The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good ...The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition.In addition,we demonstrate the influences of the diffusion coefficient on stationary solutions.The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem.Finally,some numerical simulations are given to illustrate the theoretical results.展开更多
Commercially pure zirconium was processed by the surface mechanical attrition treatment(SMAT),and the microstructure observation showed that a gradient structure was induced.Nanoindentation measurements were taken to ...Commercially pure zirconium was processed by the surface mechanical attrition treatment(SMAT),and the microstructure observation showed that a gradient structure was induced.Nanoindentation measurements were taken to obtain the load-displacement curves at different depths below the treated surface.Using dimensional analysis,the local yield stress,hardness,strain hardening exponent,and elastic modulus at the corresponding depths were derived.The results showed that the yield stress and hardness varied with depth,while the strain hardening exponent and elastic modulus were approximately invariable.The finite element method was used to simulate nanoindentation at different depths below the treated surface to verify the derivation of the local elastic-plastic constitutive relationship.Stressstrain curves were computed for the treated samples through the rule of mixtures,and they agreed well with the experimental results.The analysis showed that the surface and subsurface hardening layers as well as the transition layer shared a high load applied to the samples,even though their volume fraction was small.展开更多
基金supported by the National Natural Science Foundation of China(No.51674187)the International Joint Research Center for Value-added Metallurgy and Processing of Non-ferrous Metals,China(No.2019SD0010)the Key Industry Chain(Group)-Industrial Field in Shaanxi Province,China(No.2019ZDLGY05-03)。
基金supported by National Natural Science Foundation of China(Grant No.11790273,52276028).
文摘The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition.In addition,we demonstrate the influences of the diffusion coefficient on stationary solutions.The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem.Finally,some numerical simulations are given to illustrate the theoretical results.
基金financially supported by the National Natural Science Foundation of China (Nos. 51674187 and 51671153)the Science and Technology Department of Shaanxi Province(No.2017GY-115)the Education Department of Shaanxi Province(No. 16JK1466)
文摘Commercially pure zirconium was processed by the surface mechanical attrition treatment(SMAT),and the microstructure observation showed that a gradient structure was induced.Nanoindentation measurements were taken to obtain the load-displacement curves at different depths below the treated surface.Using dimensional analysis,the local yield stress,hardness,strain hardening exponent,and elastic modulus at the corresponding depths were derived.The results showed that the yield stress and hardness varied with depth,while the strain hardening exponent and elastic modulus were approximately invariable.The finite element method was used to simulate nanoindentation at different depths below the treated surface to verify the derivation of the local elastic-plastic constitutive relationship.Stressstrain curves were computed for the treated samples through the rule of mixtures,and they agreed well with the experimental results.The analysis showed that the surface and subsurface hardening layers as well as the transition layer shared a high load applied to the samples,even though their volume fraction was small.
