Angular Function Research Articles

Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and applications.

The increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH3) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.

The VST ATLAS Quasar Survey III: Halo mass function via quasar clustering and quasar-CMB lensing cross-clustering

Abstract We exploit the VST ATLAS quasar/QSO catalogue to perform three measurements of the quasar halo mass profile. First, we make a new estimate of the angular auto-correlation function of ≈230, 000 ATLAS quasars with zphoto ≲ 2.5 and 17 < g < 22. By comparing with the ΛCDM mass clustering correlation function, we measure the quasar bias to be bQ ≈ 2.1, implying a quasar halo mass of Mhalo ≈ 8.5 × 1011h−1M⊙. Second, we cross-correlate these z ≈ 1.7 ATLAS quasars with the Planck Cosmic Microwave Background (CMB) lensing maps, detecting a somewhat stronger signal at 4′ < θ < 60′ than previous authors. Scaling these authors’ model fit to our data we estimate a quasar host halo mass of Mhalo ≈ 8.3 × 1011h−1M⊙. Third, we fit Halo Occupation Distribution (HOD) model parameters to our quasar auto-correlation function and from the derived halo mass function we estimate a quasar halo mass of Mhalo ≈ 2.5 × 1012h−1M⊙. We then compare our HOD model prediction to our quasar-CMB lensing result, confirming their consistency. We find that most (≈2/3) QSOs have halo masses within a factor of ≈3 of this average mass. An analysis based on the probability of X-ray detections of AGN in galaxies and the galaxy stellar mass function gives a similarly small mass range. Finally, we compare the quasar halo mass and luminosity functions and suggest that gravitational growth may produce the constant space density with redshift seen in the quasar luminosity function.

Prospects of Predicting the Polar Motion Based on the Results of the Second Earth Orientation Parameters Prediction Comparison Campaign

AbstractGrowing interest in Earth Orientation Parameters (EOP) resulted in various approaches to the EOP prediction algorithms, as well as in the exploitation of distinct input data, including the observed EOP values from various operational data centers and modeled effective angular momentum functions. Considering these developments and recently emerged new methodologies, the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) was pursued in 2021–2022. The campaign was led by Centrum Badań Kosmicznych Polskiej Akademii Nauk in cooperation with Deutsches GeoForschungsZentrum and under the auspices of the International Earth Rotation and Reference Systems Service. This paper provides the analysis and evaluation of the polar motion predictions submitted during the 2nd EOP PCC with the prediction horizons between 10 and 30 days. Our analysis shows that predictions are highly reliable with only a few occasional discrepancies identified in the submitted files. We demonstrate the accuracy of EOP predictions by (a) calculating the mean absolute error relative to polar motion observations from September 2021 through December 2022 and (b) assessing the stability of the predictions in time. The analysis shows unequal results for the x and y components of polar motion (PMx and PMy, respectively). Predictions of PMy are usually more accurate and have a smaller spread across all submitted files when compared to PMx. We present an analysis of similarity between the participants to indicate what methods and input data give comparable output. We also prepared the ranking of prediction methods for polar motion summarizing the achievements of the campaign.

Exact solution of the Klein–Gordon oscillator in wormhole spacetime with Heun polynomial

In this paper, we investigate the relativistic harmonic oscillator in the Ellis–Bronnikov-type wormhole spacetime with a global monopole and cosmic string. We obtain the angular and radial wave functions exactly as well as the eigenenergies. Additionally, the radial wave function is expressed in terms of Heun polynomial, and as a consequence, the oscillation frequency is quantized. Finally, we graphically analyze the influence of the wormhole, as well as the influence of the global monopole and cosmic string on the radial probability density and the eigenenergies.

Analysis of the three possible event horizons of anti-de Sitter space–time in the Klein–Gordon equation

In this paper, we calculate exactly the solution of Klein–Gordon equation in anti-de Sitter space–time. Due to spherical symmetry, the angular wave functions are given by spherical harmonics. The radial wave functions are given by local Heun functions. We analyze the behavior of the radial wave function in regions near three possible event horizon positions [Formula: see text] and investigate the decay rate, Hawking radiation and Hawking temperature for these three cases. Comparing the results, we verify that if the decay rate and Hawking radiation are greater, then the closer the event horizon is to the singularity of the black hole. Finally, we analyze the special case of a small black hole limit.

Homogenization of quasi-periodic conformal architectured materials and applications to chiral lattices

In this study, we propose to extend asymptotic periodic homogenization for non-periodic continuous microstructured media, assuming that the non-periodic geometry (called quasi-periodic) can be designed by a conformal planar transformation of a periodic parent domain architectured media with periodically disposed unit cells. Conformal transformations are shown to play a privileged role in the design of circular macroscopic heterogeneous domains tessellated with non-periodic unit cells, obtained from a periodic parent domain architectured with these unit cells. The conditions for conformal invariance are established, leading to the general form of conformal transformation in their dependencies upon the periodic coordinates. It is shown that any conformal map can be decomposed into the product of an isotropic dilatation function of the first periodic spatial position of decreasing exponential type and a rotation characterized by an angular function linear in the second periodic position. A general theory of quasi-periodic homogenization in the framework of conformal transformations is established for the first time, leading to an expression of the tensor of quasi-periodic moduli which is fully evaluated from the solution of the elasticity boundary value problem posed over the periodic unit cell. The influence of microcurvature distortion of individual unit cells on their effective properties is evaluated. Closed-form solutions are confronted to numerical examples issued from the implementation of circular periodicity in a finite element solver, showing overall a good agreement with the identified homogenized moduli.

Accelerating Relativistic Exact-Two-Component Density Functional Theory Calculations with Graphical Processing Units.

Numerical integration of the exchange-correlation potential is an inherently parallel problem that can be significantly accelerated by graphical processing units (GPUs). In this Letter, we present the first implementation of GPU-accelerated exchange-correlation potential in the GauXC library for relativistic, 2-component density functional theory. By benchmarking against copper, silver, and gold coinage metal clusters, we demonstrate the speed and efficiency of our implementation, achieving significant speedup compared to CPU-based calculations. One GPU card provides computational power equivalent to roughly 400 CPU cores in the context of this work. The speedup further increases for larger systems, highlighting the potential of our approach for future, more computationally demanding simulations. Our implementation supports arbitrary angular momentum basis functions, enabling the simulation of systems with heavy elements and providing substantial speedup to relativistic electronic structure calculations. This advancement paves the way for more efficient and extensive computational studies in the field of density functional theory.

Investigation of time-dependent mechanical loading on the start-stop process of functionally graded rotating disks under thermal conditions

Rotating disks are used in industries, such as aerospace, automotive, and power plants. These disks are under time-dependent mechanical loading when the machine starts or stops working conditions. Thermal stresses caused by temperature changes with this time-dependent mechanical load create dangerous conditions. Therefore, the estimation of the elastic limit angular velocity and acceleration as a criterion for the initiation of plastic deformations has special importance in the start-stop process. An analytical Homotopy perturbation method is used to solve the heat transfer equation and the governing Navier equations in both radial and tangential directions of functionally graded rotating disks with non-uniform thickness. The Tamura-Tomoto-Ozawa model is implemented to calculate the yield stress at a different radius of the disk. The obtained results will be verified with the higher-order finite difference method. The effect of thickness parameter, type of thermal and boundary conditions on the angular velocity and acceleration, and also the starting radius of the plastic deformations are investigated by numerical examples. It is shown that by defining the appropriate temperature gradient on the outer surface of the disk and the parameters in the time-dependent angular velocity function, the level of stresses can be controlled and optimized in all working processes.

Short-range expansion for the quantum many-body problem

In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy s-wave correlated pair and spectator particles, while terms that include energy derivatives and larger orbital angular momentum two-body functions appear at subleading orders. The validity of the expansion is tested for the two-body case, as well as the many-body case, where infinite neutron matter is considered. An accurate and consistent description of both coordinate-space two-body densities and the one-body momentum distribution is obtained. These results show the possibility to utilize such an expansion for describing different observables in strongly-interacting many-body systems, including nuclear, atomic and condensed-matter systems. This work also opens the path for a systematic description of large momentum transfer reactions in nuclear systems sensitive to short-range correlations, provides a link between such experiments and low-energy nuclear physics, and motivates measurement of new observables in these experiments.

Magnetic Fields in Ministarburst Complex Sgr B2

We report the first arcsecond-resolution observations of the magnetic field in the ministarburst complex Sgr B2. SMA polarization observations revealed magnetic field morphology in three dense cores of Sgr B2 N(orth), M(ain), and S(outh). The total plane-of-sky magnetic field strengths in these cores are estimated to be 4.3–10.0 mG, 6.2–14.7 mG, and 1.9–4.5 mG derived from the angular dispersion function method after applying the correction factors of 0.21 and 0.5. Combining with analyses of the parsec-scale polarization data from Stratospheric Observatory for Infrared Astronomy, we found that a magnetically supercritical condition is present from the cloud scale (∼10 pc) to core scale (∼0.2 pc) in Sgr B2, which is consistent with the burst of star formation activities in the region likely resulting from a multiscale gravitational collapse from the cloud to dense cores.

Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function

Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, such procedures are only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called ‘angular dependence function’; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK.

Orientation time correlation functions up to the fourth cumulant for liquid water

The orientation time correlation functions (OTCFs) of molecular liquids are related to many experimental observations but subtle in theoretical calculations. Usually, the OTCFs at different timescales are described by distinct approaches. The OTCFs at short times were expanded into a series in an order of molecular angular velocity components, and the second cumulant (SC) of the series gave a single-frequency integral over one-mode propagation function weighted by a rotational density of states (DOS) of the liquid, whereas the OTCFs at long times displayed an exponential decay according to the Debye theory. In this paper, we derived the series of the OTCFs up to the fourth cumulant (FC), which gave a sum of twofold frequency integrals over two-mode propagation functions weighted by a product of two rotational DOSs associated with one or two molecular axes. With no need of any fitting parameter, the OTCFs calculated up to the SC and up to the FC were compared with simulation results for liquid water. With the power spectra of angular velocity autocorrelation function, which have a finite value at zero frequency, as the inputs, the OTCFs in both SC and FC schemes resulted in an exponential decay at long times, while the decay times were smaller than the simulation values. The positive results were the calculations with stable rotational instantaneous-normal-mode spectra, which have a linear behavior extrapolated to zero at low frequencies. As the stable rotational INM spectra were used as the inputs, the OTCFs in the SC scheme produced a slow power-law decay, but the OTCFs in the FC scheme captured the simulation behaviors from short to long timescale, including an exponential decay, with the decay times of the 2nd-rank OTCFs close to the simulation values.

Cartesian atomic cluster expansion for machine learning interatomic potentials

Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modeling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message-passing frameworks. Such frameworks typically use spherical harmonics as angular basis functions, followed by Clebsch-Gordan contraction to maintain rotational symmetry. We propose a mathematically equivalent and simple alternative that performs all operations in the Cartesian coordinates. This approach provides a complete set of polynormially independent features of atomic environments while maintaining interaction body orders. Additionally, we integrate low-dimensional embeddings of various chemical elements, trainable radial channel coupling, and inter-atomic message passing. The resulting potential, named Cartesian Atomic Cluster Expansion (CACE), exhibits good accuracy, stability, and generalizability. We validate its performance in diverse systems, including bulk water, small molecules, and 25-element high-entropy alloys.

Toward the measurement of neutrino masses: Performance of cosmic magnification with submillimeter galaxies

Context. The phenomenon of magnification bias can induce a non-negligible angular correlation between two samples of galaxies with nonoverlapping redshift distributions. This signal is particularly clear when background submillimeter galaxies are used, and has been shown to constitute an independent cosmological probe. Aims. This work extends prior studies on the submillimeter galaxy magnification bias to the massive neutrino scenario, with the aim being to assess its sensitivity as a cosmological observable to the sum of neutrino masses. Methods. The measurements of the angular cross-correlation function between moderate redshift GAMA galaxies and high-redshift submillimeter H-ATLAS galaxies are fit to the weak lensing prediction down to the arcmin scale. The signal is interpreted under the halo model, which is modified to accommodate massive neutrinos. We discuss the impact of the choice of cosmological parametrization on the sensitivity to neutrino masses. Results. The currently available data on the magnification bias affecting submillimeter galaxies are sensitive to neutrino masses when a cosmological parametrization in terms of the primordial amplitude of the power spectrum (As) is chosen over the local root mean square of smoothed linear density perturbations (σ8). A clear upper limit on the sum of neutrino masses can be derived if the value of As is either fixed or assigned a narrow Gaussian prior, a behavior that is robust against changes to the chosen value.

Interstellar Polarization Survey. IV. Characterizing the Magnetic Field Strength and Turbulent Dispersion Using Optical Starlight Polarization in the Diffuse Interstellar Medium

Angular dispersion functions are typically used to estimate the fluctuations in polarization angle around the mean magnetic field orientation in dense regions, such as molecular clouds. The technique provides accurate turbulent-to-regular magnetic field ratios, 〈Bt2〉1/2/Bpos , which are often underestimated by the classic Davis–Chandrasekhar–Fermi method. We assess the technique's suitability to characterize the turbulent and regular plane-of-sky magnetic field in low-density structures of the nearby interstellar medium (ISM), particularly when the turbulence outer scale, δ, is smaller than the smallest scale observed, ℓ min. We use optical polarization maps of three intermediate-latitude fields (∣b∣ ≳ 7.°5) with dimensions of 0.°3 × 0.°3, sourced from the Interstellar Polarization Survey–General ISM catalog. We decomposed the H i emission detected by the Galactic All-Sky Survey within our fields to estimate the multiphase ISM properties associated with the structure coupled to the magnetic field. We produced maps of the plane-of-sky magnetic field strength (B pos), mass density (ρ), and turbulent velocity dispersion (σ v,turb). In the regions with well-defined structures at d < 400 pc, the average B – ranges from ∼3 μG to ∼9 μ G, depending on the method and physical properties. In the region where structures extend up to 1000 pc, B pos varies from ∼1 to ∼3 μ G. The results agree with previous estimations in the local, diffuse ISM. Finally, optical starlight polarization and thermal dust polarization at 353 GHz consistently reveal a highly regular plane-of-sky magnetic field orientation unfazed by diffuse dust structures observed at 12 μm.

Thermal stresses associated with a thermosensitive multilayered disc analysed due to point heating

In this paper, analytical solutions are presented for temperature and thermal behavior of a thermosensitive multilayered annular disc due to point heat source. Convective heating is applied to both the innermost and outermost layers. The nonlinearity of the thermal diffusivity equation is dealt using Kirchhoff’s transformation technique. A finite integral transform in the form of Bessel’s function is used to deal with the radial variable r. Fourier transform and angular eigen functions are also used to solve the thermal diffusivity equation. Deflection, resultant forces, shearing forces, resultant moments and thermal stresses are obtained. A mathematical representation is formulated for a 3-layered disc, with the inner, middle and outer layers composed of copper, zinc and aluminum respectively. The results are depicted graphically.

Methodological refinement of the submillimeter galaxy magnification bias

Aims. The main goal of this work is to test the results of a methodological improvement in the measurement of the magnification bias signal on a sample of submillimeter galaxies. In particular, we investigate the constraining power of cosmological parameters within the ΛCDM model. We also discuss important points that can affect the results. Methods. We measured the angular cross-correlation function between a sample of foreground GAMA II galaxies in a single wide spectroscopic redshift bin of 0.2 &lt; z &lt; 0.8 and a sample of background submillimeter galaxies from Herschel-ATLAS. We focused on the photometric redshift range of 1.2 &lt; z &lt; 4.0, with an improved methodological framework. Interpreting the weak lensing signal within the halo model formalism and performing a Markov chain Monte Carlo (MCMC) algorithm, we obtained the posterior distribution of both the halo occupation distribution and cosmological parameters within a flat ΛCDM model. Our analysis was also performed with additional galaxy clustering information via a foreground angular auto-correlation function. Results. We observed an overall remarkable improvement in terms of uncertainties in both the halo occupation distribution and cosmological parameters with respect to previous results. A priori knowledge about β, the logarithmic slope of the background integral number counts, is found to be paramount to derive constraints on σ8 when using the cross-correlation data alone. Assuming a physically motivated prior distribution for β, we obtain mean values of Ωm = 0.23−0.06+0.03 and σ8 = 0.79−0.10+0.10 and an unconstrained distribution for the Hubble constant. These results are likely to suffer from sampling variance, since one of the fields, G15, appears to have an anomalous behavior with a systematically higher cross-correlation. We find that removing it from the sample yields mean values of Ωm = 0.27−0.04+0.02 and σ8 = 0.72−0.04+0.04 and, for the first time, a (loose) restriction of the Hubble constant is obtained via this observable: h = 0.79−0.14+0.13. The addition of the angular auto-correlation of the foreground sample in a joint analysis tightens the constraints, but also reveals a discrepancy between both observables that might be an aggravated consequence of sampling variance or due to the presence of unmodeled aspects on small and intermediate scales.

Large-scale Overdensity of Lyman Break Galaxies around the z = 6.3 Ultraluminous Quasar J0100 + 2802

We study the environment of the z = 6.33 ultraluminous quasar SDSS J010013.02+280225.8 (J0100) to understand its association with large-scale structure. Theoretical models propose high-redshift quasars as markers of galaxy overdensities residing in the most massive dark matter halos (DMHs) in the early Universe. J0100 is an ultraluminous quasar with the most massive black hole known at z ≳ 6, suggesting a high likelihood of residing in a massive DMH. We present wide-field (∼522 arcmin2) imaging in the r, i, and z bands from the Large Binocular Cameras on the Large Binocular Telescope, with Y- and J-band imaging from the Wide-field Infrared Camera on the Canada–France–Hawaii Telescope, centered on J0100. Applying color selections, we identify 23 objects as i-dropout Lyman break galaxy (LBG) candidates in the J0100 field. We use the deep photometric catalog in the 1.27 deg2 COSMOS field to calculate the density of LBGs in a blank field, and to estimate the selection completeness and purity. The observed surface density of LBG candidates in the J0100 field corresponds to a galaxy overdensity of δ = 4 (at 8.4σ). This large-scale overdensity suggests that the ∼22 arcmin2 overdensity found by Kashino et al. using JWST data extends out to much larger scales. We calculate the angular autocorrelation function of the candidates and find a positive correlation on ≲10′ scales as well as evidence of asymmetries in their spatial distribution, further suggesting the direct detection of large-scale structure in the field of the ultraluminous quasar J0100.

Pedestrian Pose Recognition Based on Frequency-Modulated Continuous-Wave Radar with Meta-Learning.

With the continuous advancement of autonomous driving and monitoring technologies, there is increasing attention on non-intrusive target monitoring and recognition. This paper proposes an ArcFace SE-attention model-agnostic meta-learning approach (AS-MAML) by integrating attention mechanisms into residual networks for pedestrian gait recognition using frequency-modulated continuous-wave (FMCW) millimeter-wave radar through meta-learning. We enhance the feature extraction capability of the base network using channel attention mechanisms and integrate the additive angular margin loss function (ArcFace loss) into the inner loop of MAML to constrain inner loop optimization and improve radar discrimination. Then, this network is used to classify small-sample micro-Doppler images obtained from millimeter-wave radar as the data source for pose recognition. Experimental tests were conducted on pose estimation and image classification tasks. The results demonstrate significant detection and recognition performance, with an accuracy of 94.5%, accompanied by a 95% confidence interval. Additionally, on the open-source dataset DIAT-μRadHAR, which is specially processed to increase classification difficulty, the network achieves a classification accuracy of 85.9%.

New physics couplings from angular coefficient functions of B¯→D*(Dπ)ℓν¯ℓ

The Belle Collaboration has recently measured the complete set of angular coefficient functions for the exclusive decays B¯→D*(Dπ)ℓν¯ℓ, with ℓ=e, μ, in four bins of the parameter w=mB2+mD*2−q22mBmD*, with q the lepton pair momentum [M. T. Prim (Belle Collaboration), ]. Under the assumption that physics beyond the Standard Model does not contribute to such modes, the measurements are useful to determine the hadronic form factors describing the B→D* matrix elements of the Standard Model weak current, and to improve the determination of |Vcb|. On the other hand, they can be used to assess the impact of possible new physics contributions. In a bottom-up approach, we extend the Standard Model effective Hamiltonian governing this mode with the inclusion of the full set of Lorentz invariant d=6 operators compatible with the gauge symmetry of the theory. The measured angular coefficient functions can tightly constrain the couplings in the generalized Hamiltonian. We present the first results of this analysis, discussing how improvements can be achieved when more complete data on the angular coefficient functions will be available. Published by the American Physical Society 2024