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We explore the energy spectrum and eigenstates of two-component atomic Fermi superfluids with tunable pairing interactions in the presence of spin-dependent ultra long-range Rydberg molecule (ULRM) potentials, within the Bogoliubov-de Gennes formalism. The attractive ULRM potentials lead to local density accumulation, while their difference results in a local polarization potential and induces the in-gap Yu-Shiba-Rusinov (YSR) states whose energies lie below the bulk energy gap. A transition from equal-population to population-imbalance occurs as the pairing strength falls below a critical value, accompanied by the emergence of local Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like states characterized by out-of-phase wave functions and lower energies compared to the YSR states. The negative contribution emanating from the FFLO-like states also causes a sign change in the gap function within the ULRM potentials. Depending on the Rydberg state generating the ULRM potentials, the transition towards population-imbalance can be on either the BCS or the Bose-Einstein condensation side of the Fermi superfluid. Additionally, spin-polarized bound states arise along with oscillatory ``clumpy states" to compensate for the local density difference. Finally, we discuss possible experimental realizations and measurements of the composite Rydberg atom-Fermi superfluid system., Comment: 12 pages, 7 figures, submitted

We propose the scheme realizing the two-level control over the unitary operators $U_k$ creating the required quantum state of the system $S$. These operators are controlled by the superposition state of the auxiliary subsystem $R$ which is governed by two control centers. The first-level control center (main control) creates the equal-probability pure state of $R$ with certain distribution of phase factors that, in turn, govern the power of the second-level control center $C$ that applies the special $V$-operators to the same subsystem $R$ changing its state and thus controlling the applicability of $U_k$. In addition, the above phases are responsible for the entanglement in the subsystem $R$. We find the direct relation between this entanglement and the number of operators $U_k$ that can be controlled by $C$. The simple example of a two-level control system governing the creation of entangled state of the two-qubit system $S$ is presented., Comment: 27 pages 5 figures

Here, we consider new nonadditive entropy of the apparent horizon $S_K=S_{BH}/(1+\gamma S_{BH})$ with $S_{BH}$ being the Bekenstein--Hawking entropy. This is an alternative of the R\'{e}nyi and Tsallis entropies, that allow us by utilizing the holographic principle to develop of a new model of holographic dark energy. When $\gamma\rightarrow 0$ our entropy becomes the Bekenstein--Hawking entropy $S_{BH}$. The generalized Friedmann's equations for Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) space-time for the barotropic matter fluid with $p=w\rho$ were obtained. We compute the dark energy pressure $p_D$, density energy $\rho_D$ and the deceleration parameter corresponding to our model. From the second modified Friedmann's equation a dynamical cosmological constant was obtained. We show that at some model parameters $w$ and $\beta$ there are two phases, universe acceleration and deceleration or the phase of the eternal inflation. Thus, our model, by virtue of the holographic principle, can describe the universe inflation and late time of the universe acceleration. The holographic dark energy model with the generalized entropy of the apparent horizon can be of interest for new cosmology., Comment: 6 pages, 7 figures

The Lee-Huang-Yang (LHY) energy correction at the edge of the mean-field stability regime is known to give rise to beyond mean-field structures in a wide variety of systems. In this work, we analytically derive the LHY energy for two-, three- and four-component one-dimensional bosonic short-range interacting mixtures across the mean-field stability regime. For varying intercomponent attraction in the two-component setting, quantitative deviations from the original LHY treatment emerge being imprinted in the droplet saturation density and width. On the other hand, for repulsive interactions an unseen early onset of phase-separation occurs for both homonuclear and heteronuclear mixtures. Closed LHY expressions for the fully-symmetric three- and four-component mixtures, as well as for mixtures comprised of two identical components coupled to a third independent component are provided and found to host a plethora of mixed droplet states. Our results are expected to inspire future investigations in multicomponent systems for unveiling exotic self-bound states of matter and unravel their nonequilibrium quantum dynamics., Comment: 18 pages, 6 figures

The $2\nu2\beta$ decay of $^{150}$Nd to the first excited 740.5 keV $0^{+}_{1}$ level of $^{150}$Sm was measured over 5.845 yr with the help of a four-crystal low-background HPGe $\gamma$ spectrometry system in the underground low-background laboratory STELLA of LNGS-INFN. A 2.381 kg highly purified Nd-containing sample was employed as the decay source. The expected de-excitation gamma-quanta of the $0^{+}_{1}$ level with energies 334.0 keV and 406.5 keV were observed both in one-dimensional spectrum and in coincidence data resulting in the half-life $T_{1/2}=[0.83^{+0.18}_{-0.13}\mathrm{(stat)}^{+0.16}_{-0.19}\mathrm{(syst)}]\times 10^{20}$ yr. Interpreting an excess of the 334.0-keV peak area as an indication of the $2\beta$ decay of $^{150}$Nd to the 334.0 keV $2^+_1$ excited level of $^{150}$Sm with a half-life of $T_{1/2}=[1.5^{+2.3}_{-0.6}\mathrm{(stat)}\pm 0.4\mathrm{(syst)}]\times10^{20}$ yr, the $2\nu2\beta$ half-life of $^{150}$Nd for the transition to the 0$^{+}_{1}$ level is $T_{1/2}=[1.03^{+0.35}_{-0.22}\mathrm{(stat)}^{+0.16}_{-0.19}\mathrm{(syst)}]\times 10^{20}$ yr, in agreement with the previous experiments. Both half-life values reasonably agree with the theoretical calculations in the framework of proton-neutron QRPA with isospin restoration combined with like nucleon QRPA for description of excited states in the final nuclei. For $2\nu2\beta$ and $0\nu2\beta$ transitions of $^{150}$Nd and $^{148}$Nd to several excited levels of $^{150}$Sm and $^{148}$Sm, limits were set at level of $T_{1/2}>10^{20}-10^{21}$ yr., Comment: 61 pages, 19 figures, 14 tables

Many microscopic models with the interaction between the next-nearest neighbours as a key parameter for cuprate physics have inspired us to study the diagonal superexchange interaction in a CuO$_2$ layer. Our investigation shows that models with extended hopping provide a correct representation of magnetic interactions only in a hypothetical square CuO$_2$ layer, where the diagonal superexchange interaction with the next-nearest neighbors always has the AFM nature. The conclusions are based on the symmetry prohibition on FM contribution to the diagonal superexchange between the next-nearest neighbors for a simple square CuO$_2$ layer rather than for a real CuO$_2$ layer, where diagonal AFM superexchange may be overestimated. We also discuss the reasons for magnetic frustration effects and high sensitivity of spin nanoinhomogeneity to square symmetry breaking., Comment: 7 pages, 4 figures

We present experimental evidence of Sb incorporation inside InAs/GaA(001) quantum dots exposed to an antimony flux immediately before capping with GaAs. The Sb composition profile inside the nanostructures as measured by cross-sectional scanning tunneling and electron transmission microscopies show two differentiated regions within the quantum dots, with an Sb rich alloy at the tip of the quantum dots. Atomic force microscopy and transmission electron microscopy micrographs show increased quantum-dot height with Sb flux exposure. The evolution of the reflection high-energy electron-diffraction pattern suggests that the increased height is due to changes in the quantum-dot capping process related to the presence of segregated Sb atoms. These structural and compositional changes result in a shift of the room-temperature photoluminescence emission from 1.26 to 1.36 microns accompanied by an order of magnitude increase in the room-temperature quantum-dot luminescence intensity., Comment: 16 pages, 11 figures

The performance of Hamamatsu 8" photomultiplier tubes (PMTs) of the type used in the SuperNEMO neutrinoless double-beta decay experiment (R5912-MOD), is investigated as a function of exposure to helium (He) gas. Two PMTs were monitored for over a year, one exposed to varying concentrations of He, and the other kept in standard atmospheric conditions as a control. Both PMTs were exposed to light signals generated by a Bi-207 radioactive source that provided consistent large input PMT signals similar to those that are typical of the SuperNEMO experiment. The energy resolution of PMT signals corresponding to 1 MeV energy scale determined from the Bi-207 decay spectrum, shows a negligible degradation with He exposure; however the rate of after-pulsing shows a clear increase with He exposure, which is modelled and compared to diffusion theory. A method for reconstructing the partial pressure of He within the PMT and a method for determining the He breakdown point, are introduced. The implications for long-term SuperNEMO operations are briefly discussed.

This manuscript presents a working model linking chemical disorder and transport properties in correlated-electron perovskites with high-entropy formulations and a framework to actively design them. We demonstrate this new learning in epitaxial Sr$x$(Ti,Cr,Nb,Mo,W)O$3$ thin films that exhibit exceptional crystalline fidelity despite a diverse chemical formulation where most B-site species are highly misfit with respect to valence and radius. X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy confirm a unique combination of chemical disorder and structural perfection in thick epitaxial layers. This combination produces significant electron correlation, low electrical resistivity, and an optical transparency window that surpasses that of constituent end-members, with a flattened frequency- and temperature-dependent response. We address the computational challenges of modeling such systems and investigate short-range ordering using cluster expansion. These results showcase that unusual d-metal combinations access an expanded property design space that is predictable using end-member characteristics -- though unavailable to them -- thus offering performance advances in optical, spintronic, and quantum devices.

Models of the galaxy-halo connection are needed to understand both galaxy clusters and large scale structure. To make said models, we need a robust method that assigns galaxies to halos and matches the observed and simulated stellar-halo mass relation. We employ an empirical Subhalo Abundance Matching (SHAM) model implemented in the halos module of SkyPy which assigns blue and red galaxies based on the Peng et al. (2010) (arXiv:1003.4747v2) model containing three parameters: $M_\mu$ (halo mass where half the galaxies assigned should be quenched), $\sigma$ (transition width from star forming to quenched) and $b$ (baseline quenched fraction at low mass). We test two sets of galaxy stellar mass functions for four populations of galaxies (central/satellite, blue/red) and run parameter estimation using Approximate Bayesian Computation over each model when compared to a set of applicable literature models. For the Weigel et al. (2016) (arXiv:1604.00008v1) galaxies we find best fit values of log $M_\mu = 11.94^{+0.02}_{-0.02}$, $\sigma = 0.49^{+0.04}_{-0.04}$ and $b = 0.31^{+0.01}_{-0.01}$. For the Birrer et al. (2014) (arXiv:1401.3162v2) galaxies we find best fit values of log $M_\mu = 11.93^{+0.01}_{-0.01}$, $\sigma = 0.53^{+0.04}_{-0.04}$ and $b = 0.51^{+0.05}_{-0.04}$. Overall, we demonstrate that these constraints produce a model that is consistent with literature models for the central galaxies. Future research will focus on the normalisation of the satellite galaxies in order to better constrain the $b$ parameter., Comment: 10 pages, 9 figures

We explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. These are classified by utilizing the second-order sign correlation function and the ratio of incompressible versus compressible kinetic energies. They involve, vortex configurations ranging from vortex dipoles to vortex clusters and randomly distributed vortex-antivortex pairs. The incompressible kinetic energy spectrum features Kolmogorov ($k^{-5/3}$) and Vinen like ($k^{-1}$) scaling in the infrared regime, while a $k^{-3}$ decay in the ultraviolet captures the presence of vortices. The compressible spectrum shows $k^{-3/2}$ scaling within the infrared and $k$ power law in the case of enhanced sound-wave emission suggesting thermalization. Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. Our findings offer insights into the turbulent response of exotic phases-of-matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics., Comment: 18pages, 10 figures

The evolution of the orbits of bodies ejected from the Earth, Moon, Mercury and Mars was studied. At ejection velocities about 12-14 km/s, the fraction of bodies ejected from the Earth that fall back onto the Earth was about 0.15-0.25. The total number of bodies ejected from the Earth and delivered to the Earth and Venus probably did not differ much. The probability of collisions of bodies ejected from the Earth with the Moon moving in its present orbit was of the order of 0.01. Probabilities of collisions of bodies ejected from the Earth with Mercury were about 0.02-0.08 at ejection velocities greater than 11.3 km/s. The probabilities of collisions of bodies ejected from the Earth with Mars did not exceed 0.025. For the ejection of bodies from the present orbit of the Moon, probabilities of collisions of ejected bodies with planets were similar to those ejected from the Earth if we consider smaller ejection velocities from the Moon than from the Earth. The probability of a collision of a body ejected from Mars with Mars usually did not exceed 0.04 at an ejection velocity greater than 5.3 km/s. The fraction of bodies ejected from Mars and collided with Mercury was typically less than 0.08. Probabilities of collisions of bodies ejected from Mars with the Earth and Venus were about 0.1-0.2 (each) at an ejection velocity between 5.05 and 10 km/s. Most of bodies ejected from Mercury fall back onto Mercury. Probabilities of collisions of bodies ejected from Mercury with the Earth typically did not exceed 0.02 and 0.1 at an ejection velocity less than 8 km/s and 15 km/s, respectively. The fraction of bodies ejected from Mercury and collided with Venus was greater than that with the Earth typically by an order of magnitude. Probabilities of collisions of bodies with Venus were about 0.1-0.3 at a velocity of ejection from Mercury between 4.3 and 10 km/s., Comment: 6 pages. arXiv admin note: substantial text overlap with arXiv:2411.04218

African agriculture is undergoing rapid transformation. Annual maps of crop fields are key to understanding the nature of this transformation, but such maps are currently lacking and must be developed using advanced machine learning models trained on high resolution remote sensing imagery. To enable the development of such models, we delineated field boundaries in 33,746 Planet images captured between 2017 and 2023 across the continent using a custom labeling platform with built-in procedures for assessing and mitigating label error. We collected 42,403 labels, including 7,204 labels arising from tasks dedicated to assessing label quality (Class 1 labels), 32,167 from sites mapped once by a single labeller (Class 2) and 3,032 labels from sites where 3 or more labellers were tasked to map the same location (Class 4). Class 1 labels were used to calculate labeller-specific quality scores, while Class 1 and 4 sites mapped by at least 3 labellers were used to further evaluate label uncertainty using a Bayesian risk metric. Quality metrics showed that label quality was moderately high (0.75) for measures of total field extent, but low regarding the number of individual fields delineated (0.33), and the position of field edges (0.05). These values are expected when delineating small-scale fields in 3-5 m resolution imagery, which can be too coarse to reliably distinguish smaller fields, particularly in dense croplands, and therefore requires substantial labeller judgement. Nevertheless, previous work shows that such labels can train effective field mapping models. Furthermore, this large, probabilistic sample on its own provides valuable insight into regional agricultural characteristics, highlighting variations in the median field size and density. The imagery and vectorized labels along with quality information is available for download from two public repositories., Comment: 22 pages, 8 figures

We present the results of determining the parameters characterizing the shape and orientation of residual velocity ellipsoids from the Gaia DR3 red giants and subgiants. We show the distribution of velocity dispersions in the Galactic plane obtained from three components of the spatial velocity, as well as the coordinate distribution of the intersection points of the velocity ellipsoid axes with the celestial sphere, in particular the deviations of the longitudes and latitudes of the vertices of stellar regions located within spheres with a radius of 1 kpc centered in the Galactic mid-plane. The area of the Galactic disk under study is in the range of Galactocentric coordinates 0 < R < 15 kpc and $120^\circ < \theta < 240^\circ$. We show that the vertex deviations in some regions of the Galactic mid-plane can reach $30^\circ$ in longitude, and $15^\circ$ in latitude. This indicates the presence of kinematic distortions of the stellar velocity field, especially noticeable in the angular range of $150^\circ < \theta < 210^\circ$ at a distance of approximately 13 kpc. We propose the angles of deviation of longitudes and latitudes of the ellipsoid axes of residual stellar velocities to be considered as kinematic signatures of various Galactic deformations determined from real fields of spatial velocities. We present the distribution of parameters characterizing the shapes of velocity ellipsoids, as well as their distribution of the semi-axes length ratios. We note a local feature in this distribution and in the distribution of the elongation measurements of the ellipsoids. We perform a comparison of the results obtained from the tensor of deformation velocities and from the observed spatial velocities., Comment: 14 pages, 16 figures

The exact recursion relations are used to study the mixed half-integer spin-(3/2, 7/2) Blume-Capel Ising ferrimagnetic system on the Bethe lattice. Ground-state phase diagrams are computed in the $({D_{A}}/{q|J|}, {D_{B}}/{q|J|})$ plane to reveal different possible ground states of the model. Using the thermal changes of the order-parameters, interesting temperature dependent phase diagrams are constructed in the ($D_{A}/|J|$, $kT/|J|$), ($D_{B}/|J|$, $kT/|J|$) planes as well as in the ($D/|J|$, $kT/|J|$) plane where $D=D_A=D_B$. It is revealed that the system exhibits first- and second-order phase transitions and compensation temperatures for specific model parameter values. Under the constraint of an external magnetic field, the model also produces multi-hysteresis behaviors as single, double and triple hysteresis cycles. Particularly, the impacts of the ferrimagnetic coupling $J$ on the remanent magnetization and the coercitive fields for selected values of the other physical parameters of the system are pointed out. Our numerical results are qualitatively consistent with those reported in the literature., Comment: 17 pages, 13 figures (Published version)

Modulational instability (MI) is a fundamental phenomenon in the study of nonlinear dynamics, spanning diverse areas such as shallow water waves, optics, and ultracold atomic gases. In particular, the nonlinear stage of MI has recently been a topic of intense exploration, and has been shown to manifest, in many cases, in the generation of dispersive shock waves (DSWs). In this work, we experimentally probe the MI dynamics in an immiscible two-component ultracold atomic gas with exclusively repulsive interactions, catalyzed by a hard-wall-like boundary produced by a repulsive optical barrier. We analytically describe the expansion rate of the DSWs in this system, generalized to arbitrary inter-component interaction strengths and species ratios. We observe excellent agreement among the analytical results, an effective 1D numerical model, full 3D numerical simulations, and experimental data. Additionally, we extend this scenario to the interaction between two counterpropagating DSWs, which leads to the production of Peregrine soliton structures. These results further demonstrate the versatility of atomic platforms towards the controlled realization of DSWs and rogue waves., Comment: main (6 pages; 3 figures) and supplement (4 pages; 2 figures)

The results of the numerical investigations of the evolution of orbits of trans-Neptunian bodies at the 2 : 3 resonance with Neptune are presented. The gravitational influence of the four giant planets was taken into account. For identical initial values of the semimajor axes, eccentricities, and inclinations, but for different initial orbital orientations and initial positions in orbits, we obtained different types of variations in the difference {\Delta}{\Omega}={\Omega}-{\Omega}_N in the ascending-node longitudes of the body and Neptune, and in the perihelion argument {\omega}. When {\Delta}{\Omega} decreases and {\omega} increases during evolution, then most of the bodies leave the resonance in 20 Myr. In the case of an increase in {\Delta}{\Omega} and a decrease in {\omega}, the bodies stay in the resonance for a much longer time. Regions of eccentricities and inclinations, for which some bodies were in the {\eta}_18 secular resonance ({\Delta}{\Omega} is almost constant) and in the Kozai resonance ({\omega} is almost constant), were obtained to be larger than those predicted for small variations in the critical angle. Some bodies can at the same time be in both these resonances., Comment: 14 pages, 2 fugures

A numerical integration of the equations of motion of the Sun-planets-an object system is used to study the evolution of orbits close to the orbit of the P/1996 R2 object, which is a Jupiter-crossing object, and to the asteroidal orbit of the P/1996 N2 object, which, at the moment of its detection, had a tail similar to a cometary one. Small variations in the initial data considerably affect the evolution of orbits close to that of the P/1996 R2 object. The time elapsed up to the ejection of the object into a hyperbolic orbit varied from 3*10^4 to 2.7*10^7 yr. Some objects were in resonances with Jupiter and Saturn for a long time. For about 20 percent of the runs, objects reached the Earth's orbit during evolution. Orbital elements of the P/1996 N2 object changed quasi-periodically over the considered time span of 200 Myr. Variations in the semimajor axis, eccentricity, and inclination were equal to 0.04 AU, 0.11 deg, and 3.5 deg, respectively., Comment: 14 pages, 2 figures

Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets were found., Comment: 7 pages, 1 fugure

The powerful EHF radiation generated in a relativistic high-voltage pulsed magnetron of the 8 mm range is experimentally investigated. The factors that negatively affect the generation of EHF radiation are experimentally investigated and analyzed. It is determined that the processes that reduce the efficiency and duration of the generation pulse also include low pressure in the vacuum diode of the magnetron. It is known that the main residual gases in the vacuum diode of a magnetron are air components. During magnetron operation, there is a significant increase in the pressure of the residual atmosphere: hydrocarbons, water vapor, and hydrogen. A vacuum system was designed to evacuate these gases to ensure optimal operation of the magnetron. For the new vacuum system, a cryogenic condensation-adsorption pump was developed and applied, which allowed to increase the rate of pumping out the main residual gases. The peculiarity of the developed pump is that the pumping element with the adsorbent has a working surface that is twice as large as the one in the corrugated form of the sorption cartridge. Another feature of the pump is its efficiency, which is achieved through the use of nitrogen vapor for cooling the inter-wall gap. The use of cryogenic pumping means made it possible to obtain a pressure of 1E-6 Torr, which led to a 25 percent increase in the EHF radiation of the relativistic magnetron., Comment: 5 pages, 5 figures

The physics of glass has been a significant topic of interest for decades. Dynamical facilitation is widely believed to be an important characteristic of glassy dynamics, but the precise mechanism is still under debate. We propose a lattice model of glass called the facilitated random walk (FRW). Each particle performs continuous time random walk in the presence of its own random local kinetic constraints. The particles do not interact energetically. Instead, they interact kinetically with a hopping rate resampling rule under which motions of a particle can randomly perturb the local kinetic constraints of other particles. This dynamic interaction is reversible, following a rate restoration rule. A step-by-step reversal of the particle motions exactly restore the previous constraints, modeling randomness quenched in the configuration space of glass. The model exhibits stretched exponential relaxation and dynamical heterogeneity typical of glasses. Despite the lack of explicit facilitation rule, the FRW shows facilitation behaviors closely analogous to those of the kinetically constrained models (KCM). The FRW is a coarse-grained version of the distinguishable particle lattice model (DPLM) and this exemplifies that compatible defect and atomistic models can complement each other on the study of glass.

The sensitivity and field of view of the MeerKAT radio telescope provides excellent opportunities for commensal transient searches. We carry out a commensal transient search in supernova and short gamma-ray burst fields using methodologies established in Chastain et al. (2023). We search for transients in MeerKAT L-band images with 30 minute integration times, finding 13 variable sources. We compare these sources to the VLASS and RACS survey data, and examine possible explanation for the variability. We find that 12 of these sources are consistent with variability due to interstellar scintillation. The remaining source could possibly have some intrinsic variability. We also split the MeerKAT L-band into an upper and lower half, and search for transients in images with an 8 second integration time. We find a source with a duration of 8 to 16 seconds that is highly polarized at the lowest frequencies. We conclude that this source may be consistent with a stellar flare. Finally, we calculate accurate upper and lower limits on the transient rate using transient simulations., Comment: submitted to ApJ

Enhancement of the bremsstrahlung X-ray radiation (BSXR) power generated by the high-current relativistic electron beam (REB) of a pulsed direct-action accelerator TEMP-B is being curried out to use in particular for studying the radiation resistance of walls material of radioactive waste containers. For this the magnetic field in which REB is transported in the drift chamber is taken higher at some distance before the converter to provide REB diameter on the converter the same as in the drift chamber. Scheme of power supply and creation of the required magnetic field for the REB current transportation through the whole distance from the diode to the converter is developed. Higher BSXR dose per REB current pulse at the same energy resource is obtained., Comment: 4 pages, 6 figures

Results of research are presented concerning operative modes of a high-voltage (relativistic) pulsed magnetron for the 8 mm wavelength range. Technical solutions are proposed for improving the output system of the device, such as to increase the efficiency of power extraction from the field-particle interaction space. The stability of the magnetron operation has been increased, enhanced quantitative indices of the output power to 381 kW in each of the two linear polarizations. And a stabilized frequency spectrum from 35.7 to 40 GHz of the EHF radiation generated., Comment: 4 pages, 6 figures

A closed proof of existence of solutions to third Painlev\'e' equation (Painlev\'e' transcendents) vanishing at arbitrary given point distinct from zero is presented. The structure of the set of Painlev\'e' transcendents with common parameters vanishing at a given point is described. The approximate explicit representation of a Painlev\'e' transcendent in vicinity of its non-zero root is given., Comment: Outline of changes as compared to the first version: Eq.s (A,3), (A.4) were fixed with adjusting of their discussions; Fig. 3 and Fig. 4 were amended a bit; two bibliographical items were added; a number of obvious misprints were handled; many multifarious petty non-principal modifications of the text were carried out

In order to support the creation of reliable machine learning models for anomaly detection, this project focuses on preprocessing, enhancing, and organizing a medical imaging dataset. There are two classifications in the dataset: normal and abnormal, along with extra noise fluctuations. In order to improve the photographs' quality, undesirable artifacts, including visible medical equipment at the edges, were eliminated using central cropping. Adjusting the brightness and contrast was one of the additional preprocessing processes. Normalization was then performed to normalize the data. To make classification jobs easier, the dataset was methodically handled by combining several image subsets into two primary categories: normal and pathological. To provide a strong training set that adapts well to real-world situations, sophisticated picture preprocessing techniques were used, such as contrast enhancement and real-time augmentation (including rotations, zooms, and brightness modifications). To guarantee efficient model evaluation, the data was subsequently divided into training and testing subsets. In order to create precise and effective machine learning models for medical anomaly detection, high-quality input data is ensured via this thorough approach. Because of the project pipeline's flexible and scalable design, it can be easily integrated with bigger clinical decision-support systems.

Migration of bodies under the gravitational influence of almost formed planets was studied, and probabilities of their collisions with the Earth and other terrestrial planets were calculated. Based on the probabilities, several conclusions on the accumulation of the terrestrial planets have been made. The outer layers of the Earth and Venus could accumulate similar planetesimals from different regions of the feeding zone of the terrestrial planets. The probabilities of collisions of bodies during their dynamical lifetimes with the Earth could be up to 0.001-0.01 for some initial semi-major axes between 3.2 and 3.6 AU, whereas such probabilities did not exceed 10^-5 at initial semi-major axes between 12 and 40 AU. The total mass of water delivered to the Earth from beyond Jupiter's orbit could exceed the mass of the Earth's oceans. The zone of the outer asteroid belt could be one of the sources of the late-heavy bombardment. The bodies that came from the zone of Jupiter and Saturn typically collided with the Earth and the Moon with velocities from 23 to 26 km/s and from 20 to 23 km/s, respectively., Comment: Proc. IAU Symp. No. 374 "Astronomical Hazards for Life on Earth" (Busan, Rep. of Korea, August 9-11, 2022), ed. by G. Tancredi, Cambridge University Press, Manuscript ID IAU-22-0331, 6 p., in press

The heat engine of magnetic black holes in Einstein-AdS gravity coupled to rational nonlinear electrodynamics, as the working substance, is studied. The dynamical negative cosmological constant is considered as a thermodynamic pressure. We investigate the efficiency of black hole heat engines in extended space thermodynamics for rectangle closed path in the $P - V$ plane and the maximally efficient Carnot cycles. The exact efficiency formula which is written in terms of the mass of the black hole is obtained. It was demonstrated that the black hole efficiency decreases when the nonlinear electrodynamics coupling increases and the black hole efficiency increases if the magnetic charge increases. The relation between the efficiency, event horizon radiuses (entropy) and pressure is obtained. We study an efficiency of the holographic heat engine of a cycle in the vicinity of a critical point. Thus, the heat engine of our model can produce work., Comment: 15 pages, 4 figures, published in Can.J.Phys

This study analyzes the motion of bodies ejected from the Earth or the Moon. We studied the ejection of bodies from several points on the Earth's surface, as well as from the most far point of the Moon from the Sun. Different velocities and angles of ejection of bodies were considered. The dynamical lifetimes of bodies reached a few hundred million years. Over the entire considered time interval, the values of the probability of a collision of a body ejected from the Earth with the Earth were approximately 0.3, 0.2, and 0.15-0.2 at an ejection velocity vej equaled to 11.5, 12, and 14 km/s, respectively. At vej<11.3 km/s, most of the ejected bodies fell back onto the Earth. The total number of bodies delivered to the Earth and Venus probably did not differ much. The probabilities of collisions of bodies with Mercury and Mars usually did not exceed 0.1 and 0.02, respectively. At vej>11.5 km/s, the probability of a collision of a body ejected from the Earth with the Moon was about 15-35 times less than that with the Earth, and it was about 0.01. The probability of a collision with the Earth for a body ejected from the Moon moving in its present orbit was about 0.3-0.32, 0.2-0.22, and 0.1-0.14 at vej=2.5 km/s, vej=5 km/s, and at 12

The motion of planetesimals was studied in the Proxima Centauri and TRAPPIST 1 exoplanetary systems. The size of the feeding zone of planet Proxima Centauri c is discussed. It was noted that after hundreds of Myrs, some planetesimals could still move in elliptical resonant orbits inside the feeding zone of this planet that had been mainly cleared from planetesimals. The probability of a collision of a planetesimal initially located in the feeding zone of planet c with inner planet b was obtained to be about 0.0002 and 0.001 at initial eccentricity of orbits of planetesimals equal to 0.02 or 0.15, respectively. A lot of icy material and volatiles could be delivered from the icy zone near the orbit of planet c to inner planets b and d. The inclinations of orbits of 80% of the planetesimals that moved between 500 or 1200 AU from the star did not exceed 10o. It was obtained that several planets in the TRAPPIST-1 system accumulated planetesimals initially located at the same distance. Outer layers of neighbouring TRAPPIST-1 planets can include similar material., Comment: Proc. IAU Symposium 393 "Planetary Science and Exoplanets in the Era of the James Webb Space Telescope" (August 13-15, 2024, Cape Town, South Africa). 5 pages, in press

Recent observations of the Galactic component of the high-energy neutrino flux, together with the detection of the diffuse Galactic gamma-ray emission up to sub-PeV energies, open new possibilities to study the acceleration and propagation of cosmic rays in the Milky Way. At the same time, both large non-astrophysical backgrounds at TeV energies and scarcity of neutrino events in the sub-PeV band currently limit these analyses. Here we use the sample of cascade events with estimated neutrino energies above 200 TeV, detected by the partially deployed Baikal Gigaton Volume Detector (GVD) in six years of operation, to test the continuation of the Galactic neutrino spectrum to sub-PeV energies. We find that the distribution of the arrival directions of Baikal-GVD cascades above 200 TeV in the sky suggests an excess of neutrinos from low Galactic latitudes with the chance probability of 1.4e-2. We find the excess above 200 TeV also in the most recent IceCube public data sets, both of cascades and tracks. The chance probability of the excess in the combined IceCube and Baikal-GVD analysis is 3.4e-4. The flux of Galactic neutrinos above 200~TeV challenges often-used templates for neutrino search based on cosmic-ray simulations., Comment: 8 pages, 5 figures, revtex 4.2. V2: minor corrections and clarifications, results unchanged. Version accepted by Astrophys. J

A review of the results on the migration of celestial bodies in the Solar System and in some exoplanetary systems is presented. Some problems of planet accumulation and migration of planetesimals, small bodies and dust in the forming and present Solar System are considered. It has been noted that the outer layers of the Earth and Venus could have accumulated similar planetesimals from different areas of the feeding zone of the terrestrial planets.The formation of the embryos of the Earth and the Moon from a common rarefied condensation with subsequent growth of the main mass of the embryo of the Moon near the Earth is also discussed. The influence of changes in the semimajor axis of Jupiter's orbit on the formation of the asteroid belt is discussed, as well as the influence of planetesimals from the feeding zone of the giant planets on the formation of bodies beyond the orbit of Neptune. The migration of bodies to the terrestrial planets from different distances from the Sun is considered. It is noted that bodies from the feeding zone of the giant planets and from the outer asteroid belt could deliver to the Earth a quantity of water comparable to the mass of water in the Earth's oceans. The migration of bodies ejected from the Earth is considered. The probabilities of collisions of dust particles with the Earth are usually an order of magnitude greater than the probabilities of collisions of their parent bodies with the Earth. The migration of planetesimals is considered in exoplanetary systems Proxima Centauri and TRAPPIST-1. The amount of water delivered to the inner planet Proxima Centauri b, may have been more than the amount delivered to the Earth. The outer layers of neighboring planets in the TRAPPIST-1 system may contain similar material if there were many planetesimals near their orbits during the late stages of planetary accumulation., Comment: 14 pages

Explainable AI (XAI) holds the promise of advancing the implementation and adoption of AI-based tools in practice, especially in high-stakes environments like healthcare. However, most of the current research lacks input from end users, and therefore their practical value is limited. To address this, we conducted semi-structured interviews with clinicians to discuss their thoughts, hopes, and concerns. Clinicians from our sample generally think positively about developing AI-based tools for clinical practice, but they have concerns about how these will fit into their workflow and how it will impact clinician-patient relations. We further identify training of clinicians on AI as a crucial factor for the success of AI in healthcare and highlight aspects clinicians are looking for in (X)AI-based tools. In contrast to other studies, we take on a holistic and exploratory perspective to identify general requirements for (X)AI products for healthcare before moving on to testing specific tools.

The motion of bodies ejected from the Earth was studied, and the probabilities of collisions of such bodies with the present terrestrial planets were calculated. The dependences of these probabilities on velocities, angles and points of ejection of bodies were studied. These dependences can be used in the models with different distributions of ejected material. On average, about a half and less than 10\% of initial ejected bodies remained moving in elliptical orbits in the Solar System after 10 and 100 Myr, respectively. A few ejected bodies collided with planets after 250 Myr. As dynamical lifetimes of bodies ejected from the Earth can reach hundreds of million years, a few percent of bodies ejected at the Chicxulub and Popigai events about 36-65 Myr ago can still move in the zone of the terrestrial planets and have small chances to collide with planets, including the Earth. The fraction of ejected bodies that collided with the Earth was greater for smaller ejection velocity. The fractions of bodies delivered to the Earth and Venus probably did not differ much for these planets and were about 0.2-0.3 each. Such obtained results testify in favour of that the upper layers of the Earth and Venus can contain similar material. The fractions of bodies ejected from the Earth that collided with Mercury and Mars did not exceed 0.08 and 0.025, respectively. The fractions of bodies collided with Jupiter were of the order of 0.001. In most calculations the fraction of bodies collided with the Sun was between 0.2 and 0.5. Depending on parameters of ejection, the fraction of bodies ejected into hyperbolic orbits could vary from 0 to 1. Small fractions of material ejected from the Earth can be found on other terrestrial planets and Jupiter, as the ejected bodies could collide with these planets. Bodies ejected from the Earth could deliver organic material to other celestial objects, e.g. to Mars., Comment: 24 pages, 4 figures

We discuss results from our global QCD analyses including nuclear data off deuterium from various measurements, as well as off $\htri$ and $\hetri$ targets from the \mara{} experiment. We simultaneously determine the parton distribution functions of the proton, the higher-twist terms, and the nucleon off-shell correction functions responsible for the modifications of the partonic structure in bound protons and neutrons. In particular, we study the neutron-proton asymmetry of the off-shell correction and its interplay with the treatment of the higher-twist terms. We observe that the data on the $\hetri/\htri, \hetri/\hdeu$, and $\htri/\hdeu$ cross section ratio are in good agreement with the predictions based on a single isoscalar off-shell function. We provide the corresponding predictions on the ratio $F_2^n/F_2^p$, on the $d$ and $u$ quark distributions in the proton and in the $\htri$ and $\hetri$ nuclei, as well as for future measurements of the EMC effect with parity-violating Deep Inelastic Scattering (DIS)., Comment: 8 pages, 4 figures, proceedings of DIS2024

The plasma opacity in stars depends mainly on the local state of matter (the density, temperature, and chemical composition at the point of interest), but in supernova ejecta it also depends on the expansion velocity gradient, because the Doppler effect shifts the spectral lines differently in different ejecta layers. This effect is known in the literature as the expansion opacity. The existing approaches to the inclusion of this effect, in some cases, predict different results in identical conditions. In this paper we compare the approaches of Blinnikov (1996) and Friend and Castor (1983) - Eastman and Pinto (1993) to calculating the opacity in supernova ejecta and give examples of the influence of different approximations on the model light curves of supernovae.

The nonequilibrium turbulent response of driven three-dimensional dipolar gases is monitored by dynamically crossing the supersolid-to-superfluid phase transition and vice versa utilizing a periodically modulated scattering length. Following the generation of vortical defects in the bulk, a direct cascade front emerges transporting energy from larger to smaller length scales and leading to a nonequilibrium quasi-steady state at long evolution times. This quasi-steady state is evidenced by the self-similar character of the momentum distributions featuring an algebraic reduction at large momenta with scaling exponents supporting the existence of wave turbulence. We observe that supersolidity sustaining higher-lying momenta, associated with the roton minimum, promotes the emergence of turbulence. Our results provide a stepping stone for unravelling and exploiting turbulent and self-similar behavior in anisotropically interacting quantum gases amenable in current experiments., Comment: 6 pages, 4 figures, 4 pages Supplemental material

We consider a spin valve composed of a superconducting film (S) between two ferromagnetic insulators (FI) on two sides. In the dirty limit the superconductor is described by Usadel equations. Appropriate boundary conditions were chosen for two S-FI interfaces, which are described via the interface parameter spin mixing angle. By numerically solving the Usadel equations, the density of states (DOS) at different spin mixing angles were obtained. It was shown previously that critical temperature of such FI-S-FI structure depends on the mutual alignment of the FI layers magnetization. We follow the evolution of DOS at change of misalignment of ferromagnets magnetization and probe the zero bias peak creation. The DOS characteristic features may give a fruitful information about triplet superconducting components creation and interplay inside the S layer.

The electron spin polarization on half-metallic double-perovskites is usually conditioned to the ordered rock-salt arrangement of the transition-metal ions along the lattice. In this work, we investigate a polycrystalline sample of the Ca1.5La0.5MnRuO6 compound by employing x-ray powder diffraction, high resolution transmission electron microscopy, x-ray absorption and magnetic circular dichroism at the Mn-L2,3 and Ru-M2,3 edges, magnetometry, electrical transport and first principles calculations in order to show that this is a fully disordered material exhibiting near room temperature ferrimagnetism and half-metallic conductivity, with significant intergrain tunneling magnetoresistance. These unprecedented results are compared to those of archetypical ordered double-perovskites, and discussed in terms of the Mn and Ru valences and their orbital hybridization., Comment: 13 pages, 6 figures

The monograph summarizes the studies of the temperature limits for the existence of a supercooled liquid phase of the components of nanodisperse structures. Original in situ methods for studying supercooling during crystallization in nanodispersed systems are proposed. The results of long-term studies of the features of crystallization of particles on different substrates, or as part of layered film systems are presented. The influence of the interaction at the melt-substrate (matrix) interface, as well as the conditions of preparation of the samples on the values of the limiting supercooling are determined.

Generating simulations to train intelligent agents in game-playing and robotics from natural language input, from user input or task documentation, remains an open-ended challenge. Existing approaches focus on parts of this challenge, such as generating reward functions or task hyperparameters. Unlike previous work, we introduce FACTORSIM that generates full simulations in code from language input that can be used to train agents. Exploiting the structural modularity specific to coded simulations, we propose to use a factored partially observable Markov decision process representation that allows us to reduce context dependence during each step of the generation. For evaluation, we introduce a generative simulation benchmark that assesses the generated simulation code's accuracy and effectiveness in facilitating zero-shot transfers in reinforcement learning settings. We show that FACTORSIM outperforms existing methods in generating simulations regarding prompt alignment (e.g., accuracy), zero-shot transfer abilities, and human evaluation. We also demonstrate its effectiveness in generating robotic tasks., Comment: neurips 2024, project website: https://cs.stanford.edu/~sunfanyun/factorsim/

We explore effective approaches for describing the dynamics of induced interactions amongst two non-interacting distinguishable impurities - Bose polarons - when their couplings to the host species are switched on. First, we evaluate the time-dependent characteristics of each polaron through reduced single-particle models. Their validity is ultimately judged by comparing to observables obtained within a many-body variational approach. We argue that utilizing a time-dependent optimization process with the effective mass and frequency being fitting parameters leads to an accurate matching on the level of one-body observables with the prediction of the many-body method. Next, we construct two-body effective models, which besides the effective parameters of the single polaron, include a contact interaction potential modelling the induced interactions. It is shown that the instantaneous coupling strength obtained with a time-dependent optimization process allows for an accurate description of the impurities two-body correlation dynamics when compared to the many-body calculations. In this sense, it is possible to describe the dynamical crossover from correlated to anti-correlated impurity patterns related to the transition from attractive to repulsive induced interactions. Our results should facilitate the description of strongly particle-imbalanced mixtures via reduced models and hence their experimental understanding., Comment: 17 pages, 9 figures

We report the first measurement of the azimuthal anisotropy of J$/\psi$ at forward rapidity ($1.2<|\eta|<2.2$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The second Fourier coefficient ($v_2$) of the azimuthal distribution of $J/\psi$ is determined as a function of the transverse momentum ($p_T$) using the event-plane method. The measurements were performed for several selections of collision centrality: 0\%--50\%, 10\%--60\%, and 10\%-40\%. We find that in all cases the values of $v_2(p_T)$, which quantify the elliptic flow of J$/\psi$, are consistent with zero. The results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the J$/\psi$ within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{_{NN}}}=200$ GeV., Comment: 369 authors from 72 institutions, 12 pages, 7 figures, 5 tables. v1 is version submitted to Physical Review C. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

We present the first forward-rapidity measurements of elliptic anisotropy of open-heavy-flavor muons at the BNL Relativistic Heavy Ion Collider. The measurements are based on data samples of Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The measurements are performed in the pseudorapidity range $1.2<|\eta|<2$ and cover transverse momenta $1

We present the radio afterglow of short gamma-ray burst (GRB) 230217A, which was detected less than 1 day after the gamma-ray prompt emission with the Australia Telescope Compact Array (ATCA) and the Karl G. Jansky Very Large Array (VLA). The ATCA rapid-response system automatically triggered an observation of GRB 230217A following its detection by the Neil Gehrels Swift Observatory and began observing the event just 32 minutes post-burst at 5.5 and 9 GHz for 7 hours. Dividing the 7-hour observation into three time-binned images allowed us to obtain radio detections with logarithmic central times of 1, 2.8 and 5.2 hours post-burst, the first of which represents the earliest radio detection of any GRB to date. The decline of the light curve is consistent with reverse shock emission if the observing bands are below the spectral peak and not affected by synchrotron self-absorption. This makes GRB 230217A the fifth short GRB with radio detections attributed to a reverse shock at early times ($<1$ day post-burst). Following brightness temperature arguments, we have used our early radio detections to place the highest minimum Lorentz factor (${\Gamma}_{min} > 50$ at $\sim1$ hour) constraints on a GRB in the radio band. Our results demonstrate the importance of rapid radio follow-up observations with long integrations and good sensitivity for detecting the fast-evolving radio emission from short GRBs and probing their reverse shocks., Comment: 11 pages, 3 figures, submitted to ApJL

Rare-earth oxides (REOs) are an important class of materials owing to their unique properties, including high ionic conductivities, large dielectric constants, and elevated melting temperatures, making them relevant to several technological applications such as catalysis, ionic conduction, and sensing. The ability to predict these properties at moderate computational cost is essential to guiding materials discovery and optimizing materials performance. Although density-functional theory (DFT) is the favored approach for predicting electronic and atomic structures, its accuracy is limited in describing strong electron correlation and localization inherent to REOs. The newly developed strongly constrained and appropriately normed (SCAN) meta-generalized-gradient approximations (meta-GGAs) promise improved accuracy in modeling these strongly correlated systems. We assess the performance of these meta-GGAs on binary REOs by comparing the numerical accuracy of thirteen exchange-correlation approximations in predicting structural, magnetic, and electronic properties. Hubbard U corrections for self-interaction errors and spin-orbit coupling are systematically considered. Our comprehensive assessment offers insights into the physical properties and functional performance of REOs predicted by first-principles and provides valuable guidance for selecting optimal DFT functionals for exploring these materials.

We explore the ground states and quench dynamics of one-dimensional quantum droplets with spin-orbit coupling (SOC) and an imbalance in intracomponent interactions. A plethora of miscible ground state stripe and standard (i.e., non-modulated) droplets is found depending on the SOC wavenumber and building upon Gaussian to flat-top background for increasing (decreasing) atom number (interactions). Deformations among the states were accompanied by spin population transfer caused by the Rabi coupling and could be controlled by adjusting the interactions or the SOC parameters. When considering a trap, we identified a transition from a bound to a trapped gas many-body state, characterized by a sign change of the chemical potential, which occurred at lower (larger) atom numbers for tighter traps (stronger interactions). The droplet's breathing motion was accompanied by minor population transfer, and its frequency increases for a larger intracomponent interaction ratio or reaching a maximum at SOC wavenumbers, where the transition from non-modulated flat-top to stripe droplets occurred. We witness droplet fragmentation for abrupt changes in the Rabi coupling while large amplitude quenches of the SOC wavenumber trigger spin-demixing, resulting in constant amplitude but opposite direction motion of untrapped droplets or in-trap out-of-phase oscillating droplets. Our findings have implications for controlled spin-demixing processes of droplets and the excitation of relevant magnetic bound states., Comment: 13 pages, 11 figures

We present deep, wideband multifrequency radio observations (144 MHz$-$8 GHz) of the remarkable galaxy group NGC 741, which yield crucial insights into the interaction between the infalling head-tail radio galaxy (NGC 742) and the main group. Our new data provide an unprecedentedly detailed view of the NGC 741-742 system, including the shock cone, disrupted jets from NGC 742, the long ($\sim$ 255 kpc) braided southern radio tail, and eastern lobe-like structure, and reveal, for the first time, complex radio filaments throughout the tail and lobe, and a likely vortex ring behind the shock cone. The cone traces the bow shock caused by the supersonic ($\mathcal{M}\sim2$) interaction between the head-tail radio galaxy NGC 742 and the intragroup medium (IGrM) while the ring may have been formed by interaction between the NGC 742 shock and a previously existing lobe associated with NGC 741. This interaction plausibly compressed and re-accelerated the radio plasma. We estimate that shock-heating by NGC 742 has likely injected $\sim$2-5$\times$10$^{57}$ erg of thermal energy into the central 10 kpc cooling region of the IGrM, potentially affecting the cooling and feedback cycle of NGC 741. A comparison with Chandra X-ray images shows that some of the previously detected thermal filaments align with radio edges, suggesting compression of the IGrM as the relativistic plasma of the NGC 742 tail interacts with the surrounding medium. Our results highlight that multi-frequency observations are key to disentangling the complex, intertwined origins of the variety of radio features seen in the galaxy group NGC 741, and the need for simulations to reproduce all the detected features., Comment: 26 pages, 15 figures, submitted to ApJ

DarkSide-20k (DS-20k) is a dark matter detection experiment under construction at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. It utilises ~100 t of low radioactivity argon from an underground source (UAr) in its inner detector, with half serving as target in a dual-phase time projection chamber (TPC). The UAr cryogenics system must maintain stable thermodynamic conditions throughout the experiment's lifetime of over 10 years. Continuous removal of impurities and radon from the UAr is essential for maximising signal yield and mitigating background. We are developing an efficient and powerful cryogenics system with a gas purification loop with a target circulation rate of 1000 slpm. Central to its design is a condenser operated with liquid nitrogen which is paired with a gas heat exchanger cascade, delivering a combined cooling power of more than 8 kW. Here we present the design choices in view of the DS-20k requirements, in particular the condenser's working principle and the cooling control, and we show test results obtained with a dedicated benchmarking platform at CERN and LNGS. We find that the thermal efficiency of the recirculation loop, defined in terms of nitrogen consumption per argon flow rate, is 95 % and the pressure in the test cryostat can be maintained within $\pm$(0.1-0.2) mbar. We further detail a 5-day cool-down procedure of the test cryostat, maintaining a cooling rate typically within -2 K/h, as required for the DS-20k inner detector. Additionally, we assess the circuit's flow resistance, and the heat transfer capabilities of two heat exchanger geometries for argon phase change, used to provide gas for recirculation. We conclude by discussing how our findings influence the finalisation of the system design, including necessary modifications to meet requirements and ongoing testing activities., Comment: 44 pages, 25 figures, 1 table. Updated to match the published journal version

In this paper we propose a new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.