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数学研究 2018年第1期51卷 89-114页

作者： Lin Wang Haijun Yu School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing 100190 China

Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the Cahn-Hilliard equation with provable unconditional stability. In this scheme the non-linear bulk force are treated explicitly with two second-order linear stabilization terms. The semi-discretized equation is a linear elliptic system with constant coefficients, thus robust and efficient solution procedures are guaranteed. Rigorous error analysis show that, when the time step-size is small enough, the scheme is second order accurate in time with a prefactor controlled by some lower degree polynomial of 1/ε. Here ε is the interface thickness parameter. Numerical results are presented to verify the accuracy and efficiency of the scheme.

关键词： phase field model Cahn-Hilliard equation unconditionally stable stabilized semi-implicit scheme high order time marching

Activating Bip-orbitals in Dispersed Clusters of Amorphous BiOxfor Electrocatalytic Nitrogen Reduction

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Angewandte Chemie 2023年第15期135卷

作者： Dr. Jianxin Kang Xiangyu Chen Rutong Si Prof. Xiang Gao Prof. Shuo Zhang Prof. Gilberto Teobaldi Prof. Annabella Selloni Li-Min Liu Prof. Lin Guo School of Chemistry Beijing Advanced Innovation Center for Biomedical Engineering Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology Beihang University Beijing 100191 China Beijing Computational Science Research Center Beijing 100193 China School of Physics Beihang University Beijing 100191 China Center for High Pressure Science and Technology Advanced Research Beijing 100190 China Shanghai Synchrotron Radiation Facility Shanghai Institute of Applied Physics Chinese Academy of Sciences Shanghai 201204 China Scientific Computing Department STFC UKRI Rutherford Appleton Laboratory Didcot OX11 0QX UK School of Chemistry University of Southampton Highfield Southampton SO17 1BJ UK Department of Chemistry Princeton University Princeton NJ 08544 USA

Catalytic strategies based on main group metals are significantly less advanced than those of transition metal catalysis, leaving untapped areas of potentially fruitful research. We here demonstrate an effective approach for the modulation of Bi 6p energy levels during the construction of atomically dispersed clusters of amorphous BiO x . Bi oxidation state is proposed to strongly affects the nitrogen fixation activity, with the half-occupied p z orbitals of the Bi 2+ ions being highly efficient toward electron injection into the inert N 2 molecule. With sufficient catalytic sites to adsorb and activate N 2 , the bonding between N 2 and catalyst is able to be in situ identified. The catalyst shows an outstanding Faraday efficiency (≈30 %) and high yield (≈113 μg h −1 mg −1 cat ) in NH 3 production, outperforming most of the existing catalysts in aqueous solution. These results lay the basis for developing the potential of p- block elements for catalysis of multi-electron reactions.

关键词： Amorphous Nanomaterial Electrocatalysis In Situ Identification Nitrogen Fixation p-Orbitals

An Adaptive Lagrangian Algorithm for Optimal Portfolio Deleveraging with Cross-Impact

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Journal of Systems Science & Complexity 2017年第5期30卷 1121-1135页

作者： XU Fengmin SUN Min DAI Yuhong School of Economics and Finance Xi'an Jiaotong UniversityXi'an 710049China School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Science//Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program with box constraints and a singly quadratic constraint. Under some assumptions, the authors give an optimal trading priority and show that the optimal solution must be achieved when the quadratic constraint is active. Further, the authors propose an adaptive Lagrangian algorithm for the model, where a piecewise quadratic root-finding method is used to find the Lagrangian multiplier. The convergence of the algorithm is established. The authors also present some numerical results, which show the usefulness of the algorithm and validate the optimal trading priority.

关键词： Adaptive Lagrangian algorithm deleveraging price cross-impact

Peter H. Rose - Father of Ion Implantation: The Early Years

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Peter H. Rose - Father of Ion Implantation: The Early Years

International Conference on Ion Implantation Technology (IIT)

作者： Andrew Wittkower Geoffrey Ryding ESAT/STADIUS Center for Dynamical Systems Signal Processing and Data Analytics KU Leuven Leuven Belgium State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In 1996, President Clinton presented Peter Rose with the National Medal of Technology and Innovation. This paper describes his innovations in ion implantation technology which led to the award presented twenty years l... 详细信息

ISBN: (纸本)9781538668306

关键词： Ion implantation Ion sources Business Technological innovation Acceleration Particle beams

A Gradient enhanced 1-minimization for sparse approximation of polynomial chaos expansions

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arXiv 2018年

作者： Guo, Ling Narayan, Akil Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Mathematics Department and Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT84112 United States Institute of Computational Mathematics and Scientific Engineering Computing Amss Chinese Academy of Sciences Beijing China

We investigate a gradient-enhanced 1-minimization for constructing sparse polynomial chaos expansions. In addition to function evaluations, measurements of the function gradient is also included to accelerate the identification of expansion coeficients. By designing appropriate preconditioners to the measurement matrix, we show gradient-enhanced 1 minimization leads to stable and accurate coeficient recovery. The framework for designing preconditioners is quite general and it applies to recover of functions whose domain is bounded or unbounded. Comparisons between the gradient enhanced approach and the standard 1-minimization are also presented and numerical examples suggest that the inclusion of derivative information can guarantee sparse recovery at a reduced computational cost. Copyright © 2018, The Authors. All rights reserved.

关键词： Recovery

Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrödinger equation

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arXiv 2018年

作者： Chen, Chuchu Hong, Jialin Ji, Lihai Department of Mathematics Michigan State University Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a kind of damped stochastic nonlinear Schrödinger equation with multiplicative noise. It is shown that the stochastic conformal multi-symplectic method preserves the discrete stochastic conformal multi-symplectic conservation law, the discrete charge exponential dissipation law almost surely, and we also deduce the recurrence relation of the discrete global energy. Numerical experiments are preformed to verify the good performance of the proposed stochastic conformal multi-symplectic method, compared with a Crank-Nicolson type method. Finally, we present the mean square convergence result of the proposed numerical method in temporal direction numerically.60H15, 37K05, 65P10 Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

A foundation model for atomistic materials chemistry

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arXiv 2023年

作者： Batatia, Ilyes Benner, Philipp Chiang, Yuan Elena, Alin M. Kovács, Dávid P. Riebesell, Janosh Advincula, Xavier R. Asta, Mark Avaylon, Matthew Baldwin, William J. Berger, Fabian Bernstein, Noam Bhowmik, Arghya Blau, Samuel M. Cărare, Vlad Darby, James P. De, Sandip Pia, Flaviano Della Deringer, Volker L. Elijošius, Rokas El-Machachi, Zakariya Falcioni, Fabio Fako, Edvin Ferrari, Andrea C. Genreith-Schriever, Annalena George, Janine Goodall, Rhys E.A. Grey, Clare P. Grigorev, Petr Han, Shuang Handley, Will Heenen, Hendrik H. Hermansson, Kersti Holm, Christian Hofmann, Stephan Jaafar, Jad Jakob, Konstantin S. Jung, Hyunwook Kapil, Venkat Kaplan, Aaron D. Karimitari, Nima Kermode, James R. Kroupa, Namu Kullgren, Jolla Kuner, Matthew C. Kuryla, Domantas Liepuoniute, Guoda Margraf, Johannes T. Magdău, Ioan-Bogdan Michaelides, Angelos Harry Moore, J. Naik, Aakash A. Niblett, Samuel P. Norwood, Sam Walton O’Neill, Niamh Ortner, Christoph Persson, Kristin A. Reuter, Karsten Rosen, Andrew S. Schaaf, Lars L. Schran, Christoph Shi, Benjamin X. Sivonxay, Eric Stenczel, Tamás K. Svahn, Viktor Sutton, Christopher Swinburne, Thomas D. Tilly, Jules van der Oord, Cas Vargas, Santiago Varga-Umbrich, Eszter Vegge, Tejs Vondrák, Martin Wang, Yangshuai Witt, William C. Zills, Fabian Csányi, Gábor Engineering Laboratory University of Cambridge Trumpington St and JJ Thomson Ave Cambridge United Kingdom Berlin Germany Department of Materials Science and Engineering University of California BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Mathematics Department University of British Columbia 1984 Mathematics Rd VancouverBCV6T 1Z2 Canada Institute of Condensed Matter Theory and Solid State Optics Friedrich Schiller University Jena Germany Molecular Foundry Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Bayreuth Germany Fritz-Haber-Institute of the Max-Planck-Society Berlin Germany Energy Technologies Area Lawrence Berkeley National Laboratory BerkeleyCA94720 United States U. S. Naval Research Laboratory WashingtonDC20375 United States Yusuf Hamied Department of Chemistry University of Cambridge Lensfield Road Cambridge United Kingdom Cavendish Laboratory University of Cambridge J. J. Thomson Ave Cambridge United Kingdom Department of Materials Science and Metallurgy University of Cambridge 27 Charles Babbage Road CambridgeCB3 0FS United Kingdom Chemix Inc. SunnyvaleCA94085 United States Inorganic Chemistry Laboratory Department of Chemistry University of Oxford OxfordOX1 3QR United Kingdom Scientific Computing Department Science and Technology Facilities Council Daresbury Laboratory Keckwick Lane DaresburyWA4 4AD United Kingdom BASF SE Carl-Bosch-Straße 38 Ludwigshafen67056 Germany Kavli Institute for Cosmology University of Cambridge Madingley Road CambridgeCB3 0HA United Kingdom Department of Chemistry and Biochemistry University of South Carolina South Carolina29208 United States Lennard-Jones Centre University of Cambridge Trinity Ln CambridgeCB2 1TN United Kingdom Institute for Computational Physics University of Stuttgart Stuttgart70569 Germany Department of Chemistry–Ångström Uppsala University Box 538 Uppsala

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest;and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model — and its qualitative and at times quantitative accuracy — on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

One-Bit precoding and constellation range design for massive MIMO with QAM Signaling

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arXiv 2018年

作者： Sohrabi, Foad Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S3G4 Canada State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing100190 China

The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpreted as a decrease in the effective minimum distance of the QAM constellation. Using the obtained SER expression, we propose a QAM constellation range design for the singleuser case. It is shown that in the massive MIMO limit, a reasonable choice for constellation range with one-bit precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of p 2/π or about 0:8. The corresponding minimum distance reduction translates to about 2dB gap between the performance of one-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity heuristic algorithm for one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multi-user downlink. We propose to scale the constellation range for infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of p 2/π for one-bit precoding. The proposed one-bit precoding scheme is shown to be within 2dB of infinite-resolution ZF. In term of number of antennas, one-bit precoding requires about 50% more antennas to achieve the same performance as infinite-resolution precoding. Copyright © 2018, The Authors. All rights reserved.

关键词： Quadrature amplitude modulation

An adaptive multi-fidelity pc-based ensemble kalman inversion for inverse problems

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arXiv 2018年

作者： Yan, Liang Zhou, Tao Department of Mathematics Southeast University Nanjing210096 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by high dimensional nonlinear PDEs, as EKI requires a relatively large ensemble size to guarantee its performance. In this paper, we propose an adaptive multi-fidelity polynomial chaos (PC) based EKI technique to address this challenge. Our new strategy combines a large number of low-order PC surrogate model evaluations and a small number of high-fidelity forward model evaluations, yielding a multi-fidelity approach. Especially, we present a new approach that adaptively constructs and refines a multi-fidelity PC surrogate during the EKI simulation. Since the forward model evaluations are only required for updating the low-order multifidelity PC model, whose number can be much smaller than the total ensemble size of the classic EKI, the entire computational costs are thus significantly reduced. The new algorithm was tested through the two-dimensional time fractional inverse diffusion problems and demonstrated great effectiveness in comparison with PC based EKI and classic EKI. Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

Thermal Stress and Reliability Analysis of TSV-Based 3-D ICs With a Novel Adaptive Strategy Finite Element Method

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Thermal Stress and Reliability Analysis of TSV-Based 3-D ICs...

作者： Zhou, Hao Zhu, Hengliang Cui, Tao Pan, David Z. Zhou, Dian Zeng, Xuan State Key Laboratory of ASIC and Systems Department of Microelectronics Fudan University Shanghai200433 China State Key Laboratory of Scientific and Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China Department of Electrical and Computer Engineering University of Texas at Austin AustinTX78712 United States Department of Electrical Engineering University of Texas at Dallas RichardsonTX75080 United States

Thermomechanical stress is one of the most important issues in performance and reliability analysis of through silicon via-based 3-D integrated circuits (3-D ICs), where an accurate numerical approach is generally needed to produce stress models and identify weak points in the structure. In this paper, we propose a knowledge-oriented nonuniform (KONU) refinement strategy for 3-D IC stress simulation under the framework of a parallel adaptive finite element method (FEM), and apply it in 3-D IC stress and reliability analysis. Parallel adaptive FEM is promising for solving large-scale problems due to its high accuracy and parallel efficiency. It produces refined meshes based on the a posteriori error analysis, which has the quasi-optimal convergence rate for solving the problem. It has high parallel efficiency, which makes it suitable for handling large and complex structures in 3-D ICs. The KONU refinement strategy developed in this paper can efficiently reduce the number of refinement iterations in parallel adaptive FEM for 3-D IC thermomechanical stress simulation and improves the computational efficiency. It is demonstrated in this paper through several examples that parallel adaptive FEM for thermomechanical stress evaluation can be widely applied in 3-D IC reliability analysis, where accurate stress simulation and modeling is exceptionally important to produce accurate results. © 2018 IEEE.

关键词： Reliability analysis