scholarly journals On Converting Any One-Step Method to a Variational Integrator of the Same Order

Author(s):  
George W. Patrick ◽  
Charles Cuell ◽  
Raymond J. Spiteri ◽  
William Zhang

In the formalism of constrained mechanics, such as that which underlies the SHAKE and RATTLE methods of molecular dynamics, we present an algorithm to convert any one-step integration method to a variational integrator of the same order. The one-step method is arbitrary, and the conversion can be automated, resulting in a powerful and flexible approach to the generation of novel variational integrators.

1990 ◽  
Vol 9 (3) ◽  
pp. 247-252 ◽  
Author(s):  
Sander Greenland ◽  
Alberto Salvan
Keyword(s):  
One Step ◽  

2018 ◽  
Vol 54 (68) ◽  
pp. 9438-9441 ◽  
Author(s):  
Nathalie M. Pinkerton ◽  
Khadidja Hadri ◽  
Baptiste Amouroux ◽  
Leah Behar ◽  
Christophe Mingotaud ◽  
...  

A novel, one-step method for the synthesis of functional, organic–inorganic hybrid nanoparticles is reported.


Minerals ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 658 ◽  
Author(s):  
Xiaohui Yang ◽  
Yi Liu ◽  
Chunjie Yan ◽  
Ronghua Peng ◽  
Hongquan Wang

Geopolymer-TiO2 nanocomposites were prepared by two different techniques, namely the two-step acidification calcination treatment and one-step adding method. The potential photocatalytic activities of geopolymer-TiO2 nanocomposites prepared by the two different methods were tested and compared. Nanocomposites prepared via the one-step process showed better photocatalytic activity. The amount of TiO2 particles loaded on the surface of the foaming materials was investigated by XRD and SEM-Mapping. By comparing with the sample obtained from two-step treatment, the TiO2 particles were distributed uniformly on the surface of the foaming materials for the sample obtained from the one-step method in this study. Results showed that the specific surface area of the geopolymer-TiO2 prepared by the one-step treatment process (28.67 m2/g) was significantly lower than the two-step acidification calcination process (215.04 m2/g), while the photocatalytic efficiency with methylene blue trihydrate (MB) was better. This is due to the more stable structure of geopolymer-TiO2 nanocomposites, the better dispersion and more loading of TiO2 particles on the foaming materials surfaces, leading to the enhanced photocatalytic activity.


Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7604
Author(s):  
Hasan Shabbir ◽  
Tomasz Tokarski ◽  
Ditta Ungor ◽  
Marek Wojnicki

In this work, we report the synthesis method of carbon quantum dots (CDs) using the one-step method for fast and effective metal ion determination. Ascorbic acid was used as an inexpensive and environmentally friendly precursor. High-pressure and high-temperature reactors were used for this purpose. Microscopic characterization revealed the size of CDs was in the range of 2–6 nm and they had an ordered structure. The photoluminescence properties of the CDs depend on the process temperature, and we obtained the highest PL spectra for 6 h of hydrothermal reaction. The maximum emission spectra depend poorly on synthesis time. Further characterization shows that CDs are a good contender for sensing Fe3+ in aqueous systems and can detect concentrations up to 0.49 ppm. The emission spectra efficiency was enhanced by up to 200% with synthesis time.


2018 ◽  
Vol 11 (1) ◽  
pp. 46 ◽  
Author(s):  
Fei Ye ◽  
Yunbin Yuan ◽  
Bingfeng Tan ◽  
Zhiguo Deng ◽  
Jikun Ou

The predicted parts of ultra-rapid orbits are important for (near) real-time Global Navigation Satellite System (GNSS) precise applications; and there is little research on GPS/GLONASS/BDS/Galileo/QZSS five-system ultra-rapid precise orbit determination; based on the one-step method and double-difference observation model. However; the successful development of a software platform for solving five-system ultra-rapid orbits is the basis of determining and analyzing these orbits. Besides this; the different observation models and processing strategies facilitate to validate the reliability of the various ultra-rapid orbits. In this contribution; this paper derives the double-difference observation model of five-system ultra-rapid precise orbit determination; based on a one-step method; and embeds this method and model into Bernese v5.2; thereby forming a new prototype software platform. For validation purposes; 31 days of real tracking data; collected from 130 globally-distributed International GNSS Service (IGS) multi-GNSS Experiment (MGEX) stations; are used to determine a five-system ultra-rapid precise orbit. The performance of the software platform is evaluated by analysis of the orbit discontinuities at day boundaries and by comparing the consistency with the MGEX orbits from the Deutsches GeoForschungsZentrum (GFZ); between the results of this new prototype software platform and the ultra-rapid orbit provided by the International GNSS Monitoring and Assessment System (iGMAS) analysis center (AC) at the Institute of Geodesy and Geophysics (IGG). The test results show that the average standard deviations of orbit discontinuities in the three-dimension direction are 0.022; 0.031; 0.139; 0.064; 0.028; and 0.465 m for GPS; GLONASS; BDS Inclined Geosynchronous Orbit (IGSO); BDS Mid-Earth Orbit (MEO); Galileo; and QZSS satellites; respectively. In addition; the preliminary results of the new prototype software platform show that the consistency of this platform has been significantly improved compared to the software package of the IGGAC.


2012 ◽  
Vol 51 (12) ◽  
pp. 2172-2187 ◽  
Author(s):  
Noora Eresmaa ◽  
Jari Härkönen ◽  
Sylvain M. Joffre ◽  
David M. Schultz ◽  
Ari Karppinen ◽  
...  

AbstractA new three-step idealized-profile method to estimate the mixing height from vertical profiles of ceilometer backscattering coefficient is developed to address the weaknesses found with such estimates that are based on the one-step idealized-profile method. This three-step idealized-profile method fits the backscattering coefficient profile of ceilometer measurements into an idealized scaled vertical profile of three error functions, thus having the potential to determine three aerosol layers (one for the surface layer, one for the mixing height, and one for the artificial layer caused by the weakened signal). This three-step idealized-profile method is tested with ceilometer and radiosounding data collected during the Helsinki Testbed campaign (2 January 2006–13 March 2007). Excluding cases with low aerosol concentration in the boundary layer, cases with clouds present, and cases with precipitation present, the resulting dataset consists of 97 simultaneous backscattering coefficient profiles and radiosoundings. The three-step method is compared with the one-step method and other commonly employed algorithms. A strong correlation (correlation coefficient r = 0.91) between the mixing heights as determined by the three-step method using ceilometer data and those determined from radiosoundings is an improvement over the same correlation using the one-step method (r = 0.28), as well as the other algorithms.


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