In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
High-performance graphite materials have important roles in aerospace and nuclear reactor technologies because of their outstanding chemical stability and high-temperature performance.Their traditional production meth...High-performance graphite materials have important roles in aerospace and nuclear reactor technologies because of their outstanding chemical stability and high-temperature performance.Their traditional production method relies on repeated impregnation-carbonization and graphitization,and is plagued by lengthy preparation cycles and high energy consumption.Phase transition-assisted self-pressurized selfsintering technology can rapidly produce high-strength graphite materials,but the fracture strain of the graphite materials produced is poor.To solve this problem,this study used a two-step sintering method to uniformly introduce micro-nano pores into natural graphite-based bulk graphite,achieving improved fracture strain of the samples without reducing their density and mechanical properties.Using natural graphite powder,micron-diamond,and nano-diamond as raw materials,and by precisely controlling the staged pressure release process,the degree of diamond phase transition expansion was effectively regulated.The strain-to-failure of the graphite samples reached 1.2%,a 35%increase compared to samples produced by fullpressure sintering.Meanwhile,their flexural strength exceeded 110 MPa,and their density was over 1.9 g/cm^(3).The process therefore produced both a high strength and a high fracture strain.The interface evolution and toughening mechanism during the two-step sintering process were investigated.It is believed that the micro-nano pores formed have two roles:as stress concentrators they induce yielding by shear and as multi-crack propagation paths they significantly lengthen the crack propagation path.The two-step sintering phase transition strategy introduces pores and provides a new approach for increasing the fracture strain of brittle materials.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
A comprehensive understanding of the dynamic frictional characteristics in rock joints under high normal load and strong confinement is essential for ensuring the safety of deep engineering construction and mitigating...A comprehensive understanding of the dynamic frictional characteristics in rock joints under high normal load and strong confinement is essential for ensuring the safety of deep engineering construction and mitigating geological disasters.This study conducted shear experiments on rough rock joints under displacement-controlled dynamic normal loads,investigating the shear behaviors of joints across varying initial normal loads,normal loading frequencies,and normal loading amplitudes.Experimental results showed that the peak/valley shear force values increased with initial normal loads and normal loading frequencies but showed an initial increase followed by a decrease with normal loading amplitudes.Dynamic normal loading can either increase or decrease shear strength,while this study demonstrates that higher frequencies lead to enhanced friction.Increased initial normal loading and normal loading frequency result in a gradual decrease in joint roughness coefficient(JRC)values of joint surfaces after shearing.Positive correlations existed between frictional energy dissipation and peak shear forces,while post-shear joint surface roughness exhibited a negative correlation with peak shear forces through linear regression analysis.This study contributes to a better understanding of the sliding responses and shear mechanical characteristics of rock joints under dynamic disturbances.展开更多
A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the densit...A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.展开更多
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Natural Science Foundation of Shanghai(24ZR1400800)he Natural Science Foundation of China(U23A20685,52073058,91963204)+1 种基金the National Key R&D Program of China(2021YFB3701400)Shanghai Sailing Program(23YF1400200)。
文摘High-performance graphite materials have important roles in aerospace and nuclear reactor technologies because of their outstanding chemical stability and high-temperature performance.Their traditional production method relies on repeated impregnation-carbonization and graphitization,and is plagued by lengthy preparation cycles and high energy consumption.Phase transition-assisted self-pressurized selfsintering technology can rapidly produce high-strength graphite materials,but the fracture strain of the graphite materials produced is poor.To solve this problem,this study used a two-step sintering method to uniformly introduce micro-nano pores into natural graphite-based bulk graphite,achieving improved fracture strain of the samples without reducing their density and mechanical properties.Using natural graphite powder,micron-diamond,and nano-diamond as raw materials,and by precisely controlling the staged pressure release process,the degree of diamond phase transition expansion was effectively regulated.The strain-to-failure of the graphite samples reached 1.2%,a 35%increase compared to samples produced by fullpressure sintering.Meanwhile,their flexural strength exceeded 110 MPa,and their density was over 1.9 g/cm^(3).The process therefore produced both a high strength and a high fracture strain.The interface evolution and toughening mechanism during the two-step sintering process were investigated.It is believed that the micro-nano pores formed have two roles:as stress concentrators they induce yielding by shear and as multi-crack propagation paths they significantly lengthen the crack propagation path.The two-step sintering phase transition strategy introduces pores and provides a new approach for increasing the fracture strain of brittle materials.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金Projects(52174092,51904290)supported by the National Natural Science Foundation,ChinaProject(BK20220157)supported by the Natural Science Foundation of Jiangsu Province,China+1 种基金Project(232102321009)supported by Henan Province Science and Technology Key Project,ChinaProject(2022YCPY0202)supported by Fundamental Research Funds for the Central Universities,China。
文摘A comprehensive understanding of the dynamic frictional characteristics in rock joints under high normal load and strong confinement is essential for ensuring the safety of deep engineering construction and mitigating geological disasters.This study conducted shear experiments on rough rock joints under displacement-controlled dynamic normal loads,investigating the shear behaviors of joints across varying initial normal loads,normal loading frequencies,and normal loading amplitudes.Experimental results showed that the peak/valley shear force values increased with initial normal loads and normal loading frequencies but showed an initial increase followed by a decrease with normal loading amplitudes.Dynamic normal loading can either increase or decrease shear strength,while this study demonstrates that higher frequencies lead to enhanced friction.Increased initial normal loading and normal loading frequency result in a gradual decrease in joint roughness coefficient(JRC)values of joint surfaces after shearing.Positive correlations existed between frictional energy dissipation and peak shear forces,while post-shear joint surface roughness exhibited a negative correlation with peak shear forces through linear regression analysis.This study contributes to a better understanding of the sliding responses and shear mechanical characteristics of rock joints under dynamic disturbances.
基金Projects(11372055,11302033)supported by the National Natural Science Foundation of ChinaProject supported by the Huxiang Scholar Foundation from Changsha University of Science and Technology,ChinaProject(2012KFJJ02)supported by the Key Labortory of Lightweight and Reliability Technology for Engineering Velicle,Education Department of Hunan Province,China
文摘A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
