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A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle pairs. Due to the requirement that the particles must be static, coupling via the momenta partitions the set of particles into a set of clusters, and transforms the partition function into a sum over the different cluster decompositions. This allows us to derive a formula for the density that finite clusters can carry in the infinite system. In a simplified example, we then demonstrate that in two and higher dimensions this density has a threshold, beyond which the particles form infinite clusters. The transition is accompanied by a singularity in the free energy. We also show that infinite clusters are always present in condensed phases, most likely submacroscopic in liquids and macroscopic in crystals., Comment: 12 pages

In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity in the thermodynamic quantities which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail., Comment: 13 pages, minor changes

We explore the stability and fate of gravitational triple systems comprising a central massive body and a tight binary of less massive pairs. Our present purpose is two fold; (1) to improve the Hill-type stability criterion for the binary in those systems, and (2) to examine the fate of the triple systems after the binary break-up, with particular attention to the effects of the eccentricities of the inner and outer orbits. We perform direct Newtonian N-body simulations over much longer integration times than previous studies, which is essential to determine the eventual fate of those systems statistically in a reliable fashion. We obtain an empirical fitting formula of the binary stability boundary that incorporates effects of the inner and outer eccentricities, the mutual inclination of the inner and outer orbits, and the mass ratios of the three bodies. We also find that those triple systems are stable for a much longer timescale after the binary break-up, and that their final fates (ejection of the outer body, merger to the central massive body, and collision of two less massive bodies) are very sensitive to the initial outer eccentricity., Comment: 22 pages, 14 figures, submitted to ApJ

This study proposes an adaptive experimental design framework for a channel-simulation-based base station (BS) design that supports the joint optimization of transmission power and placement. We consider a system in which multiple transmitters provide wireless services over a shared frequency band. Our objective is to maximize the average throughput within an area of interest. System operators can design the system configurations prior to deployment by iterating them through channel simulations and updating the parameters. However, accurate channel simulations are computationally expensive; therefore, it is preferable to configure the system using a limited number of simulation iterations. We develop a solver for the problem based on Bayesian optimization (BO), a black-box optimization method. The numerical results demonstrate that our proposed framework can achieve 18-22% higher throughput performance than conventional placement and power optimization strategies., Comment: 5 pages, 7 figures, 1 table. This work has been published in IEEE Networking Letters under CC BY-NC-ND 4.0 (DOI: 10.1109/LNET.2024.3469175)

To utilize half-metallic Heusler alloys in practical spintronic devices, such as magnetic sensors and magnetic memories, the key is to realize highly textured and structurally ordered polycrystalline thin films. In this study, we fabricated polycrystalline Co2FeGa0.5Ge0.5 (CFGG) Heusler alloy films deposited on a [001]-oriented Ag buffer layer, which was achieved by introducing N2 into Ar during the sputtering process, on a thermally oxidized Si substrate. We obtained strongly [001]-oriented CFGG films with B2 ordering and a high saturation magnetization close to the theoretical value, which can provide highly spin-polarized electric and spin current sources in spintronic devices with industrial viability., Comment: 16 papers, 5 figures

Magnetic materials with negative spin polarization have attracted attention for their potential to increase the design freedom of spintronic devices. This study investigated the effects of off-stoichiometry on the atomic ordering, microstructure, and magneto-transport properties in Mn2+xV1-xGa (x = -0.2, 0, +0.2, +0.4) Heusler alloy films, which are predicted to have large negative spin polarization derived from a pseudo band gap in the majority spin channel. The Mn2+xV1-xGa films epitaxially grown on MgO(001) substrates exhibits variations of B2 and L21 order with the Mn concentration. A high-quality L21 ordered film was achieved in the Mn-rich composition (x = +0.2) with B2 and L21 order parameters of 0.97 and 0.86, respectively, and a saturation magnetization of 1.4 {\mu}B/f.u, which agrees the Slater-Pauling rule. Scanning transmission electron microscopy observations showed that B2 and L21 phases coexist in Mn-poor and stoichiometric films, while the L21 phase is dominant in the Mn-rich film with small amounts of Mn-V and Mn-Ga disorders, as revealed by laboratory and anomalous X-ray diffraction. Combined first-principles calculations and anisotropic magnetoresistance analysis confirm that the addition of excess Mn preserves the high spin polarization by suppressing the formation of detrimental antisites of V atoms occupying Mn sites. Therefore, the Mn-rich composition is promising for negatively spin-polarized charge injection in Mn2VGa-based spintronic applications.

(Reduced) Using the recent cosmological high-resolution zoom-in simulations, NewHorizon and Galactica, in which the evolution of black hole spin is followed on the fly, we have tracked the cosmic history of a hundred of black holes (BHs) with a mass greater than 2x10^4 Ms. For each of them, we have studied the variations of the three dimensional angle (Psi) subtended between the BH spins and the angular momentum vectors of their host galaxies. The analysis of the individual evolution of the most massive BHs suggests that they are generally passing by three different regimes. First, for a short period after their birth, low mass BHs (<3x10^4 Ms) are rapidly spun up by gas accretion and their spin tends to be aligned with their host galaxy spin. Then follows a second phase in which the accretion of gas onto low mass BHs (<10^5 Ms) is quite chaotic and inefficient, reflecting the complex and disturbed morphologies of forming proto-galaxies at high redshifts. The variations of Psi are rather erratic during this phase and are mainly driven by the rapid changes of the direction of the galaxy angular momentum. Then, in a third and long phase, BHs are generally well settled in the center of galaxies around which the gas accretion becomes much more coherent (>10^5 Ms). In this case, the BH spins tend to be well aligned with the angular momentum of their host galaxy and this configuration is generally stable even though BH merger episodes can temporally induce misalignment. We have also derived the distributions of cos(Psi) at different redshifts and found that BHs and galaxy spins are generally aligned. Finally, based on a Monte Carlo method, we also predict statistics for the 2-d projected spin-orbit angles lambda. In particular, the distribution of lambda traces well the alignment tendency in the 3-d analysis. Such predictions provide an interesting background for future observational analyses., Comment: Accepted for publication in A&A (12/03/2024)

Observed protostellar outflows exhibit a variety of asymmetrical features, including remarkable unipolar outflows and bending outflows. Revealing the formation and early evolution of such asymmetrical protostellar outflows, especially the unipolar outflows, is essential for a better understanding of the star and planet formation because they can dramatically change the mass accretion and angular momentum transport to the protostars and protoplanetary disks. Here, we perform the three-dimensional non-ideal magnetohydrodynamics simulations to investigate the formation and early evolution of the asymmetrical protostellar outflows in magnetized turbulent isolated molecular cloud cores. We find, for the first time to our knowledge, that the unipolar outflow forms even in the single low-mass protostellar system. The results show that the unipolar outflow is driven in the weakly magnetized cloud cores with the dimensionless mass-to-flux ratios of $\mu=8$ and $16$. Furthermore, we find the $\textit{protostellar rocket effect}$ of the unipolar outflow, which is similar to the launch and propulsion of a rocket. The unipolar outflow ejects the protostellar system from the central dense region to the outer region of the parent cloud core, and the ram pressure caused by its ejection suppresses the driving of additional new outflows. In contrast, the bending bipolar outflow is driven in the moderately magnetized cloud core with $\mu=4$. The ratio of the magnetic to turbulent energies of a parent cloud core may play a key role in the formation of asymmetrical protostellar outflows., Comment: 24 pages, 6 figures, accepted for publication in ApJ

Recent advances in the study of materials with topological electronic band structures have revealed magnetic materials exhibiting giant anomalous Hall effects (AHE). The giant AHE has not only attracted the research interest in its mechanism but also opened up the possibility of practical application in magnetic sensors. In this article, we describe simulation-based investigations of AHE magnetic sensors for the applications to read head sensors (readers) of hard disk drives. With the shrinking of magnetic recording patterns, the reader technology, which currently uses multilayer-based tunnel magnetoresistance (TMR) devices, is associated with fundamental challenges, such as insufficient spatial resolution and signal-to-noise ratio (SNR) in sensors with dimensions below 20 nm. The structure of an AHE-based device composed of a single ferromagnetic material is advantageous for magnetic sensors with nanoscale dimensions. We found that AHE readers using topological ferromagnets with giant AHE, such as Co2MnGa, can achieve a higher SNR than current TMR readers. The higher SNR originates from the large output signal of the giant AHE as well as from the reduced thermal magnetic noise, which is the dominant noise in TMR readers. We highlight a major challenge in the development of AHE readers: the reduction in the output signal due to the shunting of the bias current and the leakage of the Hall voltage through the soft magnetic shields surrounding the AHE reader. We propose reader structures that overcome this challenge. Finally, we discuss the scope for future research to realize AHE readers., Comment: Revised version after peer-review

We develop a high-throughput method for measuring the composition dependence of magnetoresistance (MR) and spin-transfer-torque (STT) effects in current-perpendicular-to-plane giant magnetoresistance (CPP-GMR) devices and report its application to the CoFe system. The method is based on the use of composition-gradient films deposited by combinatorial sputtering. This structure allows the fabrication of devices with different compositions on a single substrate, drastically enhancing the throughput in investigating composition dependence. We fabricated CPP-GMR devices on a single GMR film consisting of a Co$_{x}$Fe$_{1-x}$ (0 $\le$ $\textit{x}$ $\le$ 1) composition-gradient layer, a Cu spacer layer, and a NiFe layer. The MR ratio obtained from resistance-field measurements exhibited the maximum in the broad Co concentration range of 0.3 $\le$ $\textit{x}$ $\le$ 0.65. In addition, the STT efficiency was estimated from the current to induce magnetization reversal of the NiFe layer by spin injection from the Co$_{x}$Fe$_{1-x}$ layer. The STT efficiency was also the highest around the same Co concentration range as for the MR ratio, and this correlation was theoretically explained by the change in the spin polarization of the Co$_{x}$Fe$_{1-x}$ layer. The results revealed the Co$_{x}$Fe$_{1-x}$ composition range suitable for spintronic applications, demonstrating the advantages of the developed method., Comment: 19 pages, 5 figures

Multi-level magnetic recording is a new concept for increasing the data storage capacity of hard disk drives. However, its implementation has been limited by a lack of suitable media capable of storing information at multiple levels. Herein, we overcome this problem by developing dual FePt-C nanogranular films separated by a Ru-C breaking layer with a cubic crystal structure. The FePt grains in the bottom and top layers of the developed media exhibited different effective magnetocrystalline anisotropies and Curie temperatures. The former is realized by different degrees of ordering in the L10-FePt grains, whereas the latter was attributed to the diffusion of Ru, thereby enabling separate magnetic recordings at each layer under different magnetic fields and temperatures. Furthermore, the magnetic measurements and heat-assisted magnetic recording simulations showed that these media enabled 3-level recording and could potentially be extended to 4-level recording, as the up-down and down-up states exhibited non-zero magnetization.

Nearly a hundred of binary black holes (BBHs) have been discovered with gravitational-wave signals emitted at their merging events. Thus, it is quite natural to expect that significantly more abundant BBHs with wider separations remain undetected in the universe, or even in our Galaxy. We consider a possibility that star-BH binary candidates may indeed host an inner BBH, instead of a single BH. We present a detailed feasibility study of constraining the binarity of the currently available two targets, Gaia BH1 and Gaia BH2. Specifically, we examine three types of radial velocity (RV) modulations of a tertiary star in star-BBH triple systems; short-term RV modulations induced by the inner BBH, long-term RV modulations induced by the nodal precession, and long-term RV modulations induced by the von Zeipel-Kozai-Lidov oscillations. Direct three-body simulations combined with approximate analytic models reveal that Gaia BH1 system may exhibit observable signatures of the hidden inner BBH if it exists at all. The methodology that we examine here is quite generic, and is expected to be readily applicable to future star-BH binary candidates in a straightforward manner., Comment: 21 pages, 11 figures, 1 table, ApJ, in press

We have discovered a new phenomenon that inductance oscillates as a function of the angle between an in-plane magnetic field and an electric current direction in permalloy films, which we have named "the anisotropic magneto-inductance (AML) effect". We have investigated the dependences of the AML effect on the size and voltage. The length, frequency, and amplitude dependences suggest that the AML effect should be evaluated in terms of "inductivity". Inductors based on this AML effect have the potential to be variable, on-chip, and one billion times smaller than the small commercial inductor.

We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into infinite permutation cycles is simultaneous with off-diagonal long-range order. If the cycle lengths tend to infinity not slower than the square of the linear extension of the system, there is also Bose-Einstein condensation. (ii) If the pair potential is also nonnegative, cycles composed of a nonzero fraction of the total number of particles do appear if the density exceeds a temperature-dependent threshold value. The two together constitute the proof that in such a system Bose-Einstein condensation takes place at high enough densities., Comment: 66 pages, combined from 2106.10032[math-ph], 2108.02659 [math-ph], 2208.08931[math-ph]. arXiv admin note: text overlap with arXiv:2208.08931, arXiv:2106.10032, arXiv:2108.02659

We develop a general framework to compute photometric variations induced by the oblique rotation of a star with an axisymmetric inhomogeneous surface. We apply the framework to compute lightcurves of white dwarfs adopting two simple models of their surface inhomogeneity. Depending on the surface model and the location of the observer, the resulting lightcurve exhibits a departure from a purely sinusoidal curve that are observed for a fraction of white dwarfs. As a specific example, we fit our model to the observed phase-folded lightcurve of a fast-spinning white dwarf ZTF J190132.9+145808.7 (with the rotation period of 419s). We find that the size and obliquity angle of the spot responsible for the photometric variation are $\dts \approx 60^\circ$ and $\thetaS \approx 60^\circ$ or $90^\circ$, respectively, implying an interesting constraint on the surface distribution of the magnetic field on white dwarfs., Comment: 25 pages, 9 figures, accepted for publication in PASJ

While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange stability'', which roughly refers to the stability against the escape of a body from the system, or ``disruption'' of the triple system, in contrast to ``Lyapunov-like stability'' that is related to the chaotic nature of the system dynamics. We compute the evolution of triple systems using direct $N$-body simulations up to $10^7 P_\mathrm{out}$, which is significantly longer than previous studies (with $P_\mathrm{out}$ being the initial orbital period of the outer body). We obtain the resulting disruption timescale $T_\mathrm{d}$ as a function of the triple orbital parameters with particular attention to the dependence on the mutual inclination between the inner and outer orbits, $i_\mathrm{mut}$. By doing so, we have clarified explicitly the difference between Lagrange and Lyapunov stabilities in astronomical triples. Furthermore, we find that the von Zeipel-Kozai-Lidov oscillations significantly destabilize inclined triples (roughly with $60^\circ < i_\mathrm{mut} < 150^\circ$) relative to those with $i_\mathrm{mut}=0^\circ$. On the other hand, retrograde triples with $i_\mathrm{mut}>160^\circ$ become strongly stabilized with much longer disruption timescales. We show the sensitivity of the normalized disruption timescale $T_\mathrm{d}/P_\mathrm{out}$ to the orbital parameters of triple system. The resulting $T_\mathrm{d}/P_\mathrm{out}$ distribution is practically more useful in a broad range of astronomical applications than the stability criterion based on the Lyapunov divergence., Comment: 13 pages, 3 figures, ApJ, in press

In this third paper of a series that started with arXiv:2106.10032 [math-ph] and continued with arXiv:2108.02659 [math-ph] we show that in $d\geq 3$ dimensions at low temperatures or high densities bosons interacting via pair potentials that are both positive and positive type form permutation cycles whose length diverges proportionally with the number of particles. Based on the second-cited paper, this implies Bose-Einstein condensation., Comment: 29 pages, end of the proof about the coupling of cycles rewritten. arXiv admin note: text overlap with arXiv:1710.04441

We examine the stability of hierarchical triple systems using direct $N$-body simulations without adopting a secular perturbation approximation. We estimate their disruption timescales in addition to the mere stable/unstable criterion, with particular attention to the mutual inclination between the inner and outer orbits. First, we improve the fit to the dynamical stability criterion by \citet{Mardling1999,Mardling2001} widely adopted in the previous literature. Especially, we find that that the stability boundary is very sensitive to the mutual inclination; coplanar retrograde triples and orthogonal triples are much more stable and unstable, respectively, than coplanar prograde triples. Next, we estimate the disruption timescales of triples satisfying the stability condition up to $10^9$ times the inner orbital period. The timescales follow the scaling predicted by \citet{Mushkin2020}, especially at high $e_\mathrm{out}$ where their random walk model is most valid. We obtain an improved empirical fit to the disruption timescales, which indicates that the coplanar retrograde triples are significantly more stable than the previous prediction. We furthermore find that the dependence on the mutual inclination can be explained by the energy transfer model based on a parabolic encounter approximation. We also show that the disruption timescales of triples are highly sensitive to the tiny change of the initial parameters, reflecting the genuine chaotic nature of the dynamics of those systems., Comment: 33 pages, 19 figures, 1 table, ApJ, in press. Comments welcome

We perform photometric (the Lomb-Scargle periodogram, autocorrelation, and wavelet) and asteroseismic analyses of 92 Kepler solar-like main-sequence stars to understand the reliability of the measured stellar rotation periods. We focus on the 70 stars without reported stellar companions, and classify them into four groups according to the quarter-to-quarter variance of the Lomb-Scargle period and the precision of the asteroseismic period. We present detailed individual comparison among photometric and asteroseismic constraints for these stars. We find that most of our targets exhibit significant quarter-to-quarter variances in the photometric periods, suggesting that the photometrically estimated period should be regarded as a simplified characterization of the true stellar rotation period, especially under the presence of the latitudinal differential rotation. On the other hand, there are a fraction of stars with a relatively small quarter-to-quarter variance in the photometric periods, most of which have consistent values for asteroseismically and photometrically estimated rotation periods. We also identify over ten stars whose photometric and asteroseismic periods significantly disagree, which would be potentially interesting targets for further individual investigations.

We present an analytic model of the lightcurve variation for stars with non-evolving starspots on a differentially rotating surface. The Fourier coefficients of the harmonics of the rotation period are expressed in terms of the latitude of the spot, $\ell_{s}$, and the observer's line-of-sight direction, $\ell_{o}$, including the limb darkening effect. We generate different realizations of multi-spots according to the model, and perform mock observations of the resulting lightcurve modulations. We discuss to what extent one can recover the properties of the spots and the parameters for the differential rotation law from the periodogram analysis. Although our analytical model neglects the evolution of spots on the stellar surface (dynamical motion, creation and annihilation), it provides a basic framework to interpret the photometric variation of stars, in particular from the existing Kepler data and the future space-born mission. It is also applicable to photometric modulations induced by rotation of various astronomical objects., Comment: 31 pages, 15 figures, accepted for publication in PASJ

Recent ALMA observations on disk substructures suggest the presence of embedded protoplanets in a large number disks. The primordial configurations of these planetary systems can be deduced from the morphology of the disk substructure and serve as initial conditions for numerical investigation of their future evolution. Starting from the initial configurations of 12 multi-planetary systems deduced from ALMA disks, we carried out two-stage N-body simulation to investigate the evolution of the planetary systems at the disk stage as well as the long term orbital stability after the disk dispersal. At the disk stage, our simulation includes both the orbital migration and pebble/gas accretion effects. We found a variety of planetary systems are produced and can be categorised into distant giant planets, Jupiter-like planets, Neptune-like planets and distant small planets. We found the disk stage evolution as well as the final configurations are sensitive to both the initial mass assignments and viscosity. After the disk stage, we implement only mutual gravity between star and planets and introduce stochastic perturbative forces. All systems are integrated for up to 10 Gyr to test their orbital stability. Most planetary systems are found to be stable for at least 10 Gyr with perturbative force in a reasonable range. Our result implies that a strong perturbation source such as stellar flybys is required to drive the planetary system unstable. We discuss the implications of our results on both the disk and planet observation, which may be confirmed by the next generation telescopes such as JWST and ngVLA., Comment: 41 pages, 16 figures, accepted for publication in ApJ

In this report on education systems in Repeatedly High Performing Jurisdictions (RHPJs) the authors present data on the assessment approaches used at the end of basic secondary education. These assessments are conducted at around the age of 16, at approximately the stage when students in England, Wales and Northern Ireland take the General Certificate of Secondary Education (GCSEs). The aim of this report is to bring some clarity and lesser-known facts to current debate. To this end, the authors present data collated in a desk-based study of all jurisdictions globally that have repeatedly performed highly in international comparisons. The authors reveal the forms of assessment that are used at the end of basic secondary education within each jurisdiction. This enables clarification of how common high-stakes testing actually is within what are arguably the world's most successful education systems. Across the jurisdictions the stated purposes of assessments at this stage of education are considered. This includes an exploration of earliest aspirations behind external examinations in England. In particular the authors examine the use of qualifications in progression, as this is of particular importance in current discussion. Since the use of assessment for accountability is perhaps its most controversial purpose, this phenomenon is explored in some renowned education systems: those of Shanghai in China, Estonia and Finland. Overall, the authors provide an evidence-based argument that when it comes to high-stakes testing at age 16, England, Wales and Northern Ireland are by no means as atypical as some would believe. The approach to assessment is, in fact, strikingly similar to the approaches of many of the countries whose educational achievements are most admired.