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arXiv 2019年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China Department of Mathematics and International Center for Mathematics Southern University of Science and Technology Shenzhen Guangdong Province China Division of Science and Technology BNU-HKBU United International College Zhuhai Guangdong Province China NCMIS and LSEC Inst. of Compl. Math. and Sci./Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of consistency error, we present sharp maximum-norm error estimates which reflect the temporal regularity. As our analysis is built on nonuniform time steps, we may resolve the intrinsic initial singularity by using the graded meshes. Moreover, we propose an adaptive time-stepping strategy for large time simulations. Numerical experiments are presented to show the effectiveness of the proposed scheme. This seems to be the first second-order maximum principle preserving scheme for the time-fractional Allen-Cahn *** Codes 35Q99, 65M06, 65M12, 74A50 Copyright © 2019, The Authors. All rights reserved.

关键词： Maximum principle

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Phase field simulation of stress evolution during solidification

Phase field simulation of stress evolution during solidifica...

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Proceedings of the 14th International Conference on Crystal Growth and the 12th Internatioanl Conference on Vapor Growth and Epitaxy

作者： Uehara, Takuya Tsujino, Takahiro Dept. of Energy Conversion Science Graduate School of Energy Science Kyoto University Yoshida Hon-machi Sakyo-ku Kyoto 606-8501 Japan Dept. of Compl. Sci. and Engineering Nagoya University Furo-cho Chikusa-ku Nagoya 464-8603 Japan

Stress evolution during solidification is simulated by using the phase field model. The coupling equations for phase transformation, temperature and stress/strain are derived based on thermo-dynamical theory including elastic strain energy, which is summarized as follows: phase transformation is governed by the phase field equation in which not only temperature but also stress are introduced as parameters. In the heat conduction equation, the effect of latent heat generation due to phase change and the heat generation due to mechanical work are taken into account. The volumetric change associated with temperature variation and phase transformation is expressed in the constitutive equation, while, in this paper, the stress or flow in liquid is neglected for simplicity. In order to verify the efficiency of these equations, numerical simulations are carried out by using a simple model of the finite element method. The effects of transformation expansion coefficient for two cases of dilatation and contraction are simulated, and qualitatively adequate results are presented. © 2004 Elsevier B.V. All rights reserved.

关键词： Stress analysis

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Erratum: Numerical implementation of exact analytical solution for oblique propagation in a cholesteric liquid crystal (Microwave Opt Technol Lett (2002) 35 (397-400))

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Microwave and Optical Technology Letters 2005年第2期44卷 205-205页

作者： Polo, Jr., John A. Lakhtakia, Akhlesh Department of Physics Edinboro University of Pennsylvania Edinboro PA 16444 United States Compl. and Theor. Mat. Sci. Group Department of Engineering Science Pennsylvania State University University Park PA 16802-6812 United States

No abstract available

关键词： cholesteric liquid crystal matrix polynomial propagation

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Don't try to control everything!: An emergent morphology control of a modular robot

Don't try to control everything!: An emergent morphology con...

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2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Ishiguro, Akio Shimizu, Masahiro Kawakatsu, Toshihiro Dept. of Compl. Sci. and Engineering Nagoya University Nagoya Japan Dept. of Physics Tohoku University Sendai Japan

ISBN: (纸本)0780384636

This paper discusses a fully decentralized algorithm able to control the morphology of a modular robot, consisting of many identical modules, according to the environment encountered. One of the significant features of our approach is that we explicitly exploit "emergent phenomena" stemming from the interaction between control and mechanical dynamics in order to control the morphology in real time. To this end, we particularly focus on a "functional material" and a "mutual entrainment", the former of which is used as a connection mechanism between the modules, and the latter of which plays as the core of the control mechanism for the generation of locomotion. Simulation results indicate that the proposed algorithm can induce "protoplasmic streaming", which allows us to successfully control the morphology of modular robot in real time according to the situation without losing the coherence of the entire system.

关键词： Modular robots

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Responses of slanted chiral sculptured thin films to plane waves and finite sources

Responses of slanted chiral sculptured thin films to plane w...

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Nanomodeling

作者： Wang, Fei Lakhtakia, Akhlesh Compl. and Theor. Mat. Sci. Grp. Department of Engineering Science Pennsylvania State University University Park PA 16802 United States

A theoretical investigation of the electromagnetic responses of a slanted chiral sculptured thin film (STF) to both plane waves and finite sources (such as optical beams and dipolar sources) was carried out. First, a rigorous coupled-wave analysis was implemented with algorithmic stability to obtain the planewave response;second, the angular-spectrum decomposition of the incident field was exploited to represent the reflected and the transmitted fields. The most prominent feature of the planewave responses is the circular Bragg phenomenon which is partially specular and angularly asymmetric for slanted, but nor for unslanted, chiral STFs. Correspondingly, the far-field radiation pattern of a Beltrami source configuration is spatially asymmetric in the presence of a slanted chiral STF. Also, optical beams are laterally shifted on reflection by chiral STFs. Two types of lateral shifts of Gaussian beams were studied: one is related to the Bragg reflection of co-handed beams, and the other is the Goos-Hänchen shift on total reflection.

关键词： Thin films

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How mature is nonlinear optimization?

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Applied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress

作者： Gould, Nick Toint, Philippe L. Rutherford Appleton Laboratory United Kingdom University of Namur Belgium Compl. Sci./Engineering Department Rutherford Appleton Laboratory Chilton United Kingdom Department of Mathematics University of Namur Belgium

ISBN: (纸本)0898715598

Numerical methods for solving nonlinear optimization problems have been developed for over 50 years. Has this field reached maturity? What are the current research frontiers and ongoing challenges? These are questions that this paper attempts to clarify, if not fully answer. The discussion does not explore the technical intricacies of nonlinear optimization techniques, but instead focusses on concepts and research practice. The field's vibrant nature is illustrated by a number of applications, such as adaptive lens design for spectacles, the piloting of injection of dangerous drugs to patients, the identification of parameters in biochemical models of neurons, food sterilisation or animation techniques for video games.

关键词： Optimization

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Assessment of large-scale pressurized thermal shock experiments using the FAVOR fracture mechanics computer code

Assessment of large-scale pressurized thermal shock experime...

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2004 ASME/JSME Pressure Vessels and Piping Conference

作者： Dickson, T.L. Kirk, M.T. Compl. Sci. and Engineering Division Oak Ridge National Laboratory Oak Ridge TN United States Off. of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington DC

Large-scale, experiments of pressure vessels performed at the Oak National Laboratory (ORNL)1 in the mid 1980s validated the applicability of the linear-elastic fracture mechanics (LEFM) computational methodology for application to fracture analysis of reactor pressure vessels (RPVs) in nuclear power plants. The current federal regulations to insure that nuclear RPVs maintain their structural integrity, when subjected to transients such as pressurized thermal shock (PTS) events, were derived in the early-mid 1980s from a comprehensive computational methodology of which LEFM is a major element. Recently, the United States Nuclear Regulatory Commission (USNRC) has conducted the PTS re-evaluation project that has the objective to establish a technical basis for a potential relaxation to the current PTS regulations which could have profound implications for plant license-extension considerations. The PTS re-evaluation project has primarily consisted of the development and application of an updated risk-based computational methodology that has been implemented into the Fracture Analysis of Vessels: Oak Ridge (FAVOR) computer code. LEFM continues to be a major element of the updated computational methodology. As part of the PTS re-evaluation program, there has been an extensive effort to validate that FAVOR has an accurate implementation of the LEFM methodology. This effort has consisted of the successful benchmarking of thermal analysis, stress analysis, and LEFM fracture analysis results between FAVOR and ABAQUS, a commercial general-purpose finite element computer code that has fracture mechanics capabilities, for a range of transient descriptions. The NRC has also participated in international round-robin benchmarking exercises in which FAVOR-generated solutions to well-specified PTS problems have been compared to solutions generated by other research institutions. A more fundamental aspect of the ongoing validation of FAVOR is demonstration that FAVOR can be used to

关键词： Pressure vessels

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Size effects of hair-sized structures -torsion

Size effects of hair-sized structures -torsion

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Advances in Fracture and Failure Prevention: Proceedings of the Fifth International Conference on Fracture and Strength of Solids (FEOFS2003): Second International Conference on Physics and Chemistry of Fracture and Failure Prevention (2nd ICPCF)

作者： Tong, Pin Yang, Fan Lam, David C.C. Wang, Jun Department of Mechanical Engineering Hong Kong Univ. of Sci./Technology Clear Water Bay Kowloon Hong Kong Inst. of Compl. Eng. and Science Southwest Jiaotong University Chengdu 610031 Sichuan China

Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include the strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scaled structure. This paper focus on the structural size effects on torsion of cylinders. The torsional stiffness of cylinders can be higher than conventional expectation when the cylinder size is in the nanometer - or micron-scale. Following the Saint-Venant theory of torsion, we established the equation of torsion in terms of the warping function on the basis of the nano-mechanical theory of elasticity. The torsional equations contain two higher order material length scale parameters and two conventional Lame constants. The equilibrium equation is a fourth order partial differential equation which can be reduced to two second order equations. Two formulations in terms of pseudo warping function and stress function are presented. Closed-form solutions for circular and thin wall section and series solutions for rectangular microbars have been obtained. The total torque depends only on the stresses conjugated to the strain and is only implicitly dependent on the higher order stress metrics. The solution reveals that the torsional rigidity is dependent on the higher order length scale parameters and strain gradients and increases asymptotically upward when the cylinder size is reduced to the size of the higher order length scale material parameters. The increase is most marked for thin walled cylinders, stiffening to more then 10 times the conventional value when the cylinder size is near that of the higher order length scaled parameters.

关键词： Torsional stress

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Independent component analysis for color indexing

Independent component analysis for color indexing

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作者： Zeng, Xiang-Yan Chen, Yen-Wei Nakao, Zensho Cheng, Jian Lu, Hanqing Faculty of Engineering Univ. of the Ryukyus Okinawa-ken 903-0213 Japan Inst. for Compl. Sci./Engineering Ocean Univ. of Qingdao Shandong China Natl. Lab. of Pattern Recognition Chinese Academy of Sciences China

Color histograms are effective for representing color visual features. However, the high dimensionality of feature vectors results in high computational cost. Several transformations, including singular value decomposition (SVD) and principal component analysis (PCA), have been proposed to reduce the dimensionality. In PCA, the dimensionality reduction is achieved by projecting the data to a subspace which contains most of the variance. As a common observation, the PCA basis function with the lowest frquency accounts for the highest variance. Therefore, the PCA subspace may not be the optimal one to represent the intrinsic features of data. In this paper, we apply independent component analysis (ICA) to extract the features in color histograms. PCA is applied to reduce the dimensionality and then ICA is performed on the low-dimensional PCA subspace. The experimental results show that the proposed method (1) significantly reduces the feature dimensions compared with the original color histograms and (2) outperforms other dimension reduction techniques, namely the method based on SVD of quadratic matrix and PCA, in terms of retrieval accuracy.

关键词： Independent component analysis

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FDTD simulation of 3-D surface plasmon polariton band gap waveguide structures

FDTD simulation of 3-D surface plasmon polariton band gap wa...

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IEEE Antennas and Propagation Society Symposium 2004 Digest held in Conjunction with: USNC/URSI National Radio sci.nce Meeting

作者： Lu, Meng Lu, Mingyu Carney, P. Scott Michielssen, Eric Ctr. for Compl. Electromagnetics Department of Electrical Engineering Univ. Illinois at Urbana-Champaign Urbana IL 61801 Beckman Inst. Adv. Sci. and Technol. Department of Electrical Engineering Univ. Illinois at Urbana-Champaign Urbana IL 61801

The implementation of a three-dimensional (3D) finite difference time domain (FDTD) scheme for simulating wave propagation in surface plasmon polaritons bandgap (SPPBG) waveguides, was investigated. An SPPBG structure resulted on introducing a doubly periodic perturbation in planar dielectric-plasma interface. In the direction normal to dielectric-plasma interface, the plasma half space was truncated by a perfect electrically conducting plate. The results show that straight SPPBG waveguide section allows signals to propagate with small losses.

关键词： Optical waveguides

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