Orbital Calculations Research Articles

GPU Acceleration of the Boys Function Evaluation in Computational Quantum Chemistry

ABSTRACTThe Boys function, a mathematical integral function, plays a pivotal role and is frequently evaluated in ab initio molecular orbital computations. The main contribution of this paper is to accelerate the bulk evaluation of the Boys function through the effective utilization of GPUs. The proposed GPU implementation addresses GPU‐specific programming issues such as warp divergence and coalesced/stride access to global memory, and we employ the optimal numerical evaluation method from four methods based on input values to ensure efficient computation with sufficient accuracy. Moreover, to consider actual computation of molecular integrals, we have implemented and evaluated the proposed method in two scenarios: single evaluation, which computes a single value of the Boys function for a single input, and incremental evaluation, which computes multiple values of the Boys function incrementally. The execution time of the proposed GPU implementation was evaluated for both scenarios using an NVIDIA A100 Tensor Core GPU. As a result, the GPU‐accelerated bulk evaluation has achieved a throughput of computing the values of the Boys function times per second for the single evaluation and times per second for the incremental evaluation, respectively. Our parallelized CPU and GPU implementation is available at https://github.com/sstsuji/Boys‐function‐GPU‐library.

Physical and Mutual Orbit Characteristics of Near-Earth Binary Asteroid (163693) Atira

We report physical and mutual orbit characteristics of near-Earth binary asteroid (163693) Atira. Using S-band (2380 MHz, 12.6 cm) radar observations from the Arecibo Observatory and several epochs of lightcurve observations from 2003 to 2019 with SHAPE modeling software, we determine the shape, size, rotational period, and mutual orbit of the primary and secondary components and the density of the primary component. We confirm the primary’s sidereal rotation period to be 3.398521 ± 0.000003 hr, and we find a likely spin axis orientation of ecliptic longitude and latitude (187°, −53°) ± 12°. We find the primary’s volume-equivalent diameter to be 4.92 ± 0.95 km and the secondary’s volume-equivalent diameter to be 0.80 ± 0.30 km. We find the primary component’s density to be 1.43 ± 0.87 g cm−3. We also find that the secondary has a semimajor axis of 7.8 ± 0.5 km and a sidereal orbital period of 15.577 ± 0.003 hr based on orbital calculations using delay and Doppler offsets between the primary and secondary and the timing of mutual events observed in lightcurve data. This work represents the first detailed analysis of the shape of an Atira-class asteroid.

Koopman–Hill stability computation of periodic orbits in polynomial dynamical systems using a real-valued quadratic harmonic balance formulation

In this paper, we generalize the Koopman–Hill projection method, which was recently introduced for the numerical stability analysis of periodic solutions, to be included immediately in classical real-valued harmonic balance (HBM) formulations. We incorporate it into the Asymptotic Numerical Method (ANM) continuation framework, providing a numerically efficient stability analysis tool for frequency response curves obtained through HBM. The Hill matrix, which carries stability information and follows as a by-product of the HBM solution procedure, is often computationally challenging to analyze with traditional methods. To address this issue, we generalize the Koopman–Hill projection stability method, which extracts the monodromy matrix from the Hill matrix using a matrix exponential, from complex-valued to real-valued formulations. In addition, we propose a differential recast procedure, which makes this real-valued Hill matrix immediately available within the ANM continuation framework. Using as an example a nonlinear von Kármán beam, we demonstrate that these modifications improve computational efficiency in the stability analysis of frequency response curves.

Optimization Over Families of Quasi-Periodic Orbits

Quasi-periodic orbit families in astrodynamics are usually studied from a global standpoint without much attention to the specific orbits which are computed. Instead, we focus on the computation of particular quasi-periodic orbits and develop tools to do so. These tools leverage the parametric structure of families of quasi-periodic orbits to treat orbits only as a set of orbit frequencies instead of states in phase space. We develop a retraction on the family of quasi-periodic orbits to precisely navigate through frequency space, allowing us to compute orbits with specific frequencies. The retraction allows for movements in arbitrary directions. To combat the effects of resonances which slice through frequency space we develop resonance avoidance methods which detect resonances during continuation procedures and change the step size accordingly. We also develop an augmented Newton’s method for root-finding and an augmented gradient descent method for unconstrained optimization over a family of quasi-periodic orbits. Lastly, we implement an augmented Lagrangian method to solve constrained optimization problems. We note that many of the tools developed here are applicable to a wider range of solutions defined implicitly by a system of equations, but focus on quasi-periodic orbits.

A comprehensive investigation on one-pot synthesis of imidazole derivatives: quantum computational analysis, molecular docking, molecular dynamics simulations and antiviral activity against SARS-CoV-2

New derivatives of 4-(2-(2-(2,3-dihydrobenzo[b][1,4]dioxin-6-yl)-4,5-diphenyl-1H-imidazol-1-yl)ethyl)morpholine (DDIM) have been successfully synthesised and characterised using spectral methods such as FT-IR, 1H NMR, and 13C NMR. Density functional theory (DFT) with the B3LYP/6-311G (d, p) level of theory was used to determine optimised bond parameters and single crystal XRD investigations confirmed the structure of DDIM. The results of single crystal XRD measurements aligned well with the optimised geometrical parameters from DFT calculations. Frontier molecular orbital computations provided insights into the molecule's stability, chemical reactivity and charge transfer. Atomic charges were determined using mulliken population analysis. The molecular electrostatic potential (MEP) mapped to electron density surfaces identified potential reactive sites. This molecule shows promise as a potential NLO material due to its high μβ0 value. Binding affinities were determined via molecular docking against the COVID-19 major protease (Mpro: 6WCF/6Y84/6LU7). A 100 ns molecular dynamics simulation under in silico physiological conditions confirmed the stability of the complex structure formed with the COVID-19 protein, revealing a stable conformation and binding pattern in an imidazole derivative environment. Additionally, in-silico analysis predicted favourable to moderate anti-viral activity and anticipated the compound's absorption, distribution, metabolism, excretion, and toxicity (ADMET) profiles.

Integrated precise orbit determination of GPS, BDS, and partial satellites selected from LEO constellation

Traditional precise orbit determination (POD) for Global Navigation Satellite System (GNSS) typically relies on a considerable number of global ground stations. The rapid development of large Low Earth Orbit (LEO) communication constellations in recent years presents an opportunity for integrated POD of LEO and GNSS satellites. The participation of abundant observations from onboard GNSS receivers in GNSS POD can significantly enhance the orbit precision, availability, and integrity of GNSS satellites. However, the improvement in orbit precision comes with a notable increase in computation time when a substantial number of LEO satellites are involved. In this study, we propose a method for selecting LEO satellites based on the LEO geometric dilution of precision (LGDOP) value. By identifying the LEO satellite combination corresponding to the minimum LGDOP, partial LEO satellites evenly distributed are selected from the entire LEO constellation. Using the semi-realistic simulation approach, only onboard observations of the LEO constellation are simulated to enhance GPS and BDS POD. The average accuracy of orbit determination for simulated LEO satellites is 2.27 cm in 3D directions, comparable to FengYun-3 but inferior to GRACE-FO. When onboard observations from 10 LEO satellites, selected using the minimum LGDOP method, participate in the integrated POD, the orbit precision can be improved by 10 %-14 % compared with the sequence selection method. Consequently, the LGDOP selection method optimizes the distribution of LEO satellites and demonstrates superior effectiveness in enhancing GPS and BDS POD with an equivalent number of LEO satellites. Involving 20–30 LEO satellites in the solution can enhance the orbit precision of GPS and BDS satellites by approximately 40 % and 80 % for global and regional ground stations, respectively. Increasing the number of participating LEO satellites further does not significantly improve the GPS and BDS orbit precision but does notably increase the computation time, which exceed 12 h for regional stations and 14 h for global stations. Thus, selecting approximately 20–30 LEO satellites using the proposed method effectively balances orbit determination precision and computation efficiency.

Physical parameters and orbital evolution of asteroids in retrograde orbits

Context. We studied the dynamical orbital and physical evolution of all 21 numbered and 13 selected unnumbered asteroids in retrograde orbits. Aims. Based on all published observations of studied asteroids in retrograde orbits, we computed their starting orbital elements, absolute magnitudes, and diameters, together with the non-gravitational parameters A2 and da/dt. Methods. Using publicly available orbital computation methods, we studied the dynamical evolution of orbital elements and the physical parameters of asteroids: rotation period, spin direction, and the non-gravitational parameters A2. Results. Lyapunov times (LT) for studied asteroids are short, from 60 to 36 496 yr, with a mean of 5978. Without considering non-gravitational effects, LT is longer: values range from 328 to 63 165 yr, with a mean of 6392. Over the next 10 Myr and beyond, the rotation period of the studied asteroids P decreases by approximately 8%. Moreover, 15% of the clones slow down. Conclusions. The starting spin distribution becomes flatter, with only one large maximum in the range (0–5) deg containing 279 clones (i.e. approximately 13%). However, the non-gravitational parameter da/dt has a maximum value of around (0–0.04)× 10−5 au day−2 .

Structure-preserving algorithms for guiding center dynamics based on the slow manifold of classical Pauli particle

The classical Pauli particle (CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field (AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments, demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.

Implementation and testing of single point positioning on IRNSS/NavIC receiver data

SummaryIndia has developed its own regional navigation satellite system called the Indian Regional Navigation Satellite System (IRNSS), also known as Navigation with Indian Constellation (NavIC). IRNSS/NavIC provides standard positioning and timing services for civilians and restricted services for authorized users. In this paper, single point positioning is implemented on the NavIC receiver data. Estimation techniques of the least squares method and extended Kalman filter are implemented after applying broadcast‐based clock corrections, orbit computation, relative time correction, and ionosphere delay correction for single and dual frequency. A data extraction and storage module is developed to store computed parameters at every intermediate stage in separate files. This is followed by an error plotter module to plot the extracted parameters for each satellite and to separately analyze their performance and the obtained errors. The estimated receiver position is visualized on Google Earth. The absolute error in both estimation techniques ranges between 5 and 15 m throughout the period.

2,4-dichloro-6-(1,4,5-triphenyl-1H-imidazol-2-yl) phenol: synthesis, DFT analysis, Molecular docking, molecular dynamics, ADMET properties against COVID-19 main protease (Mpro: 6WCF/6Y84/6LU7)

ABSTRACT New derivatives of 2,4-dichloro-6-(1,4,5-triphenyl-1H-imidazol-2-yl) phenol (DPIP) have been successfully synthesised and characterised using spectral methods such as FT-IR, 1H NMR and 13C NMR. Density functional theory (DFT) approach at B3LYP/6-311 G (d, p) level of theory is used to determine optimised bond parameters and single crystal XRD investigation of related derivatives confirms the structure of DPIP bond parameters. The single crystal XRD measurements and the optimised geometrical parameters produced by the DFT calculation agree well. The FT-IR bands seen in the experiment were attributed to distinct normal modes of the molecule. Frontier molecular orbital computations described the molecule stability, chemical reactivity and charge transfer. Atomic charges determined via Mulliken population analysis on the different DPIP atoms. MEP, which is mapped to the electron density surfaces, has discovered potential reactive sites of the molecule. The reported molecule is used as a potential NLO material since it has a high μβ0 value. Binding affinities were discovered using molecular docking against the COVID-19 major protease (Mpro: 6WCF/6Y84/6LU7). The behaviour of the complex structure formed by the Covid-19 protein under in silico physiological conditions was then confirmed by a 100 ns molecular dynamic simulation which looked at the structure stability over time and revealed a stable conformation and binding pattern in an environment of imidazole derivatives. Furthermore, favourable to moderate anti-viral activity was revealed by an in-silico analysis that anticipated the compound absorption, distribution, metabolism, excretion and toxicity profiles (ADMET).

Delayed Orbital Floor Reconstruction Using Mirroring Technique and Patient-Specific Implants: Proof of Concept.

Enophthalmos is a severe complication of primary reconstruction following orbital floor fractures, oncological resections, or maxillo-facial syndromes. The goal of secondary orbital reconstruction is to regain a symmetrical globe position to restore function and aesthetics. In this article, we present a method of computer-assisted orbital floor reconstruction using a mirroring technique and a custom-made titanium or high-density polyethylene mesh printed using computer-aided manufacturing techniques. This reconstructive protocol involves four steps: mirroring of the healthy orbit computer tomography files at the contralateral affected site, virtual design of a customized implant, computer-assisted manufacturing (CAM) of the implant using Direct Metal Laser Sintering (DMLS) or Computer Numerical Control (CNC) methods, and surgical insertion of the device. Clinical outcomes were assessed using 3dMD photogrammetry and computed tomography measures in 13 treated patients and compared to a control group treated with stock implants. An improvement of 3.04 mm (range 0.3-6 mm) in globe protrusion was obtained for the patients treated with patient-specific implants (PSI), and no major complications have been registered. The technique described here appears to be a viable method for correcting complex orbital floor defects needing delayed reconstruction.

Introduction of the Runge-Kutta method in GPS orbit computation

In all Global Navigation Satellite Systems (GNSS) applications, the determination of the satellite orbits is an important task. In this study, we present the equations given in the Interface Specification Document of GPS and the Runge-Kutta method in the computation of the position P, velocity V, and acceleration A of the GPS satellites using the broadcast ephemeris. The definition of the differential equation describing the GPS satellite's motion has enabled us to introduce the Runge-Kutta method in the GPS orbit computation; this method uses the initial conditions determined in this study from the Keplerian elements provided in the broadcast ephemeris files. The Lagrange interpolation method is used for comparison of the results, where the vectors P, V, and A are estimated using the precise ephemeris. The difference not exceeding 2.4 m was obtained in the X, Y, and Z axes during seven days on the position of the GPS satellite number 9 tested in this study. In velocity and acceleration, the difference is about a few mm/s and mm/s2, respectively.

Primary intraorbital inflammatory lumpy lesion: A rare case report.

Eosinophilic angiocentric fibrosis (EAF) is considered to be a kind of benign IgG4-related disease, and it is more often found in the nasal cavity. We present a pretty rare case of orbital EAF that is unlike any other reported case for this case is an IgG4 negative orbital EAF and successfully treated by the fronto orbitozygomatic approach surgery. This is a 68-year-old man from a rural area of Inner Mongolia Autonomous Region, went to our hospital for a 2-month history of vision loss with a local hospital orbital computer tomography which showed that there was a lesion in his left orbit. The inspection of the patient revealed that the patient left eye was protruding outward and the left eyelid unable to complete open or close. And his left eyeball movement had difficulty in all directions. Postoperative pathology diagnosed that this was a case of IgG4-negative EAF case. Orbital EAF. Surgical radical resection and postoperative glucocorticoid therapy. After surgery, the left eye vision of this patient increased to 0.6 tested in the standard logarithmic visual acuity chart. And his left eyeball movement dysfunction and eyeball outward protruding get a partially relief. EAF occurring in the orbit is a very rare disease and immunohistochemical results of EAF can be IgG4 negative.

Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

Periodic orbit families around asteroids serve as potential trajectories for space probes, mining facilities, and deep space stations. Bifurcations of these families provide additional candidate orbits for efficient trajectory design around asteroids. While various bifurcations of periodic orbit families around asteroids have been extensively studied, period-multiplying bifurcations have received less attention. This paper focuses on studying period-multiplying bifurcations of periodic orbit families around asteroids. In particular, orbits with periods of approximately 7 and 17 times that of the rotational period of asteroid 216 Kleopatra were computed. The computation of high-period orbits provides insights into the numerical aspects of simulating long-duration trajectories around asteroids. The previous literature uses single-shooting and multiple-shooting methods to compute bifurcations of periodic orbit families around asteroids. Computational difficulties were encountered while using the shooting methods to obtain period-multiplying bifurcations of periodic orbit families around asteroids. This work used the Legendre–Gauss collocation method to compute period-multiplying bifurcations around asteroids. This study recommends the use of collocation methods to obtain long-duration orbits around asteroids when computational difficulties are encountered while using shooting methods.

Quality assessment of the nominal attitude model of TOPEX/Poseidon using quaternion data

The altimetry mission TOPEX/Poseidon was operational between 1992 and 2005 and provided innovative insight into global and regional sea level changes and their variability. The correct modelling of the spacecraft orbit in precise orbit determination requires detailed information on the attitude of the spacecraft body and the solar array. Since the availability of attitude observations in form of quaternion data for this mission is limited, the nominal orientation model has to be used mainly. In this study, we compare the nominal and quaternion-based approaches of the TOPEX/Poseidon attitude realisation and validate the nominal model w.r.t. the observed attitude. We found good agreement between both approaches in the spacecraft-related roll, pitch, yaw, and solar array angles with slight differences of up to 0.31° on average. The best accordance is obtained in the yaw angles. A general angular offset of 0.12° and -0.19° on average is found in the pitch and solar array angle differences, respectively. Parameters estimated in the orbit computation process also reflect the good agreement between both orientation models with slightly better results when using the observed attitude. However, in some intervals, the nominal model lacks detailed information about the correct attitude. These can be adjusted using the information from the quaternion data. Such intervals indicate off-nominal spacecraft attitude events like drifts or offsets. Purely geometrically analysed, mispointing in the roll and pitch components of about 0.25° results in a change of the altimeter phase centre position in the radial direction of about 7 mm, which directly impacts the sea-level heights determined from altimetry measurements.

Sun-Earth system Lagrange point spacecraft orbit computation by numerical method and deep learning technique

In this article, the Lagrange points locations are computed in the Rotating Lagrangian Point (RLP) as well as in J2000 inertial reference frames. The well-known Sun-Earth system is considered for the circular restricted three-body problem (CRTBP). In the synodic frame, the Sun-Earth Lagrangian L1 point halo orbit is computed via Differential Correction and Lindstedt-Poincaré (LP) methods. The periodic halo orbits are expressed with respect to barycenter, heliocenter and geocenter, respectively. The deep learning-based model is further explored for the orbit accuracy obtained by the numerical method considering the third, fourth and fifth order LP method.

Developing high-power Li||S batteries via transition metal/carbon nanocomposite electrocatalyst engineering.

The activity of electrocatalysts for the sulfur reduction reaction (SRR) can be represented using volcano plots, which describe specific thermodynamic trends. However, a kinetic trend that describes the SRR at high current rates is not yet available, limiting our understanding of kinetics variations and hindering the development of high-power Li||S batteries. Here, using Le Chatelier's principle as a guideline, we establish an SRR kinetic trend that correlates polysulfide concentrations with kinetic currents. Synchrotron X-ray adsorption spectroscopy measurements and molecular orbital computations reveal the role of orbital occupancy in transition metal-based catalysts in determining polysulfide concentrations and thus SRR kinetic predictions. Using the kinetic trend, we design a nanocomposite electrocatalyst that comprises a carbon material and CoZn clusters. When the electrocatalyst is used in a sulfur-based positive electrode (5 mg cm-2 of S loading), the corresponding Li||S coin cell (with an electrolyte:S mass ratio of 4.8) can be cycled for 1,000 cycles at 8 C (that is, 13.4 A gS-1, based on the mass of sulfur) and 25 °C. This cell demonstrates a discharge capacity retention of about 75% (final discharge capacity of 500 mAh gS-1) corresponding to an initial specific power of 26,120 W kgS-1 and specific energy of 1,306 Wh kgS-1.

Effective reduced models from delay differential equations: Bifurcations, tipping solution paths, and ENSO variability

Conceptual delay models have played a key role in the analysis and understanding of El Niño-Southern Oscillation (ENSO) variability. Based on such delay models, we propose in this work a novel scenario for the fabric of ENSO variability resulting from the subtle interplay between stochastic disturbances and nonlinear invariant sets emerging from bifurcations of the unperturbed dynamics.To identify these invariant sets we adopt an approach combining Galerkin–Koornwinder (GK) approximations of delay differential equations and center-unstable manifold reduction techniques. In that respect, GK approximation formulas are reviewed and synthesized, as well as analytic approximation formulas of center-unstable manifolds. The reduced systems derived thereof enable us to conduct a thorough analysis of the bifurcations arising in a standard delay model of ENSO. We identify thereby a saddle–node bifurcation of periodic orbits co-existing with a subcritical Hopf bifurcation, and a homoclinic bifurcation for this model. We show furthermore that the computation of unstable periodic orbits (UPOs) unfolding through these bifurcations is considerably simplified from the reduced systems.These dynamical insights enable us in turn to design a stochastic model whose solutions – as the delay parameter drifts slowly through its critical values – produce a wealth of temporal patterns resembling ENSO events and exhibiting also decadal variability. Our analysis dissects the origin of this variability and shows how it is tied to certain transition paths between invariant sets of the unperturbed dynamics (for ENSO’s interannual variability) or simply due to the presence of UPOs close to the homoclinic orbit (for decadal variability). In short, this study points out the role of solution paths evolving through tipping “points” beyond equilibria, as possible mechanisms organizing the variability of certain climate phenomena.

Unexpected structural preference with metallophilic Ag-Au contacts in silver(I)-N-heterocyclic carbene cluster; experimental and theoretical approach.

A novel synthetic donor-atom-selective approach has been adopted for the synthesis of a heterobimetallic cluster of a new NCN-pincer, 1,3-bis-(1-methyl-1H-benzo[d]imidazol-2-yl-methyl)-1H-imidazol-3-ium hexafluorophosphate (1·HPF6). The complex [Ag3(1)3][PF6]3 (2) has been prepared via the Ag2O route; which undergoes transmetallation to yield a cluster that seems to be the first example of the heterobimetallic trinuclear system [Au-Ag2(1)2Cl][PF6]2, 3. Finally, the trinuclear cluster geometries of 2 and 3 were confirmed via SCXRD studies. Interestingly, Au(I) binds preferentially with soft donor Ccarbene, which transmetallated from the cluster of 2. In both the cyclic trinuclear clusters, the M-M interactions were further inspected using gauge independent atomic orbital (GIAO) computations. Both 2 and 3 are luminescent and possess σ-aromaticity; the NICS values indicate that 3 is more aromatic than 2.

In silico investigation on sensing of tyramine by boron and silicon doped C60 fullerenes

The present communication deals with the adsorption of tyramine neurotransmitter over the surface of pristine, Boron (B) and Silicon (Si) doped fullerenes. Density functional theory (DFT) calculations have been used to investigate tyramine adsorption on the surface of fullerenes in terms of stability, shape, work function, electronic characteristics, and density of state spectra. The most favourable adsorption configurations for tyramine have been computed to have adsorption energies of − 1.486, − 30.889, and − 31.166 kcal/mol, respectively whereas for the rest three configurations, it has been computed to be − 0.991, − 6.999, and − 8.796 kcal/mol, respectively. The band gaps for all six configurations are computed to be 2.68, 2.67, 2.06, 2.17, 2.07, and 2.14 eV, respectively. The band gap of pristine, B and Si doped fullerenes shows changes in their band gaps after adsorption of tyramine neurotransmitters. However, the change in band gaps reveals more in B doped fullerene rather than pristine and Si doped fullerenes. The change in band gaps of B and Si doped fullerenes leads a change in the electrical conductivity which helps to detect tyramine. Furthermore, natural bond orbital (NBO) computations demonstrated a net charge transfer of 0.006, 0.394, and 0.257e from tynamine to pristine, B and Si doped fullerenes.