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arXiv 2022年

作者： Jin, Diancong Chen, Ziheng Zhou, Tau School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Statistics Yunnan University Kunming650500 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We utilize the weak convergence method to establish the Freidlin-Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases with non-globally Lipschitz coefficients. The key ingredient in our proof is the uniform moment estimate of the controlled equation, where we handle the super-linear growth of the coefficients by an iterative argument. Our results allow both the drift and diffusion coefficients of the considered equations to super-linearly grow not only with respect to the delay variable but also to the state variable. This work extends the existing results which develop the LDPs for SDDEs with super-linearly growing coefficients only with respect to the delay *** Codes 60H10, 60F10, 60H30 Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

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Quantum algorithms for uncertainty quantification: application to partial differential equations

arXiv

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arXiv 2022年

作者： Golse, Francois Jin, Shi Liu, Nana Ecole Polytechnique CMLS PalaiseauCedex 91128 France Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China

Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations (PDEs), large numbers M >> 1 of samples are required to obtain accurate ensemble averages. This usually involves solving the PDE M times. In addition, to characterise the stochasticity in a PDE, the dimension L of the random input variables is high in most cases, and classical algorithms suffer from curse-of-dimensionality. We propose new quantum algorithms for PDEs with uncertain coefficients that are more efficient in M and L in various important regimes, compared to their classical counterparts. We introduce transformations that transfer the original d-dimensional equation (with uncertain coefficients) into d + L (for dissipative equations) or d + 2L (for wave type equations) dimensional equations (with certain coefficients) in which the uncertainties appear only in the initial data. These transformations also allow one to superimpose the M different initial data, so the computational cost for the quantum algorithm to obtain the ensemble average from M different samples is then independent of M, while also showing potential advantage in d, L and precision ǫ in computing ensemble averaged solutions or physical observables. © 2022, CC BY.

关键词： Partial differential equations

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Advanced Analysis of Arabidopsis thaliana Leaf Traits Using RGB Imaging and Machine Learning

Advanced Analysis of Arabidopsis thaliana Leaf Traits Using ...

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International Symposium on Industrial Electronics (INDEL)

作者： Rijad Sarić Edhem Čustović Martin Trtílek Amila Akagić Mathew G. Lewsey James Whelan La Trobe Institute for Sustainable Agriculture & Food (LISAF) La Trobe University Melbourne VIC Australia Australian Research Council Research Hub for Medicinal Agriculture La Trobe University Melbourne VIC Australia School of Computing Engineering and Mathematical Sciences La Trobe University (LTU) Melbourne VIC Australia Scientific Instruments Australia (SIA) Melbourne VIC Australia Photon Systems Instruments (PSI) Plant Phenotyping Research Centre Drasov Brno Czech Republic Faculty of Electrical Engineering University of Sarajevo (UNSA) Sarajevo Bosnia and Herzegovina State Key Laboratory of Plant Environmental Resilience College of Life Science Zhejiang University (ZJU) P.R. China Provincial International Science and Technology Cooperation Base on Engineering Biology Zhejiang University P.R China

ISBN: (数字)9798350352320

ISBN: (纸本)9798350352337

Image-based high-throughput plant phenotyping utilises various imaging techniques to automatically and non-invasively understand the growth of different plant species. These innovative imaging infrastructures are implemented to monitor plant development over time in indoor or outdoor environments. However, understanding the relationship between genotype and phenotype interactions under different environments remains challenging. This research study demonstrates superior extraction of leaf morphological features of different Arabidopsis thaliana ecotypes by analysing leaf geometry using a sequence of RGB images. Upon successful extraction of anatomical features, leaf length and area are converted into physical coordinates. Furthermore, considering these leaf features as 1D signals, the Fourier Spectrum is analysed, and most descriptive features are selected using PCA. Finally, leaf shape classification is established by training and testing five distinct ML models. A thorough evaluation of selected models demonstrates superiority in classifying two common leaf shapes of Arabidopsis plants.

关键词： Training Shape Biological system modeling Imaging Machine learning Feature extraction Real-time systems Reliability Testing Principal component analysis

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Uniqueness and uniform structural stability of poiseuille flows in an infinitely long pipe with navier boundary conditions

arXiv

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arXiv 2021年

作者： Wang, Yun Xie, Chunjing School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing IMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

In this paper, uniqueness and uniform structural stability of Poiseuille flows in an infinitely long pipe with Navier boundary conditions are established for axisymmetric solutions of steady Navier-Stokes system. The crucial point is that the estimate is uniform with respect both the flux of flows and slip coefficient which appeared in Navier boundary conditions. With the aid of special structure of Navier-Stokes system and the refined estimate for some quantities such as radial velocity, the uniqueness and existence of steady solutions of Navier-Stokes system can be obtained even when the external forces are large as long as the fluxes of flows are large. The delicate decomposition in the two dimensional plane for slip coefficient and frequency corresponding to Fourier variable in the axial direction plays a key role to achieve these estimates. Copyright © 2021, The Authors. All rights reserved.

关键词： Stability

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THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

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Acta Mathematica Scientia 2018年第2期38卷 651-672页

作者：张磊刘斌 School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology

This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.

关键词： Generalized two-component μ-Hunter-Saxton system viscous weakly dissipative existence global attractor period boundary conditions

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A diffuse-interface lattice Boltzmann method for the dissolution through nonlinear heterogeneous reaction

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Physics of Fluids 2025年第5期37卷

作者： Yang, Xiaofeng Zhan, Chengjie Liu, Xi Chai, Zhenhua School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China

In this work, a diffuse-interface lattice Boltzmann method (DI-LBM) is proposed for the dissolution through nonlinear heterogeneous reaction. In this method, the sharp boundary between the fluid and solid phases is replaced by a diffuse interface with a nonzero thickness. To describe the changes of physical variables from the fluid region to the solid region, a smooth function is introduced, and simultaneously, the nonlinear Robin boundary condition imposed on the fluid-solid interface is reformulated as a source term into the modified convection-diffusion equation. We then test the DI-LBM through several benchmark problems, and find that the numerical results are in agreement with the analytical solutions and available data. Finally, the present DI-LBM is adopted to study the dissolution in a two-dimensional porous medium, and the results show that with the decrease in reaction order, the reactant in the central region with a large fluid velocity reacts faster and forms a conical pathway. © 2025 Author(s).

关键词： Kinetic theory of gases

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Stabilized multiple-relaxation implicit-explicit Runge-Kutta methods for nonlinear Gross-Pitaevskii equations

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Journal of Computational Physics 2025年

作者： Dongfang Li Xiaoxi Li Jiwei Zhang Zhimin Zhang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Wuhan University Wuhan 430072 China Hubei Key Laboratory of Computational Science Wuhan University Wuhan 430072 China Department of Mathematics Wayne State University Detroit 48202 MI USA

A novel class of stabilized multiple-relaxation implicit-explicit Runge–Kutta methods is proposed for solving nonlinear Gross–Pitaevskii equations. The methods conserve the mass and the energy simultaneously in the discrete sense, and achieve arbitrarily high-order accuracy in the temporal direction. Additionally, there are several highlights in this study. Firstly, this is the first attempt to apply the stabilization approach to develop relaxation-type schemes, which effectively avoids the blow-up of the relaxation parameters due to the nonlinearity and stiffness of the problems. Secondly, the governing equations that determine the relaxation parameters are newly designed to conserve the original invariants, which can be extended to conserve more invariants of other physical models. Thirdly, the schemes are linearly implicit after obtaining the relaxation parameters, and thus are easy to implement. Several numerical experiments are carried out to confirm the effectiveness and theoretical results of the proposed methods.

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Complexity Analysis and Algorithm Design of Pooling Problem

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Journal of the Operations Research Society of China 2018年第2期6卷 249-266页

作者： Yu-Hong Dai Rui Diao Kai Fu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The pooling problem,also called the blending problem,is fundamental in production planning of *** can be formulated as an optimization problem similar with the minimum-cost flow ***,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general *** also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of *** this paper,we prove that the pooling problem is still strongly NP-hard even with only one *** means the quality is an essential difference between minimum-cost flow problem and the pooling *** solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming *** convergence of the algorithm is *** numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local *** results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

关键词： Pooling problem Complexity analysis Successive linear programming Non-monotone

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A semi-adaptive finite difference method for simulating two-sided fractional convection–diffusion quenching problems

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Journal of Computational and Applied Mathematics 2026年 472卷

作者： Rumin Dong Lin Zhu Qin Sheng Bingxin Zhao School of Mathematics and Statistics Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing Ningxia Basic Science Research Center of Mathematics Ningxia University Yinchuan 750021 China Department of Mathematics and Center for Astrophysics Space Physics and Engineering Research Baylor University Waco TX 76798-7328 USA

This paper investigates quenching solutions of an one-dimensional, two-sided Riemann–Liouville fractional order convection–diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in conjunction with standard and shifted Grünwald formulas. The advective term is handled utilizing a straightforward Euler formula, resulting in a semi-discretized system of nonlinear ordinary differential equations. The conservativeness of the proposed scheme is rigorously proved and validated through simulation experiments. The study is further advanced to a fully discretized, semi-adaptive finite difference method. Detailed analysis is implemented for the monotonicity, positivity and stability of the scheme. Investigations are carried out to assess the potential impacts of the fractional order on quenching location, quenching time, and critical length. The computational results are thoroughly discussed and analyzed, providing a more comprehensive understanding of the quenching phenomena modeled through two-sided fractional order convection–diffusion problems.

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Upper capacity entropy and packing entropy of saturated sets for amenable group actions

arXiv

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arXiv 2021年

作者： Ren, Xiankun Zhang, Wenda Zhang, Yiwei College of Mathematics and Statistics Chongqing University Chongqing 401331 China College of Mathematics and Statistics Chongqing Jiaotong University Chongqing 400074 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

Let (X, G) be a G-action topological system, where G is a countable infinite discrete amenable group and X a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version of specification. We prove that the upper capacity always carries full entropy while there is a variational principle for packing entropy of saturated sets. © 2021, CC BY-NC-ND.

关键词： Specifications

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