This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is li...This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.展开更多
The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 err...The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.展开更多
In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element schem...In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element scheme is used for the discretization in the spatial direction,and the temporal component is discretized by a new alternating direction implicit(ADI)method.Next,we strictly prove that the numerical method is stable and convergent.Finally,to confirm our theoretical analysis,some numerical examples in 2D space are presented.展开更多
法医损伤分析在法医学领域具有重要意义,但损伤形成过程的复杂性和个体差异使损伤分析对专业性要求极高。有限元方法(finite element method, FEM)以其广泛的适用性、可控的精确度和高效的计算能力,结合可视化,在法庭科学领域展现出巨...法医损伤分析在法医学领域具有重要意义,但损伤形成过程的复杂性和个体差异使损伤分析对专业性要求极高。有限元方法(finite element method, FEM)以其广泛的适用性、可控的精确度和高效的计算能力,结合可视化,在法庭科学领域展现出巨大的应用潜力。本文通过文献分析,介绍FEM的基本原理,探讨其在交通事故、枪击、工具致伤、高坠损伤分析中的应用情况,通过分析各应用场景与碰撞部位的模拟参数、模拟结果及研究侧重,评估FEM在法医损伤分析上的可行性、局限性,为法医损伤分析提供参考和技术途径。展开更多
This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is e...This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model.展开更多
在国家"523"(防治疟疾新药项目代号)任务实施50周年之际,对广州中医药大学青蒿素抗疟研究科研团队采用青蒿素复方防治疟疾的历程与所取得的进展进行评述。广州中医药大学作为"523"项目研究小组之一,其青蒿素抗疟研...在国家"523"(防治疟疾新药项目代号)任务实施50周年之际,对广州中医药大学青蒿素抗疟研究科研团队采用青蒿素复方防治疟疾的历程与所取得的进展进行评述。广州中医药大学作为"523"项目研究小组之一,其青蒿素抗疟研究科研团队相继主持了采用青蒿素及其衍生物不同剂型、剂量、疗程治疗疟疾的临床研究(1974~1989)、青蒿素复方(Artekin及Artequick)治疗疟疾的临床研究(1984~2006),并于近10年中在东南亚地区及非洲全力推行快速消灭传染源清除疟疾(Fast Elimination of Malaria by Source Eradication,FEMSE)的抗疟项目。青蒿素抗疟研究科研团队所做的探索与获得的成就为青蒿素类药物走向世界做出了重要贡献,并为全球快速消灭疟疾创建了一种简单、易行、省钱的新方法。展开更多
The Design and manufacturing of a noble piezoresistive pressure sensor(PS) for subtle pressures(<1 kPa) were presented. Meanwhile, in the studies conducted in the field of pressure sensors, the measurement of subtl...The Design and manufacturing of a noble piezoresistive pressure sensor(PS) for subtle pressures(<1 kPa) were presented. Meanwhile, in the studies conducted in the field of pressure sensors, the measurement of subtle pressures has received less attention. The limitations in the inherent gauge factor in silicon, have led to the development of polymer and composite resistive sensitive elements. However,in the development of resistance sensing elements, the structure of composite elements with reinforcement core has not been used. The proposed PS had a composite sandwich structure consisting of a nanocomposite graphene layer covered by layers of PDMS at the bottom and on the top coupled with a polyimide(PI) core. Various tests were performed to analyze the PS. The primary design target was improved sensitivity, with a finite-element method(FEM) utilized to simulate the stress profile over piezoresistive elements and membrane deflection at various pressures. The PS manufacturing process is based on Laser-engraved graphene(LEG) technology and PDMS casting. Experimental data indicated that the manufactured PS exhibits a sensitivity of 67.28 mV/kPa for a pressure range of 30-300 Pa in ambient temperature.展开更多
基金This work is supported by NSFC(Grant Nos.11771035,11771162,11571128,61473126,91430216,91530204,11372354 and U1530401),a grant from the RGC of HK 11300517,China(Project No.CityU 11302915),China Postdoctoral Science Foundation under grant No.2016M602273,a grant DRA2015518 from 333 High-level Personal Training Project of Jiangsu Province,and the USA National Science Foundation grant DMS-1315259the USA Air Force Office of Scientific Research grant FA9550-15-1-0001.Jiwei Zhang also thanks the hospitality of Hong Kong City University during the period of his visiting.
文摘This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.
基金supported in part by a grant from National Science Foundation(Project No.11301262)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613)The work of J.Wang and W.Sun was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613).
文摘The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.
基金NSF of China[grant number:11371157]Natural Science Foundation of Anhui Higher Education Institutions of China[grant number:KJ2016A492]Natural Science Foundation of Bozhou College[grant number:BSKY201426,BSKY201535].
文摘In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element scheme is used for the discretization in the spatial direction,and the temporal component is discretized by a new alternating direction implicit(ADI)method.Next,we strictly prove that the numerical method is stable and convergent.Finally,to confirm our theoretical analysis,some numerical examples in 2D space are presented.
文摘法医损伤分析在法医学领域具有重要意义,但损伤形成过程的复杂性和个体差异使损伤分析对专业性要求极高。有限元方法(finite element method, FEM)以其广泛的适用性、可控的精确度和高效的计算能力,结合可视化,在法庭科学领域展现出巨大的应用潜力。本文通过文献分析,介绍FEM的基本原理,探讨其在交通事故、枪击、工具致伤、高坠损伤分析中的应用情况,通过分析各应用场景与碰撞部位的模拟参数、模拟结果及研究侧重,评估FEM在法医损伤分析上的可行性、局限性,为法医损伤分析提供参考和技术途径。
基金supported by the National Natural Science Foundation of China(Grant Nos.51890912,51979025 and 52011530189).
文摘This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model.
文摘在国家"523"(防治疟疾新药项目代号)任务实施50周年之际,对广州中医药大学青蒿素抗疟研究科研团队采用青蒿素复方防治疟疾的历程与所取得的进展进行评述。广州中医药大学作为"523"项目研究小组之一,其青蒿素抗疟研究科研团队相继主持了采用青蒿素及其衍生物不同剂型、剂量、疗程治疗疟疾的临床研究(1974~1989)、青蒿素复方(Artekin及Artequick)治疗疟疾的临床研究(1984~2006),并于近10年中在东南亚地区及非洲全力推行快速消灭传染源清除疟疾(Fast Elimination of Malaria by Source Eradication,FEMSE)的抗疟项目。青蒿素抗疟研究科研团队所做的探索与获得的成就为青蒿素类药物走向世界做出了重要贡献,并为全球快速消灭疟疾创建了一种简单、易行、省钱的新方法。
文摘The Design and manufacturing of a noble piezoresistive pressure sensor(PS) for subtle pressures(<1 kPa) were presented. Meanwhile, in the studies conducted in the field of pressure sensors, the measurement of subtle pressures has received less attention. The limitations in the inherent gauge factor in silicon, have led to the development of polymer and composite resistive sensitive elements. However,in the development of resistance sensing elements, the structure of composite elements with reinforcement core has not been used. The proposed PS had a composite sandwich structure consisting of a nanocomposite graphene layer covered by layers of PDMS at the bottom and on the top coupled with a polyimide(PI) core. Various tests were performed to analyze the PS. The primary design target was improved sensitivity, with a finite-element method(FEM) utilized to simulate the stress profile over piezoresistive elements and membrane deflection at various pressures. The PS manufacturing process is based on Laser-engraved graphene(LEG) technology and PDMS casting. Experimental data indicated that the manufactured PS exhibits a sensitivity of 67.28 mV/kPa for a pressure range of 30-300 Pa in ambient temperature.
