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1.
In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice. 相似文献
2.
Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated. 相似文献
3.
Yaping Chen Dr. Kun Rui Prof. Jixin Zhu Prof. Shi Xue Dou Dr. Wenping Sun 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(3):703-713
Developing clean and sustainable energies as alternatives to fossil fuels is in strong demand within modern society. The oxygen evolution reaction (OER) is the efficiency-limiting process in plenty of key renewable energy systems, such as electrochemical water splitting and rechargeable metal–air batteries. In this regard, ongoing efforts have been devoted to seeking high-performance electrocatalysts for enhanced energy conversion efficiency. Apart from traditional precious-metal-based catalysts, nickel-based compounds are the most promising earth-abundant OER catalysts, attracting ever-increasing interest due to high activity and stability. In this review, the recent progress on nickel-based oxide and (oxy)hydroxide composites for water oxidation catalysis in terms of materials design/synthesis and electrochemical performance is summarized. Some underlying mechanisms to profoundly understand the catalytic active sites are also highlighted. In addition, the future research trends and perspectives on the development of Ni-based OER electrocatalysts are discussed. 相似文献
4.
P. Seelig A. Dax S. Faber M. Gerlach G. Huber T. Kühl D. Marx P. Merz W. Quint F. Schmitt H. Winter M. Würtz 《Hyperfine Interactions》1998,114(1-4):135-139
The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric
and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in 207Pb81+. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique
using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics
from an ion beam at relativistic velocities.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵,研究了CsNiCl3晶体的光谱精细结构、晶体结构、零场分裂参量、Jahn-Telller效应以及自旋单重态对Ni2+离子基态能级的影响,理论与实验相符合.在此基础上,进一步研究了以前工作中被忽略的自旋-自旋耦合作用和Trees修正对CsNiCl3晶体的光谱精细结构和零场分裂参量的影响,发现有四种机理会影响零场分裂参量:1)自旋-轨道耦合机理,2)自旋-自旋耦合机理;3)自旋-轨道与自旋-自旋联合耦合机理;4)自旋-轨道与Trees修正联合耦合机理,其中自旋-轨道耦合机理是最主要的,其他三种机理也是不可忽略的.
关键词:
基态能级
精细结构
零场分裂
自旋-自旋耦合 相似文献
6.
Blaise Faugeras Jé rô me Pousin Franck Fontvieille. 《Mathematics of Computation》2006,75(253):209-222
A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.
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9.
Murray Hodgson 《Applied Acoustics》2004,65(1):69-89
The acoustical characteristics of 14 university classrooms at the University of British Columbia were measured before and after renovation—seven of these are discussed in detail here. From these measurements, and theoretical considerations, values of quantities used to assess each classroom configuration were predicted, and used to evaluate renovation quality. Information on each renovation was determined with the help of the university campus-planning office and/or the project acoustical consultant. These were related to the evaluation results in order to determine the relationship between design and acoustical quality. The criteria focused on the quality of verbal communication in the classrooms. Room-average Speech Intelligibility (SI) and its physical correlate, Speech Transmission Index (STI), were used to quantify verbal-communication quality. A simplified STI-calculation procedure was applied. The results indicate that some renovations were beneficial, others were not. Verbal-communication quality varied from ‘poor’ to ‘good’. The effect of a renovation depends on a complex interplay between changes in the reverberation and changes in the signal-to-noise level difference, as affected by sound absorption and the source outputs. Renovations which reduce noise are beneficial unless signal-to-noise level differences remain optimal. Renovations often put too much emphasis on adding sound absorption to control reverberation, at the expense of lower speech levels, particularly at the backs of classrooms. The absorption and noise contributed by room occupants has apparently often been neglected. 相似文献
10.
We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase. 相似文献