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High-accurate and efficient numerical algorithms for the self-consistent field theory of liquid-crystalline polymers

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Computers & Mathematics with Applications 2025年 194卷 31-52页

作者： Zhijuan He Kai Jiang Liwei Tan Xin Wang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240 China

Self-consistent field theory (SCFT) is one of the most widely-used frameworks in studying the equilibrium phase behavior of inhomogeneous polymers. For liquid-crystalline polymeric systems, the primary numerical challenges in solving SCFT involve efficiently solving a large number of 6-dimensional (6D, 3D space + 2D orientation + 1D contour) partial differential equations (PDEs), accurately determining subtle energy differences between self-assembled structures, and developing effective iterative methods for nonlinear SCFT iterations. To address these challenges, this work introduces a suite of high-order and efficient numerical methods tailored to SCFT of liquid-crystalline polymers. These methods include various advanced PDE solvers, an improved Anderson iteration algorithm to accelerate SCFT calculations, and an optimization technique for adjusting the computational domain during SCFT iterations. Extensive numerical tests demonstrate the efficiency of the proposed methods. Based on these algorithms, we further explore the self-assembly behavior of liquid-crystalline polymers through 4D, 5D, and 6D simulations, uncovering intricate 3D spatial structures.

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3D LOD-FDTD for the Multi-Pole Debye Dispersive Media Using Z-Transform

3D LOD-FDTD for the Multi-Pole Debye Dispersive Media Using ...

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2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022

作者： Hou, Guilin Song, Ziheng Xie, Guoda Pan, Pan Huang, Zhixiang Anhui University School of Electronic and Information Engineering Hefei China Education of Anhui Province Anhui Province Key Laboratory of Target Recognition and Feature Extraction Anhui Luan237000 China Ministry of Education The Key Laboratory of Intelligent Computing and Signal Processing Hefei China Anhui Province Anhui University Key Laboratory of Electromagnetic Environmental Sensing Hefei230601 China Anhui University Hefei China

ISBN: (纸本)9781665452366

This paper introduces the application of unconditionally stable locally one-dimensional finite-difference time-domain(LOD-FDTD) method to 3D multi-pole Debye dispersive media model. Compared with other methods for dispersive media, the Z-transform method does not need to retain the electromagnetic values of the previous moments, has less memory footprint, and its numerical implementation is more straightforward. Through numerical examples, ZT-LOD-FDTD shows the advantages of accuracy and high computational efficiency. © 2022 IEEE.

关键词： Poles

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High order SF-SFDTD method for solving the time-dependent Schrödinger equation

High order SF-SFDTD method for solving the time-dependent Sc...

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2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022

作者： Pan, Pan Xie, Guoda Huang, Zhixiang Hou, Guilin Song, Ziheng Anhui University School of Electronic and Information Engineering Hefei China Education of Anhui Province Anhui Province Key Laboratory of Target Recognition and Feature Extraction Anhui Luan237000 China Ministry of Education The Key Laboratory of Intelligent Computing and Signal Processing Hefei China Anhui Province Anhui University Key Laboratory of Electromagnetic Environmental Sensing Hefei230601 China Anhui University Hefei China

ISBN: (纸本)9781665452366

A high-order spatial filtering-symplectic finite difference time domain (SF-SFDTD) scheme with controllable stability condition is proposed to solve the time-dependent Schrödinger equation (TDSE). Firstly, the higher-order symplectic framework for the discretization of Schrödinger equation is described, and then the spatial filtering method is carried out to extend the stability of the standard SFDTD method. Finally, a numerical example is given to evaluate the correctness of the SF-SFDTD method in numerical solving Schrödinger equation. © 2022 IEEE.

关键词： Finite difference time domain method

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Transwnet: Integrating Transformers into CNNS via Row and Column Attention for Abdominal Multi-Organ Segmentation 48

Transwnet: Integrating Transformers into CNNS via Row and Co...

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48th IEEE International Conference on Acoustics, Speech and signal processing, ICASSP 2023

作者： Xie, Yazhen Huang, Yanglin Zhang, Yuan Li, Xuanya Ye, Xiongjun Hu, Kai Xiangtan University Key Laboratory of Intelligent Computing Information Processing of Ministry of Education Xiangtan411105 China Baidu Inc. Beijing100085 China Chinese Academy of Medical Sciences and Peking Union Medical College National Cancer Center Cancer Hospital Beijing100021 China

ISBN: (纸本)9781728163277

Learning how to model global relationships and extract local details is crucial in improving the performance of multi-organ segmentation. Most existing U-shaped structure methods use feature fusion to address these two challenges, but still lack the ability to balance capturing global relationships and local details. To address these issues, we propose a novel multi-organ segmentation framework called TransWnet to mine global relationships and local details from both intra-and inter-scale perspectives. To achieve this, we innovatively design a Row and Column Swin Transformer (RCST) module that can efficiently capture global contextual features and construct local information. Specifically, we design a parallel structure of Row and Column Attention to model the global relationships of multi-scale encoded features, and further mine local information from the global relationships through a local window mechanism. Extensive experiments on the Synapse dataset show that our method outperforms state-of-The-Art approaches and achieves accurate segmentation of abdominal multi-organs. © 2023 IEEE.

关键词： Computerized tomography

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TWO-GRID ALGORITHM OF H^(1)-GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2022年第5期40卷 667-685页

作者： Tianliang Hou Chunmei Liu Chunlei Dai Luoping Chen Yin Yang School of Mathematics and Statistics Beihua UniversityJilin 132013China College of Science Hunan University of Science and EngineeringYongzhou 425199China School of Mathematics Southwest Jiaotong UniversityChengdu 611756China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element *** use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization,and backward Euler scheme for temporal ***,a priori error estimates and some superclose properties are ***,a two-grid scheme is presented and its convergence is *** the proposed two-grid scheme,the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal ***,a numerical experiment is implemented to verify theoretical results of the proposed *** theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice h=H^(2).

关键词： Semilinear parabolic integro-differential equations H^(1)-Galerkin mixed finite element method A priori error estimates Two-grid Superclose.

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Design of a Broadband MIMO Antenna with Shared Radiator

Design of a Broadband MIMO Antenna with Shared Radiator

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International Applied Computational Electromagnetics Society Symposium (ACES)

作者： Rongzhen Fang Xianliang Wu Key Laboratory of Intelligent Computing and Signal Processing Anhui University Hefei China Department of Education of Anhui Province Anhui University Hefei China

In this paper, a broadband 5G MIMO mobile antenna with a shared radiator is proposed. The working band range is 3.3-6.0GHz, covering n77, n78, n79 and WLAN 5G working bands, which can meet a large number of application scenarios of 5G mobile phones. In addition, the antenna is applied to self-decoupling, defect ground, direction diversity and other technologies and principles in the decoupling way, without the use of complex decoupling structure, to ensure that its structure is simple and easy to process, small size is suitable for today's 5G mobile phones.

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A novel position-shift method of double-phase fresnel hologram for synthesizing a complex fresnel hologram 2nd

A novel position-shift method of double-phase fresnel hologr...

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2nd International Conference on Sensor Networks and signal processing, SNSP 2019

作者： Shen, Chuan Zhu, QinQin Hong, QingQing Zhang, Cheng Wei, Sui Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei230601 China Key Laboratory of Modern Imaging and Display Technology of Anhui Province Anhui University Hefei230601 China

ISBN: (纸本)9789811549168

An ideal desired spatial light modulator that is capable of complex amplitude modulation will be one of the ultimate tools for holographic display. In this paper, an analytical method to overlap double-phase Fresnel holograms displayed on the phase-only spatial light modulators for synthesizing a complex Fresnel hologram is proposed. Two $$4f$$ configurations with the phase-only spatial light modulator inserted in the Fourier plane are employed. Different programmable blazed phase gratings can be easily implemented by encoding their phase functions onto the spatial light modulators. We theoretically analyze the implementation of the proposed system based on Fourier optics. The effects introduced by the discrete pixelated nature of the spatial light modulator are assessed. A $$4f$$ configuration of holographic display system based on two liquid crystals on silicons is designed to indicate the free position-shift of the hologram. Optical reconstructions yield satisfactory results. © Springer Nature Singapore Pte Ltd 2021.

关键词： Holographic displays

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A Relay Buffer Prediction Method Based on LSTM in Terminal Cooperative Communication

A Relay Buffer Prediction Method Based on LSTM in Terminal C...

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International Conference on Communication Technology (ICCT)

作者： Jie Fei Hui Zhi Kui Tie Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Electronic and Information Engineering Anhui University Hefei China Ceyear Technologies (AnHui) CO. LTD Bengbu China

In terminal cooperative communication, relay assisted communication with buffer has significant advantages in improving system throughput, signal-to-noise ratio, and reducing system outage probability. The existing relay methods with buffer are all fixed buffer method with a fixed size of the buffer and only considering relay wholehearted cooperation and forwarding, that is, all buffer of the relay assists communication. However, when the forwarding task is small and there is a large idle in forwarding buffer, the buffer area cannot be fully utilized. When the forwarding task is large and forwarding buffer is busy, packet loss may occur in the forwarding task. In order to improve the usage efficiency of relay buffer and reduce packet loss, this paper proposes a relay buffer prediction method based on the long short-term memory network to predict the amount of data that the relay needs to forward. According to the prediction, the size of the relay buffer is divided, so that the buffer can be dynamically adjusted on demand. Simulation results show that, compared with the fixed buffer method, the relay buffer prediction method has a better buffer usage efficiency and a lower packet loss rate.

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Multiscale Adaptive Multifractal Cross-Correlation Analysis of Multivariate Time Series

SSRN

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SSRN 2023年

作者： Jiang, Huanwen Wang, Xinyao Han, Guosheng Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

In the real world, most of the time series generated from complex systems are nonlinear. To effectively study its fractal properties, in this work, we first generalize the adaptive fractal analysis (AFA) to the adaptive multifractal cross-correlation analysis (AMFCCA), which can be used to study the multifractal cross-correlation between two time series. Considering the complexity of time series from complex systems, we extend AMFCCA to the case of multivariate time series, namely multivariate adaptive multifractal cross-correlation analysis (MV-AMFCCA). In order to detect the multifractality on different time scales, we propose multiscale adaptive multifractal cross-correlation analysis of multivariate time series (MMV-AMFCCA). By the numerical simulation on synthetic multivariate processes, our method shows the theoretical validity. Furthermore, we applied these methods to the multifractal analysis of three pollutants in urban and suburban areas in Beijing. After removing the seasonal trend, we find that the urban and suburban systems both have multifractality, especially the multifractality of the urban system are more evident than the suburban systems, the degree of multifractality in spring and winter stronger than that in summer and autumn. Therefore, our methods are suitable for systems with multiple outputs and provide more comprehensive methods for characterizing autocorrelation and cross-correlation in multivariate time series. © 2023, The Authors. All rights reserved.

关键词： Time series

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Log-Concave Sequences in Coding Theory

arXiv

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arXiv 2024年

作者： Shi, Minjia Wang, Xuan An, Junmin Kim, Jon-Lark The Key Laboratory of Intelligent Computing Signal Processing Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China State Key Laboratory of integrated Service Networks Xidian University Xi’an710071 China Department of Mathematics Sogang University Seoul Korea Republic of

We introduce the notion of logarithmically concave (or log-concave) sequences in Coding Theory. A sequence a0, a1, . . ., an of real numbers is called log-concave if a2i ≥ ai−1ai+1 for all 1 ≤ i ≤ n−1. A natural sequence of positive numbers in coding theory is the weight distribution of a linear code consisting of the nonzero values among Ai’s where Ai denotes the number of codewords of weight i. We call a linear code log-concave if its nonzero weight distribution is log-concave. Our main contribution is to show that all binary general Hamming codes of length 2r − 1 (r = 3 or r ≥ 5), the binary extended Hamming codes of length 2r (r ≥ 3), and the second order Reed-Muller codes R(2, m) (m ≥ 2) are all log-concave while the homogeneous and projective second order Reed-Muller codes are either log-concave, or 1-gap log-concave. Furthermore, we show that any MDS [n, k] code over Fq satisfying 3 ≤ k ≤ n/2 + 3 is log-concave if q ≥ q0(n, k) which is the larger root of a quadratic polynomial. Hence, we expect that the concept of log-concavity in coding theory will stimulate many interesting *** Codes 94B15 © 2024, CC BY.

关键词： Turbo codes

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