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International Journal of Heat and Mass Transfer 2021年 166卷

作者： Yong Zhao Lei Wang Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Physics China University of Geosciences Wuhan 430074 China

A Logical Approach for the Schedulability Analysis of CCSL

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A Logical Approach for the Schedulability Analysis of CCSL

Theoretical Aspects of Software engineering (TASE)

作者： Yuanrui Zhang Frédéric Mallet Huibiao Zhu Yixiang Chen MoE Engineering Research Center for Software/Hardware Co-design East China Normal University Université Nice Sophia Antipolis Nice France Shanghai Key Laboratory of Trustworthy Computing East China Normal University

The Clock Constraint Specification Language (CCSL) is a clock-based formalism for formal specification and analysis of real-time embedded systems. Previous approaches for the schedulability analysis of CCSL specifications are mainly based on model checking or SMT-checking. In this paper we propose a logical approach mainly based on theorem proving. We build a dynamic logic called 'clock-based dynamic logic' (cDL) to capture the CCSL specifications and build a proof calculus to analyze the schedule problem of the specifications. Comparing with previous approaches, our method benefits from the dynamic logic that provides a natural way of capturing the dynamic behaviour of CCSL and a divide-and-conquer way for 'decomposing' a complex formula into simple ones for an SMT-checking procedure. Based on cDL, we outline a method for the schedulability analysis of CCSL. We illustrate our theory through one example.

关键词： Clocks Schedules Dynamic scheduling Calculus Semantics Encoding Syntactics

Efficient parallel simulation of blood flows in abdominal aorta

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arXiv 2019年

作者： Qin, Shanlin Chen, Rongliang Wu, Bokai Liu, Jia Shiu, Wen-Shin Yan, Zhengzheng Cai, Xiao-Chuan Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences China Department of Computer Science University of Colorado BoulderCO80309-0430 United States

It is known that the maximum diameter for the rupture-risk assessment of the abdominal aortic aneurysm is a generally good method, but not sufficient. Alternative features obtained with computational modeling may provide additional useful criteria. Though computational approaches are noninvasive, they are often time-consuming because of the high computational complexity. In this paper, we present a highly parallel algorithm for the numerical simulation of unsteady blood flows in the patient-specific abdominal aorta. We model the blood flow with the unsteady incompressible Navier-Stokes equations, and solve the discretized system with a highly scalable domain decomposition method. With this approach, the complete flow field can be obtained in less than an hour, instead of days with older methods. We show experimentally that the proposed method offers accurate solutions of the pressure, the velocity and the wall shear stress, and the parallel efficiency is higher than 70% on a parallel computer with more than 1, 000 processor cores. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

On the complexity of an augmented lagrangian method for nonconvex optimization

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arXiv 2019年

作者： Grapiglia, Geovani N. Yuan, Ya-Xiang Departamento de Matemática Universidade Federal do Paraná Centro Politécnico Cx. postal 19.081 Paraná Curitiba81531-980 Brazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China

In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of O(| log(ǫ)|) outer iterations for the referred algorithm to generate an ǫ-approximate KKT point, for ǫ ∈ (0, 1). When the penalty parameters are unbounded, we prove an outer iteration complexity bound of O (ǫ−2/(α−1)), where α > 1 controls the rate of increase of the penalty parameters. For linearly constrained problems, these bounds yield to evaluation complexity bounds of O(| log(ǫ)|2ǫ−2) and O ( ǫ− ( 2(2+ α−1 α) +2 )), respectively, when appropriate first-order methods (p = 1) are used to approximately solve the unconstrained subproblems at each iteration. In the case of problems having only linear equality constraints, the latter bounds are improved to O(| log(ǫ)|2ǫ−(p+1)/p) and O ( ǫ− ( α−4 1 + p+1 p )), respectively, when appropriate p-order methods (p ≥ 2) are used as inner solvers. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear programming

LOW MACH NUMBER LIMIT AND FAR FIELD CONVERGENCE RATES OF POTENTIAL FLOWS IN MULTI-DIMENSIONAL NOZZLES WITH AN OBSTACLE INSIDE

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arXiv 2020年

作者： Ma, Lei Wang, Tian-Yi Xie, Chunjing School of Mathematical Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China Department of Mathematics School of Science Wuhan University of Technology 122 Luoshi Road Wuhan Hubei430070 China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing and SHL-MAC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

This paper considers the low Mach number limit and far field convergence rates of steady Euler flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, the well-posedness theory for both incompressible and compressible subsonic flows with external forces in multidimensional nozzle with an obstacle inside are established by several uniform estimates. The uniformly subsonic compressible flows tend to the incompressible flows as quadratic order of Mach number as the compressibility parameter goes to zero. Furthermore, we also give the convergence rates of both incompressible flow and compressible flow at far fields as the boundary of nozzle goes to flat even when the forces do not admit convergence rate at far fields. The convergence rates obtained for the flows at far fields clearly describe the effects of the external force. Copyright © 2020, The Authors. All rights reserved.

关键词： Nozzles

One family of 13315 stable periodic orbits of the non-hierarchical unequal-mass triple system

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arXiv 2020年

作者： Li, Xiaoming Li, Xiaochen Liao, Shijun MOE Key Laboratory of Disaster Forecast and Control in Engineering School of Mechanics and Construction Engineering Jinan University Guangzhou510632 China Department of Earth Atmospheric and Planetary Sciences Massachusetts Institute of Technology CambridgeMA02139 United States School of Civil Engineering and Transportation South China University of Technology Guangzhou510641 China Department of Engineering Science University of Oxford OxfordOX1 3PJ United Kingdom Center of Advanced Computing School of Naval Architecture Ocean and Civil Engineering Shanghai Jiaotong University Shanghai200240 China School of Physics and Astronomy Shanghai Jiaotong University Shanghai200240 China

The three-body problem has been studied for more than three centuries1, 2, and has received much more attention in recent years3–5. It shows complex dynamical phenomena due to the mutual gravitational interaction of the three bodies. Triple systems are common in astronomy, but all observed periodic triple systems are hierarchical up till now6–8. It is traditionally believed that bound non-hierarchical triple systems are almost unstable and disintegrate into a stable binary system and a single star5, and thus stable periodic orbits of non-hierarchical triple systems are rather scarce. Here we report one family of 13315 stable periodic orbits of the non-hierarchical triple system with unequal mass. Compared with the narrow mass region (only 10−5) of the stable figure-eight solution9, our newly-found stable periodic orbits can have fairly large mass region. It is found that many of these newly-found stable periodic orbits have the mass ratios close to those of the hierarchical triple systems that have been measured by the astronomical observation. It implies that these stable periodic orbits of the non-hierarchical triple system with distinctly unequal masses can be quite possibly observed in practice. Our investigation also suggests that there should exist an infinite number of stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses. Obviously, these stable periodic orbits of the non-hierarchical unequal-mass triple system have broad impact for the astrophysical scenario: they could inspire the theoretical and observational study of the non-hierarchical triple system, the formation of triple stars6, the gravitational waves pattern10 and the gravitational waves observation11 of the non-hierarchical triple system. Copyright © 2020, The Authors. All rights reserved.

关键词： Gravitational effects

On the clean numerical simulation(CNS) of chaotic dynamic systems

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Journal of Hydrodynamics 2017年第5期29卷 729-747页

作者：廖世俊 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China MOE Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong UniversityShanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of ＂true＂（convergent） solution and numerical noises at the same level. Today, this defect can be overcome by means of the ＂clean numerical simulation＂（CNS） with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent（reliable） chaotic solutions can be obtained in an arbitrary long（but finite） interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are ＂self-excited＂, i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.

关键词： Chaos reliable numerical simulation clean numerical simulation（CNS） three-body problem turbulence origin of randomness

Photocatalytic Hydrogen Production on a sp2-Carbon-Linked Covalent Organic Framework

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Angewandte Chemie 2022年第42期134卷

作者： Si Ma Prof. Dr. Tianqi Deng Dr. Ziping Li Zhenwei Zhang Ji Jia Qizhen Li Prof. Dr. Gang Wu Prof. Dr. Hong Xia Prof. Dr. Shuo-Wang Yang Prof. Dr. Xiaoming Liu College of Chemistry Jilin University Changchun 130012 P.R. China Institute of Advanced Semiconductors & Zhejiang Provincial Key Laboratory of Power Semiconductor Materials and Devices ZJU-Hangzhou Global Scientific and Technological Innovation Center Hangzhou 311200 P.R. China State Key Laboratory of Silicon Materials & School of Materials Science and Engineering Zhejiang University Hangzhou 310027 P.R. China Department of Biomedical Engineering Southern University of Science and Technology Shenzhen 518055 P.R. China Institute of High Performance Computing Agency for Science Technology and Research 1 Fusionopolis Way #16-16 Connexis Singapore 138632 Singapore State Key Laboratory on Integrated Optoelectronics College of Electronic Science and Technology Jilin University Changchun 130012 P.R. China

Two-dimensional covalent organic frameworks (2D-COFs) have emerged as attractive platforms for solar-to-chemical energy conversion. In this study, we have implemented a gradient heating strategy to synthesize a sp 2 -carbon-linked triazine-based COF, COF-JLU100, exhibiting high crystallinity, large surface area, good durability and carrier mobility for solar-driven photocatalytic hydrogen evolution. The Pt-doped COF-JLU100 demonstrated a high hydrogen evolution rate of over 100 000 μmol g −1 h −1 for water splitting under visible-light illumination (λ>420 nm). Experimental and theoretical studies corroborate that the cyano-vinylene segments in COF-JLU100 extend the π-delocalization and enable fast charge transfer and separation rates as well as good dispersion in water. Moreover, COF-JLU100 can be prepared by low-cost and easily available monomers and has excellent stability, which is desirable for practical solar-driven hydrogen production.

关键词： Covalent Organic Frameworks Gradient Heating Hydrogen Evolution Photocatalysis sp2 Carbon Linkage

Low-rank matrix optimization using polynomial-filtered subspace extraction

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arXiv 2019年

作者： LI, YONGFENG LIU, HAOYANG WEN, ZAIWEN YUAN, YAXIANG Beijing International Center for Mathematical Research Peking University China Beijing International Center for Mathematical Research Peking University State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScinceChinese Academy of Sciences China

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at each iteration which takes most of the computation time. In order to reduce the cost, we propose an inexact algorithm framework based on a polynomial subspace extraction. The idea is to use an additional polynomial-filtered iteration to extract an approximated eigenspace, and project the iteration matrix on this subspace, followed by an optimization update. The accuracy of the extracted subspace can be controlled by the degree of the polynomial filters. This kind of subspace extraction also enjoys the warm start property: The subspace of the current iteration is refined from the previous one. Then this framework is instantiated into two algorithms: The polynomial-filtered proximal gradient method and the polynomial-filtered alternating direction method of multipliers. We give a theoretical guarantee to the two algorithms that the polynomial degree is not necessarily very large. They share the same convergence speed as the corresponding original methods if the polynomial degree grows with an order (log k) at the k-th iteration. If the warm-start property is considered, the degree can be reduced to a constant, independent of the iteration k. Preliminary numerical experiments on several low-rank matrix optimization problems show that the polynomial filtered algorithms usually provide multi-fold speedups. Copyright © 2019, The Authors. All rights reserved.

关键词： Extraction

Impacts of prior parameter distributions on Bayesian evaluation of groundwater model complexity

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Water Science and engineering 2018年第2期11卷 89-100页

作者： Saeideh Samani Ming Ye Fan Zhang Yong-zhen Pei Guo-ping Tang Ahmed Elshall Asghar A.Moghaddam Department of Earth Sciences University of Tabriz Department of Scientific Computing Florida State University School of Computer Science and Software Engineering Tianjin Polytechnic University Department of Earth Ocean and Atmospheric Science Florida State University Key Laboratory of Tibetan Environment Changes and Land Surface Processes Institute of Tibetan Plateau Research Chinese Academy of Sciences Environmental Sciences Division Oak Ridge National Laboratory

This study used the marginal likelihood and Bayesian posterior model probability for evaluation of model complexity in order to avoid using over-complex models for numerical simulations. It focused on investigation of the impacts of prior parameter distributions(involved in calculating the marginal likelihood) on the evaluation of model complexity. We argue that prior parameter distributions should define the parameter space in which numerical simulations are made. New perspectives on the prior parameter distribution and posterior model probability were demonstrated in an example of groundwater solute transport modeling with four models, each simulating four column experiments. The models had different levels of complexity in terms of their model structures and numbers of calibrated parameters. The posterior model probability was evaluated for four cases with different prior parameter distributions. While the distributions substantially impacted model ranking, the model ranking in each case was reasonable for the specific circumstances in which numerical simulations were made. For evaluation of model complexity, it is thus necessary to determine the parameter spaces for modeling, which can be done by conducting numerical simulation and usineg engineering judgment based on understanding of the system being studied.

关键词： Marginal likelihood Posterior model probability Advection-dispersion equation Mobile-immobile model Groundwater model