA) and non-orthogonal multiple access (NOMA), by analytically comparing their achievable sum throughput and proposing corresponding algorithms. Interestingly, we prove that given only one available IRS beamforming vector, the NOMA-based scheme generally achieves a larger throughput than the TDMA-based scheme, whereas the latter can potentially outperform the former if multiple IRS beamforming vectors are available to harness the favorable time selectivity of the IRS. To strike a flexible balance between the system performance and the associated signaling overhead incurred by more IRS beamforming vectors, we then propose a general hybrid TDMA-NOMA scheme with user grouping, where the devices in the same group transmit simultaneously via NOMA while devices in different groups occupy orthogonal time slots. By controlling the number of groups, the hybrid TDMA-NOMA scheme is applicable for any given number of IRS beamforming vectors available. Despite of the non-convexity of the considered optimization problem, we propose an efficient algorithm based on alternating optimization. Simulation results illustrate the practical superiorities of the active IRS over the passive IRS in terms of the coverage extension and supporting multiple energy-limited devices, and demonstrate the effectiveness of our proposed hybrid MA scheme for flexibly balancing the performance-cost tradeoff.

The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases. The exact inverse and linear seesaw formulas are derived, respectively; and possible deviations of the $3\times 3$ active neutrino mixing matrix from its unitary limit are discussed by calculating the effective Jarlskog invariants and unitarity nonagons., Comment: 23 pages, 1 figure. Minor changes, references added. Accepted for publication in Nucl. Phys. B

Antenna arrays have a long history of more than 100 years and have evolved closely with the development of electronic and information technologies, playing an indispensable role in wireless communications and radar. With the rapid development of electronic and information technologies, the demand for all-time, all-domain, and full-space network services has exploded, and new communication requirements have been put forward on various space/air/ground platforms. To meet the ever increasing requirements of the future sixth generation (6G) wireless communications, such as high capacity, wide coverage, low latency, and strong robustness, it is promising to employ different types of antenna arrays with various beamforming technologies in space/air/ground communication networks, bringing in advantages such as considerable antenna gains, multiplexing gains, and diversity gains. However, enabling antenna array for space/air/ground communication networks poses specific, distinctive and tricky challenges, which has aroused extensive research attention. This paper aims to overview the field of antenna array enabled space/air/ground communications and networking. The technical potentials and challenges of antenna array enabled space/air/ground communications and networking are presented first. Subsequently, the antenna array structures and designs are discussed. We then discuss various emerging technologies facilitated by antenna arrays to meet the new communication requirements of space/air/ground communication systems. Enabled by these emerging technologies, the distinct characteristics, challenges, and solutions for space communications, airborne communications, and ground communications are reviewed. Finally, we present promising directions for future research in antenna array enabled space/air/ground communications and networking.

Reconfigurable meta-surface (RMS) is proposed as a very promising and novel technology, which is composed of a large number of low-cost passive elements, and can achieve passive beamforming by controlling the amplitude and phase of incident electromagnetic (EM) waves. Therefore, in order to solve the challenges of high power consumption and high cost of existing base stations (BSs), we propose a low-cost and low-power consumption transmissive RMS multi-antenna system in this paper. Specifically, we first provide an overview of the transmissive RMS multi-antenna system, including its advantages, network architecture, transmission mechanism, modulation principle, channel model and channel estimation technique. Then, we address transceiver design and optimization for downlink (DL) and uplink (UL), and some numerical results are also given to verify the effectiveness of the proposed algorithm. Finally, several potential research directions of the transmissive RMS multi-antenna system are given to inspire further investigation in future work.

We have developed a new analytic method to calculate the galaxy two-point correlation functions (TPCFs) accurately and efficiently, applicable to surveys with finite, regular, and mask-free geometries. We have derived simple, accurate formulas of the normalized random-random pair counts $RR$ as functions of the survey area dimensions. We have also suggested algorithms to compute the normalized data-random pair counts $DR$ analytically. With all edge corrections fully accounted for analytically, our method computes $RR$ and $DR$ with perfect accuracy and zero variance in $O(1)$ and $O(N_{\rm g})$ time, respectively. We test our method on a galaxy catalogue from the EAGLE simulation. Our method calculates $RR+DR$ at a speed 3 to 6 orders of magnitude faster than the brute-force Monte Carlo method and 2.5 orders of magnitude faster than tree-based algorithms. For a galaxy catalogue with 10 million data points in a cube, this reduces the computation time to under 1 minute on a laptop. Our analytic method is favored over the traditional Monte Carlo method whenever applicable. Some applications in the study of correlation functions and power spectra in cosmological simulations and galaxy surveys are discussed. However, we recognize that its applicability is very limited for realistic surveys with masks, irregular shapes, and/or weighted patterns., Comment: 16 pages, 3 figures; accepted by ApJ; revised to match the accepted version; code accessible on https://github.com/chongchonghe/analytic-2pcf/tree/v1.0.0

A novel single-sideband (SSB) time-modulated technique with 2-bit phase shifters is proposed. The timemodulated module is implemented by adding periodic phase modulation to 2-bit phase shifters, which is simpler without performance loss compared to existing SSB time-modulated method. During one modulation period, four phase states (0, {\pi}/2, {\pi}, 3{\pi}/2) of 2-bit phase shifters are switched in sequence. After the modulation, the SSB time modulation is realized and the main power is distributed to the first harmonic component. The feasibility of the proposed method is verified by experiments. The undesired harmonics are efficiently suppressed. Meanwhile, 80{\deg} beam scanning range are realized through the proposed module.

We calculate the hydrogen and helium-ionizing radiation escaping star-forming molecular clouds, as a function of the star cluster mass and compactness, using a set of high-resolution radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds. In these simulations, presented in He, Ricotti and Geen (2019), the formation of individual massive stars are well resolved, and their UV radiation feedback and lifetime on the main sequence are modeled self-consistently. We find that the escape fraction of ionizing radiation from molecular clouds, $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$, decreases with increasing mass of the star cluster and with decreasing compactness. Molecular clouds with densities typically found in the local Universe have negligible $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$, ranging between $0.5\%$ to $5\%$. Ten times denser molecular clouds have $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle \approx 10\%-20\%$, while $100\times$ denser clouds, which produce globular cluster progenitors, have $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle \approx 20\%-60\%$. We find that $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$ increases with decreasing gas metallicity, even when ignoring dust extinction, due to stronger radiation feedback. However, the total number of escaping ionizing photons decreases with decreasing metallicity because the star formation efficiency is reduced. We conclude that the sources of reionization at $z>6$ must have been very compact star clusters forming in molecular clouds about $100\times$ denser than in today's Universe, which leads to a significant production of old globular clusters progenitors., Comment: 17 pages, 13 figures, accepted for publication in MNRAS

We present radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds, modeling the formation of individual massive stars, including their UV radiation feedback. The set of simulations have cloud masses between $m_{\rm gas}=10^3$~M$_\odot$ to $3 \times 10^5$~M$_\odot$ and gas densities typical of clouds in the local universe ($\overline n_{\rm gas} \sim 1.8\times 10^2$~cm$^{-3}$) and 10$\times$ and 100$\times$ denser, expected to exist in high-redshift galaxies. The main results are: {\it i}) The observed Salpeter power-law slope and normalisation of the stellar initial mass function at the high-mass end can be reproduced if we assume that each star-forming gas clump (sink particle) fragments into stars producing on average a maximum stellar mass about $40\%$ of the mass of the sink particle, while the remaining $60\%$ is distributed into smaller mass stars. Assuming that the sinks fragment according to a power-law mass function flatter than Salpeter, with log-slope $0.8$, satisfy this empirical prescription. {\it ii}) The star formation law that best describes our set of simulation is $d\rho_*/dt \propto \rho_{gas}^{1.5}$ if $\overline n_{gas}