High-precision Calculations Research Articles

One-loop gauge invariant amplitudes with a space-like gluon

Nowadays the particle physics has entered an era where high precision calculations are required in order to compare the theoretical predictions with the experimental data. In this paper, we explicitly compute the virtual contributions for the space-like one-jet processes, ∅→g⋆gg,∅→g⋆qq¯,∅→g⋆gH and ∅→g⋆q¯qe+e− within the auxiliary parton method. Our results, which are expected to play an important role in high precision description of small x physics, explicitly confirm the conjecture developed in Ref. [1], thus helping to bridge the gap between lowest order calculations and NLO corrections within hybrid kT-factorization scheme.

Guided Intelligent Hyper-Heuristic Algorithm for Critical Software Application Testing Satisfying Multiple Coverage Criteria

This paper proposes a novel algorithm that combines symbolic execution and data flow testing to generate test cases satisfying multiple coverage criteria of critical software applications. The coverage criteria considered are data flow coverage as the primary criterion, software safety requirements, and equivalence partitioning as sub-criteria. black The characteristics of the subjects used for the study include high-precision floating-point computation and iterative programs. The work proposes an algorithm that aids the tester in automated test data generation, satisfying multiple coverage criteria for critical software. The algorithm adapts itself and selects different heuristics based on program characteristics. The algorithm has an intelligent agent as its decision support system to accomplish this adaptability. Intelligent agent uses the knowledge base to select different low-level heuristics based on the current state of the problem instance during each generation of genetic algorithm execution. The knowledge base mimics the expert’s decision in choosing the appropriate heuristics. black The algorithm outperforms by accomplishing 100% data flow coverage for all subjects. In contrast, the simple genetic algorithm, random testing and a hyper-heuristic algorithm could accomplish a maximum of 83%, 67% and 76.7%, respectively, for the subject program with high complexity. black The proposed algorithm covers other criteria, namely equivalence partition coverage and software safety requirements, with fewer iterations. black The results reveal that test cases generated by the proposed algorithm are also effective in fault detection, with 87.2% of mutants killed when compared to a maximum of 76.4% of mutants killed for the complex subject with test cases of other methods.

Low-lying electronic states of osmium monoxide OsO

The ground state of osmium monoxide (OsO) has long been controversial. In this paper, the low-lying Λ–S and Ω electronic states of OsO have been comprehensively studied by the high-precision multi-reference calculations. The ground state of OsO is unexpectedly the closed-shell 1Σ+ state with a double bond instead of the previously reported 3Φ or 5Σ+ state; after including the spin–orbit coupling effects, the ground state becomes 3Π2. With the help of the theoretical spectroscopic constants and transition dipole moments, the emission spectra in the region of 405 nm–875 nm are assigned. Our results will facilitate the future studies of absorption and emission spectra of OsO.

Optimisation of layered shell model for analysis of reinforced concrete shear walls based on machine learning

Layered shell modelling is an effective tool for the efficient simulation of two-dimensional structural members. As machine learning (ML) provides a novel alternative for the optimisation analysis of the traditional layered shell model, it has been widely used in civil engineering applications. This study focuses on the accurate numerical simulation of reinforced concrete (RC) shear wall structures using the ML method. The user subprogram interface HYPELA2 based on the implicit solver of Marc software was compiled to implement a program package to consider the precise constitutive model of concrete. Additionally, different ML methods and loss functions were compared, and the adopted optimisation method was based on the particle swarm optimisation and L1 loss function. The analysis of constitutive parameters was realised according to the optimisation of the ML algorithm. Multiple numerical models were used to verify the stability and accuracy of the proposed layered shell model and ML method. Finally, the results obtained from comprehensive experimental research and numerical simulations were used to determine the recommended values of parameters for finite element analysis of RC shear walls to produce a novel high-precision, efficient, and universal calculation model.

MFFT: A GPU Accelerated Highly Efficient Mixed-Precision Large-Scale FFT Framework

Fast Fourier transform (FFT) is widely used in computing applications in large-scale parallel programs, and data communication is the main performance bottleneck of FFT and seriously affects its parallel efficiency. To tackle this problem, we propose a new large-scale FFT framework, MFFT, which optimizes parallel FFT with a new mixed-precision optimization technique, adopting the “high precision computation, low precision communication” strategy. To enable “low precision communication”, we propose a shared-exponent floating-point number compression technique, which reduces the volume of data communication, while maintaining higher accuracy. In addition, we apply a two-phase normalization technique to further reduce the round-off error. Based on the mixed-precision MFFT framework, we apply several optimization techniques to improve the performance, such as streaming of GPU kernels, MPI message combination, kernel optimization, and memory optimization. We evaluate MFFT on a system with 4,096 GPUs. The results show that shared-exponent MFFT is 1.23 × faster than that of double-precision MFFT on average, and double-precision MFFT achieves performance 3.53× and 9.48× on average higher than open source library 2Decomp&FFT (CPU-based version) and heFFTe (AMD GPU-based version), respectively. The parallel efficiency of double-precision MFFT increased from 53.2% to 78.1% compared with 2Decomp&FFT, and shared-exponent MFFT further increases the parallel efficiency to 83.8%.

High-precision calculation and experiments on the thermal blooming of high-energy lasers.

Thermal blooming (TB) is one of the important factors affecting the quality of high-energy laser beams. Reasonable simulation of thermal blooming is important to the application of a high-energy laser. However, reported investigations on TB simulation are mainly based on one method, such as the perturbation method or the phase screen method, which often leads to obvious errors in some conditions. In the paper, the reasonable ranges of optical generalized distortion parameters for both methods are determined based on the reported experimental data, which solves the problem of accurate TB simulations for the first time. In addition, the dynamic effect of thermal blooming is also calculated. Finally, the formula method is presented to extract the phase of thermal blooming distortion. We then use LC-SLM (Liquid crystal spatial light modulator) to emulate thermal blooming effect in the lab. The experimental results are more consistent with the numerical simulation results than conventional phase extraction methods. Our work provides a quantitatively and programmable way to accurately simulate TB with LC-SLM in the lab.

QPA: A Quantization-Aware Piecewise Polynomial Approximation Methodology for Hardware-Efficient Implementations

Piecewise polynomial approximation (PPA) on nonlinear functions plays an important role in high-precision computing. In this article, we proposed QPA, an integration of error-flattened quantization-aware PPA methods, to generate the optimized coefficients for efficient hardware implementations targeting any polynomial order. QPA incorporated four key features to minimize the fitting error and the hardware cost, including using the Remez algorithm to compute the minimax fitting polynomial, combining the fitting and quantization operations to get an error-flattened characteristic, assigning specific coefficient bit width to each multiplier to reduce the hardware cost, and fine-tuning the truncated coefficients to further reduce the fitting error. Experimental results showed that our methods consistently achieved the lowest fitting error compared with the state-of-the-art error-flattened piecewise approximation methods. We synthesized the proposed designs with 28-nm TSMC CMOS technology. The results showed that the proposed designs achieved up to 37.0% area reduction and 50.5% power consumption reduction compared to the state-of-the-art error-flattened piecewise linear (PWL) method, and up to 27.0% area reduction, 21.4% delay reduction, and 20.8% power consumption reduction compared to the state-of-the-art error-flattened piecewise quadratic (PWQ) method.

Model-dependent analysis method for energy budget of the cosmological first-order phase transition

The kinetic energy of the fluid shell in the cosmological first-order phase transition is crucial for predicting the gravitational wave signals generated by the sound wave mechanism. We propose a model-dependent method to calculate the kinetic energy fraction by dividing the bubble-fluid system into three distinct regions: the symmetric phase, the broken phase, and the bubble wall. By solving the local equation of motion of the scalar field with a phenomenological friction term, the bubble wall velocity and the boundary conditions of the fluid equations of both phases can be derived simultaneously. Then, for a given particle physics model, the fluid profiles of different hydrodynamical modes and the corresponding kinetic energy fraction can be obtained. Our method can also capture the temperature dependency of the sound speed of the plasma. Compared with the conventional model-independent method, our approach is based on an accurate equation of state derived directly from the effective potential and takes into account the contribution of the bubble wall to the energy-momentum tensor. Therefore, our method in-principle provides a more consistent and accurate result, which is crucial for high-precision calculations of the gravitational waves induced by the first-order phase transition.

Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code

In this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schrödinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used for nonlinear problems. The semi-global algorithm is briefly presented, the C++ implementation is described and five sample simulations are shown. The accompanying C++ source code package is included. The high precision benchmark (long double and float128) shows the estimated calculation costs. The presented method turns out to be faster and more accurate than the global Chebyshev propagator. Program summaryProgram Title: SemiGlobalCppCPC Library link to program files:https://doi.org/10.17632/429rszyc65.1Developer's repository link:http://gitlab.com/cosurgi/SemiGlobalCppLicensing provisions: GNU General Public License 2Programming language: C++Nature of problem: The femto- and attosecond chemistry requires fast and high precision computation tools for quantum dynamics. Conventional software has problems with providing high precision calculation results (up to 33 significant digits), especially when the computation has to be as fast as possible.Solution method: This software fills in the gap by providing the semi-global algorithm [1–3] for arbitrary number of coupled electronic states for the time dependent Hamiltonian and nonlinear inhomogeneous source term. It is implemented in a way that allows computation with precision of 15, 18 or 33 significant digits, where the computation speed can be directly controlled by setting the required error tolerance. The semi-global algorithm [1–3] is implemented in C++ providing a 10× speed boost compared to original publication of semi-global algorithm implemented in Matlab/Octave [1–3].

Accuracy of a Recent Regularized Nuclear Potential.

F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [Gygi J. Chem. Theory Comput. 2023, 19, 1300-1309.]. This potential V(r) is determined by inverting the Schrödinger equation for the wave function Ansatz ϕ(r) = exp[-h(r)]/√π with h(r) = r erf(ar) + b exp(-a2r2), where a and b are parameters. Gygi fixes b by demanding ϕ to be normalized, with the value b(a) depending on the strength of the regularization controlled by a. We begin this work by re-examining the determination of b(a) and find that the original 10-decimal tabulations of Gygi are only correct to 5 decimals, leading to normalization errors in the order of 10-10. In contrast, we show that a simple 100-point radial quadrature scheme not only ensures at least 10 correct decimals of b but also leads to machine-precision level satisfaction of the normalization condition. Moreover, we extend Gygi's plane-wave study by examining the accuracy of V(r) with high-precision finite element calculations with Hartree-Fock and LDA, GGA, and meta-GGA functionals on first- to fifth-period atoms. We find that although the convergence of the total energy appears slow in the regularization parameter a, orbital energies and shapes are indeed reproduced accurately by the regularized potential even with relatively small values of a, as compared to results obtained with a point nucleus. The accuracy of the potential is furthermore studied with s-d excitation energies of Sc-Cu as well as ionization potentials of He-Kr, which are found to converge to sub-meV precision with a = 4. The findings of this work are in full support of Gygi's contribution, indicating that all-electron plane-wave calculations can be accurately performed with the regularized nuclear potential.

Electric-dipole transition amplitudes for atoms and ions with one valence electron

Motivated by recent measurements for several alkali-metal atoms and alkali-metal-like ions, we perform a detailed study of electric dipole ($E1$) transition amplitudes in K, $\mathrm{Ca}{}^{+}$, Rb, $\mathrm{Sr}{}^{+}$, Cs, $\mathrm{Ba}{}^{+}$, Fr, and $\mathrm{Ra}{}^{+}$, which are of interest for studies of atomic parity violation, electric dipole moments, and polarizabilities. Using the all-orders correlation potential method, we perform high-precision calculations of $E1$ transition amplitudes between low-lying $s, p$, and $d$ states. We perform a robust error analysis, and compare our calculations to many amplitudes for which there are high-precision experimental determinations. We find excellent agreement, with deviations at the level of $\ensuremath{\sim}0.1$%. We also compare our results to other theoretical evaluations, and discuss the implications for uncertainty analyses. Further, combining calculations of branching ratios with recent measurements, we extract high-precision values for several $E1$ amplitudes of $\mathrm{Ca}{}^{+}, \mathrm{Sr}{}^{+}$, Cs, Fr, and $\mathrm{Ra}{}^{+}$.

An Optoelectronic Synapse Based on Two-Dimensional Violet Phosphorus Heterostructure.

Neuromorphic computing can efficiently handle data-intensive tasks and address the redundant interaction required by von Neumann architectures. Synaptic devices are essential components for neuromorphic computation. 2D phosphorene, such as violet phosphorene, show great potential in optoelectronics due to their strong light-matter interactions, while current research is mainly focused on synthesis and characterization, its application in photoelectric devices is vacant. Here, the authors combined violet phosphorene and molybdenum disulfide to demonstrate an optoelectronic synapse with a light-to-dark ratio of 106 , benefiting from a significant threshold shift due to charge transfer and trapping in the heterostructure. Remarkable synaptic properties are demonstrated, including a dynamic range (DR) of > 60dB, 128 (7-bit) distinguishable conductance states, electro-optical dependent plasticity, short-term paired-pulse facilitation, and long-term potentiation/depression. Thanks to the excellent DR and multi-states, high-precision image classification with accuracies of 95.23% and 79.65% is achieved for the MNIST and complex Fashion-MNIST datasets, which is close to the ideal device (95.47%, 79.95%). This work opens the way for the use of emerging phosphorene in optoelectronics and provides a new strategy for building synaptic devices for high-precision neuromorphic computing.

A Kronecker limit formula for indefinite zeta functions

We prove an analogue of Kronecker’s second limit formula for a continuous family of “indefinite zeta functions”. Indefinite zeta functions were introduced in the author’s previous paper as Mellin transforms of indefinite theta functions, as defined by Zwegers. Our formula is valid in dimension g=2 at s=1 or s=0. For a choice of parameters obeying a certain symmetry, an indefinite zeta function is a differenced ray class zeta function of a real quadratic field, and its special value at s=0 was conjectured by Stark to be a logarithm of an algebraic unit. Our formula also permits practical high-precision computation of Stark ray class invariants.

Experimental and kinetic modeling study of low-temperature oxidation of n-pentane

Attractiveness in advanced low-temperature combustion engines drives a constantly updated understanding of low-temperature oxidation chemistry. In this work, the low-temperature oxidation chemistry of n-pentane in two jet-stirred reactors at atmospheric pressure and in the temperature range of 500–825 K was investigated using combined analysis methods of synchrotron vacuum ultraviolet photoionization mass spectrometry, gas chromatography, and Fourier transform infrared spectroscopy. Furthermore, the gaseous mixture from JSR was collected in acetonitrile for subsequent product characterization using flow injection analysis, high-pressure and ultra-high-pressure liquid chromatography coupled to a Thermo Scientific™ Orbitrap® Q-Exactive high-resolution mass spectrometry. Numerous intermediate species were identified by these analytical methods, which contributed to unraveling the low-temperature oxidation reaction network of n-pentane. A detailed n-pentane model was tentatively developed to reduce deviations between experimental measurements and model predictions by updating the rate constants of C5 keto-hydroperoxide decomposition, C5 hydroperoxy cyclic ether decomposition, and Korcek reactions of C5 keto-hydroperoxide, and by introducing pressure-dependent rate constants for the reaction classes of Q˙OOH + O2, Q˙OOH decompositions, concerted HȮ2-elimination of RȮ2, C5 keto-hydroperoxide decomposition, C5 hydroperoxy cyclic ether decomposition, and Korcek reactions of C5 keto-hydroperoxide, and by adding more detailed sub-mechanisms for C5 cyclic ethers and C5 keto-hydroperoxides. This updated model was validated against a set of available experimental data, including jet-stirred reactor species data and ignition delay times. These exploratory updates of the kinetic model reveal the considerable influence of the rate constants of hydroperoxide decomposition and the pressure-dependent rate constants of key reaction classes on the kinetic model predictions, highlighting the future demands for high-precision quantum chemistry calculations of the pressure-dependent rate constants of the aforementioned reaction classes to reduce mechanism uncertainties and to develop accurate and robust chemical kinetic models.

Uncertainty analysis of the control rod drop based on the adaptive collocation stochastic perturbation method

There are many uncertain factors to affect the control rod drop from its design and manufacture to the chain reaction in the reactor. They have to be considered in the simulation to realistically predict the dynamic behavior of control rod drop. Different from the previous method by using the nominal and extreme values of the uncertain factors, a statistical method is applied in this paper to analyze them in the process of the control rod drop. The uncertain factors obey uniform distribution, based on which a fifth-order adaptive collocation stochastic perturbation (ACSP) method is established in this paper, which is featured with simple format, high precision, and high calculation efficiency. The mean and standard deviation of the responses (such as the final time of the control rod drop) in two different types of reactors are calculated by using the ACSP method. On this basis, the response intervals and corresponding probabilities of the control rod drop are obtained. Besides, influences of each random variable on the responses are analyzed by the sensitivity analysis. In addition, the linear correlation degree and correlation between the two are discussed through the correlation coefficient of random variables and the responses. The uncertainty analysis of control rod drop in this paper not only provides a relatively strong theoretical support for scientifically dealing with uncertain factors, but also offers specific help for the optimal design of control rod assembly.

Analysis of the effects of isolation piles on the basal stability of foundation pits against upheaval based on continuous velocity fields.

The upper bound limit analysis method is one of the main approaches to check the basal stability of foundation pits against upheaval. However, existing studies have often failed to consider the effects of external supporting structures, including isolation piles and others, on basal stability against upheaval. This study derives a formula for the coefficient of basal stability against upheaval under the action of isolation piles by simplifying the pile-soil relationship and systematically examines the impact of isolation pile parameters on basal stability against upheaval using the theory of continuous velocity fields and the upper bound limit analysis method. A comparison of simulation results indicates that this technique can accurately identify the variation trend of basal stability against upheaval under the influence of isolation piles and achieve high calculation precision under the operating conditions of wide foundation pits and short isolation piles. Accordingly, a moderate increase in isolation pile parameters produces a significant supporting effect for narrowed foundation pits. Whereas for wide foundation pits, the supporting capacity of isolation piles can be maximized when pile length equals excavation depth.

A High-Precision Calculation Method for Troposcatter Propagation Delay by Fusing Atmospheric Reanalysis Data

Troposcatter propagation delay is one of the most significant sources of errors in troposcatter time comparison. The existing methods of calculating troposcatter propagation delay face problems in terms of effectively reflecting the influence of the meteorological environment on troposcatter propagation delay, due to the insufficient spatial and temporal resolution of the meteorological data. This article proposes a high-precision calculation method for troposcatter propagation delay based on atmospheric reanalysis data. The troposcatter propagation path and the refractive index along the troposcatter data were obtained by combining 3D ray tracing with the European Centre for Medium-Range Weather Forecasts’ Reanalysis 5 (ERA5), with high spatial and temporal resolution. This found the hour-level time delay in troposcatter. The geometric delay, path delay, and total propagation delay of the troposcatter were calculated and analyzed via 12 scattering links in 6 typical geographical regions. It was found that the path delay was the main cause of the propagation delay of troposcatter, and that the proportion of geometric delay in the total propagation delay increased along with an increase in link distance. The propagation delay changed noticeably in different seasons. The path delay was higher in summer and lower in winter, the geometric delay was lower in summer and higher in winter, and the total propagation delay was mainly high in summer and low in winter. There were differences in delay date, seasonal fluctuation amplitude, and in hourly fluctuation standard deviation among different geographic areas.

Numerical study on flow stall and kinetic energy conversion of low-specific-speed centrifugal pump

Stall is a common phenomenon in centrifugal pumps under low-flow conditions; it has a significant impact on fatigue and can even damage mechanical structural components. Computational fluid dynamics was used to perform high-precision numerical calculations to describe multiple operating conditions in the computational domain. The accuracy of these numerical simulations was verified by comparing the results with the single-flow channel flow patterns captured by time-resolved particle image velocimetry and the external characteristics of the centrifugal pump. On this basis, the unsteady spatiotemporal evolution of the vortex structure under stall conditions and the kinetic energy conversion relationship were determined. The stall vortex under the rotating stall condition has a relative motion with the impeller in the circumferential direction between channels, with the characteristic propagation frequency fcs = 0.71 Hz. For stationary stall conditions, the critical stall condition has a greater kinetic energy dissipation compared with the deep stall condition, with energy differences being more than three times larger at the blade leading edge, where the stall vortex is formed.

Quantitative Interpretation of Dynamic Resistance Signal in Resistance Spot Welding

Dynamic resistance is one of the most common and important signals used to monitor and control the resistance spot welding (RSW) process. However, existing studies on the signal evolution mechanism are limited to qualitative analysis, resulting in an ambiguous interpretation of the formation mechanism for the signal features. In this paper, a collaborative simulation approach was applied for the RSW of bare DP590 steel to obtain high-precision computation of the temperature and potential distributions inside the weld. On this basis, an analytical mapping model between the dynamic resistance signal and the weld profile was developed based on basic physical laws, and the signal evolution mechanism was quantitatively revealed through the model. It was found that the main factors determining the signal evolution trend are average sheet temperature and electrode/sheet contact diameter rather than the nugget growth process. The peak resistance feature was attributed to the bilinear relationship between sheet resistivity and temperature rather than nugget formation. The resistance drop after the peak mainly arose from the increase of the electrode/sheet contact diameter rather than nugget growth. This study can help improve the comprehension of the dynamic resistance signal and the interpretability of some data-driven methods used for RSW quality monitoring and control.

A new efficient approach for the calculation of cross-sections with application to Yukawa potential

Large-scale and systematic calculations of scattering amplitudes and cross-sections for charged particle collisions are of fundamental importance for understanding the physical properties of materials in different research fields. However, the elaborated theoretical methods for cross-sections are generally restricted to a finite range of impact energies. Here, we present an efficient approach for the calculation of the scattering amplitude and cross-sections ranging from low to high collision energies based on the variable phase method, where the Wentzel–Kramers–Brillouin and Born approximations for scattering phase shifts (SPSs) are incorporated into the numerical algorithm to alleviate the computational cost. For this purpose, quantitative criteria for the validity of these approximations are established based on the properties of the turning points of the potentials. For different scattering potentials, the corresponding planes can be established as a guideline to select the optimal combination for calculating the scattering amplitude and cross-section. The demand for quantum treatment of phase shifts is reduced by one to two orders of magnitude, which strongly benefits the computation of cross-sections for high-energy scattering. It has been found that the quantum treatment for SPSs is necessary near the quantum states involving quantum tunneling and resonance. To testify the validity of the approach, the SPSs and also transport cross-sections are calculated for Yukawa potentials, and good agreements are obtained in comparison with other available high-precision calculations. The proposed numerical approach can be straightforwardly generalized to other scattering potentials and permits one to efficiently calculate the scattering cross-sections for a large energy range.