Method For Structure Calculations Research Articles

Qubit unitary coupled cluster with generalized single and paired double excitations ansatz for variational quantum eigensolver

AbstractVariational quantum eigensolver (VQE) with a unitary coupled cluster (UCC) ansatz has been suggested as a promising method for electronic structure calculations on future quantum computers. However, the complexity of the excitation terms for UCC with the single and double excitations (UCCSD) ansatz is up‐bounded to , where N is the number of electrons and M is the number of spin orbitals. The gate complexity of quantum circuit for the UCCSD ansatz is up‐bounded to using the Jordan–Wigner transformation. These complexities significantly limit the implementation of UCCSD on current Noisy Intermediate‐Scale Quantum (NISQ) devices. Herein, we developed a k‐QUpCCGSD ansatz which is based on the generalized paired double excitation operators and the particle preserving exchange gate. The former reduces the number of the excitation operators, the latter reduces the number of qubit gates for transforming excitation operators to quantum circuit. The gate complexity of the proposed k‐QUpCCGSD ansatz is up‐bounded to , which significantly reduce the complexity of the VQE algorithm on NISQ devices. The performance of the proposed ansatz on VQE is demonstrated by calculating ground‐state dissociation energy curves of the H6, LiH, H2O, and BeH2 molecules with the STO‐3G minimal basis set, and the accuracy is evaluated by comparing to the full configuration interaction (FCI) benchmarks. Moreover, we compare the number of quantum gates, especially the CNOT gates, and accuracies of various ansatzes. The assessments have shown that the accuracy of qubit unitary coupled cluster (QUCC) ansatzes is slightly worse than that of the UCC ones, but the circuit complexity of QUCC is much less than that of UCC. Among the tested QUCC ansatzes, k‐QUpCCGSD achieves higher accuracy with fewer quantum gates than QUCCSD, and k‐QUpCCGSD is a promising ansatz for VQE calculation on NISQ devices.

On-Site Risk Assessment Methodology of Historic Timber Structures: The Case Study of Santa Cruz Church

The conservation and repair of historic structures require significant resources. Therefore, it is important to conduct a complete assessment of the object. Specifically, historical timber frame structures are very common in the Spanish and Andalusian geographic area. This research proposes and develops a simplified approach to facilitate decision making when faced with this complex work. By the application of long-established non-destructive tests, such as organoleptic and measuring inspection, resistography, and electric moisture content test, combined with visual classification parameters, these data were used as boundary conditions into a simplified structural calculation method. This process, which is simpler than other calculation systems, allows compiling important information about the safety level of the structure and its critical points. Finally, it allows for a better approach to repair work while rationalizing resources. This method was applied to a historical structure, during an 18th century church repair project. The assessment methodology provided important information about the conservation state of the timber frame and its structural suitability.

Modification of Segment Structure Calculation Theory and Development and Application of Integrated Software for a Shield Tunnel

From the aspect of calculation theory, the beam–spring model method and modified routine method of shield tunnel segment structure calculation were improved, and an efficient integrated software system for segment structure calculation of shield tunnel was developed. The beam–spring method is generally calculated according to the assumption of continuous displacement between beams and joints, and the existing modified routine method assumes that the lateral pressure gradient is constant generally, which does not consider the variation in lateral pressure gradient caused by the difference in the lateral pressure coefficient of soil layers or the water level height, which has a certain deviation from the actual situation. The existing beam–spring method and modified routine method theory were improved, the discontinuous displacement between beams and joints in the beam–spring method was taken into account, and the problem of lateral pressure gradient change in the modified routine method was solved. The calculation software system developed by C# and python programming language was proposed to improve the accuracy and efficiency of segment structure calculation. Based on the actual monitoring data of the internal force of the shield tunnel segment and the adjacent shield tunnel segments under construction in Changsha, China, the segments of the shield tunnel with different cross-section sizes and different hydrogeological conditions are calculated to verify the reliability of the calculation software system. At the same time, combined with the calculation results of the software system and field test data, the stiffness reduction coefficient and equivalent foundation resistance coefficient in the modified routine method were derived to further improve the accuracy of the calculation results, which provided a new idea for the calculation of segment structure of shield tunnel with different diameters under different hydrogeological conditions.

Nuclear-electronic orbital approach to quantization of protons in periodic electronic structure calculations.

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems, such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons as well as electron-proton correlation are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.

A modified elastic constant calculation method for triclinic-like special quasi-random structures: Application to Pd-M (M = Cu, Ag) solid solutions

The mechanical properties of Palladium alloys need to be calculated using first principles due to high experiment cost. For FCC disordered Pd alloys, special quasi-random structure (SQS) is usually used for modeling at first and the calculation of mechanical properties usually begins with elastic constants. However, SQS supercells are often triclinic-like and show lower symmetry than origin FCC structure, which would lead to the elements of elastic matrix calculated by DFT aren’t equal to elastic constants. To solve this problem, a strain operation method is put forward by linear transformation, LSQS′=SDL, to modify energy-strain method. Taking Pd-M (M = Cu, Ag) random alloys as an application case, the elastic properties of Pd-Cu and Pd-Ag alloys with 5 at% concentration gradient are calculated. The calculation results are similar to experiment data and other DFT works, which indicate that the preceding formula is valid. Electron structure analysis shows that Pd valence electrons are the main contributors to metallic bonds.

Structural Reliability Analysis and Reliability Index Calculation Method Based on Measurement Uncertainty

Structural reliability is a probabilistic measure of structural reliability. Reliability indicators can be calculated from the average and standard deviation. The standard deviation only reflects the degree of dispersion of the series of measured values such as structural resistance and load effects. However, the acquisition of measurement values is related to the measurement objects, instruments, methods, conditions, and measurement personnel. It is difficult to reflect the impact of these five aspects on the measurement values of structural resistance and load effects using standard deviation. Based on this, this article deeply analyzes the measurement uncertainty evaluation theory and method and proposes to use the synthetic standard uncertainty instead of the standard deviation to calculate the standard value of the structural resistance and load effect. This article establishes the structural performance function, structural reliability calculation formula, the reliable index calculation formula, the calculation formula of variation coefficient and the calculation formula of the safety factor based on the measurement uncertainty. The conclusion of this article provides a new application approach for China national standard “Measurement Uncertainty Evaluation and Representation” and also builds a new bridge for the measurement uncertainty evaluation theory to enter the field of structural reliability analysis.

NMR Molecular Replacement Provides New Insights into Binding Modes to Bromodomains of BRD4 and TRIM24.

Structure-based drug discovery (SBDD) largely relies on structural information from X-ray crystallography because traditional NMR structure calculation methods are too time consuming to be aligned with typical drug discovery timelines. The recently developed NMR molecular replacement (NMR2) method dramatically reduces the time needed to generate ligand–protein complex structures using published structures (apo or holo) of the target protein and treating all observed NOEs as ambiguous restraints, bypassing the laborious process of obtaining sequence-specific resonance assignments for the protein target. We apply this method to two therapeutic targets, the bromodomain of TRIM24 and the second bromodomain of BRD4. We show that the NMR2 methodology can guide SBDD by rationalizing the observed SAR. We also demonstrate that new types of restraints and selective methyl labeling have the potential to dramatically reduce “time to structure” and extend the method to targets beyond the reach of traditional NMR structure elucidation.

Model of Overlying Strata Structure in Large Mining Height Excavating Condition and Calculation of Support Working Resistance

Aiming at the wide range of rock strata movement and collapse, poor stability and high damage rate of the working face support and being prone to crushing of the support in large mining height face, analog simulation, theoretical analysis, and field measurements have been carried out to analyze roof breaking structure form and calculation method of support reasonable support resistance of large mining height face. The researches show that, affected by the space of the mined-out area, the roof of the large mining height working face will take on the structural form of “combined suspended beam-nonhinged roof-hinged roof”; the interaction system between the support and the surrounding rock consists of “hinged roof structure,” “nonhingeable roof structure,” “combined suspension beam structure,” and the support. The support resistance should adapt to the change of the overlying rock structure’s instability movement, bearing the weight of the structure itself and the additional load generated by the movement. Combining with the mining conditions of Jinhuagong Coal Mine’s large mining height face in Datong mining area, the reasonable support resistance of the working face support is analyzed. The mine pressure monitoring shows that the ZZ13000/28/60 type support and shield hydraulic support can meet the requirements of roof control; the research results ensure the safe mining of the large mining height face.

Thermal–Structural Coupling Analysis for Multiple Honeycomb Plates Connected by Hinges

The dynamical model of multiple honeycomb plates connected by hinges, including the thermal–structural coupling effect, is investigated in this paper. Under the assumption of small deformations and strains, the classical plate theory is used to establish the dynamical model of the honeycomb plate. The Chebyshev polynomial is adopted to describe the deformation of the plate and the linear torsional spring to represent the elastic hinge. Using the Rayleigh–Ritz method, the characteristic equation of the honeycomb sandwich structure is derived, from which the natural frequencies are obtained. Considering the thermal effect of the plate, the thermal–structural coupling dynamical equation is obtained. The thermal conduction in the thickness direction is calculated by the finite difference method. The present model is validated by comparing with the result generated by an equivalent orthotropic plate model established by the finite element (FE) software MSC Patran. The response analysis reveals the important effect of the metal skin and the hinge stiffness on the dynamic characteristics of the honeycomb sandwich structure. Numerical simulations reveal thermal–structural coupling features for the multi-honeycomb-plate structure from the perspective of the change in dynamic characteristics and the distribution of the temperature gradient. The thermal–structural coupling calculation method adopted herein can be used to solve the thermal conduction of the plate. It serves as the theoretical method for analyzing the dynamical behavior of the solar panel subjected to the solar heat.

40× zoom optical system design based on stable imaging principle of four groups.

Based on stable imaging principle of four groups and combined with optical design software, a method for initial structure calculation of zoom optical system and optical system optimization design is proposed to solve the problems of difficult initial structure calculation, large volume, and inflection point of zoom curves of a high zoom ratio optical system. First, this paper theoretically derives the four-group stable imaging principle of the zoom optical system. Then, using the derived equations and optical design software, the initial structural parameters of the four-group zoom optical system are solved to ensure that there is no inflection point in the zoom curves. Finally, a lightweight and small 40× continuous zoom optical system is designed to verify the feasibility and effectiveness of the design method proposed in this paper. The zoom optical system has the advantages of good imaging quality, lightweight, small size, smooth zoom, and no inflection point.

Elucidation of a nutlin-derivative—HDM2 complex structure at the interaction site by NMR molecular replacement: A straightforward derivation

Protein—ligand complex structures are key in structure-based drug discovery, but their derivation largely relies on X-ray crystallography. While NMR is able to provide atomic resolution complex structures, traditional NMR structure calculation methods are too slow for drug discovery timelines. We recently developed the NMR molecular replacement (NMR2) method that substantially reduces the time needed to derive protein—ligand complex structures, mainly by bypassing the laborious protein sequential resonance assignment step. Here we show how we applied NMR2 to derive the structure of the protein HDM2 in complex with the small molecule caylin-1, an analog of nutlin, based on the HDM2—nutlin complex structure that was already derived by NMR2. This study illustrates how sparse information from a previous NMR2 structure elucidation can be employed to efficiently determine further protein-analog complex structures. We think NMR2 has the potential to become a major tool in structure-based drug discovery, especially when X-ray crystallography is difficult to implement.

Study of the monitoring system for double row steel sheet pile cofferdam engineering

The construction monitoring and control standard of the steel sheet pile cofferdam is still the standard of the foundation pit of the civil structure. In this paper, by referring to the literature related to double-wall steel sheet pile cofferdam, the detection content, structure calculation method and error analysis of double-wall steel sheet pile cofferdam project are summarised systematically. To ensure the safety of the cofferdam structure, the automatic monitoring system of steel cofferdam is established to realise the organic combination of real-time monitoring and control of steel cofferdam, so as to take timely measures to ensure the smooth progress of the project and analyse the error which will be used to improve the model and algorithm. Finally, the calculation error between the model and algorithm will shrink and be smaller, making the results more reliable.

A Comparative Study between Polyline and Straight Line Arrangements of Antislide Piles Based on Soil Arching Effect

Considering the limitations of terrain and engineering expenses, antislide piles are sometimes arranged in polylines. Studies show that this arrangement adversely affects the mechanical characteristics of antislide piles. However, there is no in‐deep understanding of this issue and the structural design and calculation method of this arrangement have not been discussed in relevant standards. Aiming at resolving this shortcoming, the polylines pile arrangement is studied in this article to provide a scientific basis for designing and calculating antislide piles. To this end, the cantilever pile is taken as the research background, and the soil arching effect between piles is taken as the research object. Then the performances of the single‐row polyline pile layout and straight line pile layout are analyzed in the Dawanjiang landslide and the results are verified from the aspects of the landslide reinforcement and the influence on the antislide pile structure. The obtained results show that the polyline pile layout is disadvantageous to the safety of the antislide pile structure, and the soil arch between piles under the polyline pile layout condition is not uniform. Meanwhile, it is found that as the polyline pile layout angle increases, the stress concentration appears at the “inflection point.” Under this circumstance, the soil arch between piles is not uniform, and the stress concentration intensifies.

Vehicle structural analysis calculation method development in order to improve noise-vibration-harshness characteristics

The article presents a calculation method of structural analysis of a vehicle through the example of a body, the purpose of which is to reduce noise pollution. The results of calculations and experimental validations of calculations, natural frequencies and oscillation modes of the body, local dynamic stiffnesses and frequency response are provided. Also, the body characteristics in natural frequencies are improved through topological and topographical optimization of the body element.

Structural reliability calculation method based on improved weighted response surface

Structural reliability calculation method based on improved weighted response surface

AI-Based Self-Learning System in Distributed Structural Health Monitoring and Control

Artificial intelligence is predicted to play a big part in self-learning, industrial automation that will negotiate the bandwidth of structural health and control systems. The industrial structural health and control system based on discrete sensors possesses insufficient spatial coverage of sensing information, while the distributed condition monitoring has been mainly studied at the sensor level, relatively few studies have been conducted at the artificial intelligence level. This paper presents an innovative method for distributed structural health and control systems based on artificial intelligence. The structural condition was divided into regional and local features, the feature extraction and characterization are performed separately. Structural abnormality recognition and risk factor calculation method were proposed by considering the response values and the distribution patterns of both the regional and the local structural behaviours. The test results show that the method can effectively identify the full-scale and local damage of the structure, respectively. Subsequently, structural safety assessment method for long-span structures at kilometres level in view of fully length strain distributions measured by distributed fiber optic sensors were developed. A series of load tests on the long-span structure were carried out. Finite element (FE) model was developed using finite element code, ABAQUS, and an extensive parametric study was conduct to explore the effect of load cases on the structural responses. The differences in the structural response results among load test, structural safety assessment and FE simulation were investigated. It is shown that AI-based self-learning system could offer suitable speed in deployment, reliability in solution and flexibility to adjust in distributed structural health monitoring and control.

A parallel orbital-updating based optimization method for electronic structure calculations

In this paper, we propose a parallel orbital-updating based optimization method for electronic structure calculations. With our method, the solution of the minimization problem for the Kohn-Sham energy functional with respect to N orbitals is replaced by the solution of N independent minimization problems for the energy functional with respect to one orbital and the orthogonalization of the N updated orbitals. This new method allows a two-level parallelization. This feature makes our approach has a great advantage in large scale parallel computing. The numerical experiments show that our new method is reliable and efficient. Hence, our new method has a great potential for large scale electronic structure calculations on modern supercomputers.

EQMO: Equation of motion method for efficient electronic structure calculations

Equation of motion method has proven efficient for electronic structure calculations of very large systems, i.e. containing several million atoms. In this work, we redesign its previously published implementation and hereby release a revised software tool, EQMO, now capable of solving a crystalline TiO2 test sample of nearly a quarter of a billion atoms on NEC SX-Aurora TSUBASA vector computer. The legacy code has been rewritten in modern free-form Fortran, and the main developments include MPI support and optimisations for parallel execution. New Version Program SummaryProgram Title: EQMOCPC Library link to program files:https://doi.org/10.17632/5m7jp4nb4y.1Developer's repository link:https://git.icm.edu.pl/herman/eqmoLicensing provisions: GPLv3Programming language: FortranJournal reference of previous version: Marek T. Michalewicz, Herbert B. Shore, N. Tit, J.W. Halley, Equation of motion method for the electronic structure of disordered transition metal oxides, Comput. Phys. Commun. 71 (1992) 222–234.Does the new version supersede the previous version?: YesReasons for the new version: Major revisionSummary of revisions: The legacy Fortran code has been rewritten in modern free-form Fortran. The OpenMP support has been replaced with OpenMPI suitable for NEC SX-Aurora TSUBASA architecture. The sequential and MPI versions can be built independently to produce two separate binary files for both x86_64 CPU and NEC vector computer. The program has been developed and tested with GNU Fortran and NEC Fortran compilers.Nature of problem: Electronic structure calculation of a large system, i.e. containing several million atoms, is a computationally demanding task. The problem is to determine electronic properties of solid state systems in an efficient manner. The program, at its current development stage, is capable of calculating electronic properties (density of electronic states) of rutile TiO2 structure distorted by point defects, and is intended to be further developed towards treating a wide range of crystalline systems.Solution method: EQMO software tool is an equation of motion implementation designed to determine electronic structure (density of electronic states) of large-scale crystalline systems. The solution method is based on solving the Schrödinger equation with a tight-binding Hamiltonian, and its physical and mathematical foundations remain unchanged with respect to the previous release. For an explicit formalism with elaborate description, the reader is referred to the literature referenced below [1,2,3,4,5,6,7,8,9,10], and in particular – to the journal reference of the previous implementation along with the supplemented dataset [5]. The program is able to perform a benchmark on a TiO2 sample of nearly a quarter of a billion atoms on NEC SX-Aurora TSUBASA vector computer, and its functionality can be further expanded.

Structural calculation analysis and design of a Towering concrete building

This Towering building is a concrete tower with a height of 199. 10m and an octagonal plane, with a complex structure. The structure is calculated as a whole through the programs of two different mechanical models, the calculation results are relatively close, and the control indicators meet the requirements of relevant specifications and regulations. This article introduces and analyzes the structural system, structural calculation and analysis methods, seismic performance objectives, and overall calculation results of the project, and details the design of the steel tower.

Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or “black-box” protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.