In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an op...In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.展开更多
A convenient and scalable technique for the synthesis of rutile titanium dioxide(TiO2) nano-rods was presented by using bulk TiO2 powder, sodium hydroxide(NaOH) and distilled water as raw materials. X-ray diffraction(...A convenient and scalable technique for the synthesis of rutile titanium dioxide(TiO2) nano-rods was presented by using bulk TiO2 powder, sodium hydroxide(NaOH) and distilled water as raw materials. X-ray diffraction(XRD) and field emission scanning electron microscopy(FESEM) studies indicate that the prepared sample is crystalline and free from any impurities, however, it has no distinct shape and possesses a huge degree of agglomeration, and the average crystal size is around 40 nm. After annealing the sample at 600 °C for 2 h, it is observed through FESEM that nano-rods are formed. And XRD analysis shows that the nano-rods are single crystalline with distinct and smooth surfaces in different sizes with average length of about 1 μm and diameter of about 80 nm. Further UV-visible spectroscopy and Raman studies were conducted for the prepared sample and the band gap of the final product is found to be 3.40 eV.展开更多
Ordered zinc oxide （ZnO） rod arrays with very high orientation were fabricated on Si substrates by using a solution method. The substrate surfaces were functionalized by Self-Assembly Monolayers （SAMs）. In the ver...Ordered zinc oxide （ZnO） rod arrays with very high orientation were fabricated on Si substrates by using a solution method. The substrate surfaces were functionalized by Self-Assembly Monolayers （SAMs）. In the very early growth stage, the oriented ZnO crystals had already grown, which appeared to be the main reason why ZnO nanorods showed very high orientation. The un-dense and un-uniform SAMs provided a surface that was heterogeneous to ZnO nucleation. Consequently, highly oriented ZnO rods were selectively grown on the ＂coin-like＂ SAM-uncovered regions. The route developed here can provide some helpful information to control the nucleation and orientation of ZnO in aqueous solution. Also, the site-selective growth mechanisms can indicate a clue to grow patterned highly oriented ZnO nanorod arrays by the organic template.展开更多
A new model of dendritic growth and solute distribution of Fe-0.04%C binary alloys was developed, which is based on the sharp interface model of dendritic growth. This innovative model improved the cellular automaton ...A new model of dendritic growth and solute distribution of Fe-0.04%C binary alloys was developed, which is based on the sharp interface model of dendritic growth. This innovative model improved the cellular automaton method, combined with the finite difference method, considered concentration field, temperature field and the shape of molten pool. This model simulated the growth morphologies of single equiaxial crystal, the relationship between tip growth velocity and time, multi-equiaxed crystals’ growth morphologies and solute distribution, the growth of columnar crystals, columnar-to-equiaxed transition after coupling temperature field, and compared with experimental results. The results indicate that crystallographic orientation has certain influence on dendritic morphologies, that the tip growth velocity tends to be stable with the extension of time in the end, that the shape of molten pool influences the growth morphologies of columnar crystals and that the solute mainly concentrates in dendritic roots and among grain boundaries. The simulated results are in accord with experimental results.展开更多
The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the...The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the steady-state solution for the case of the large Schmidt number, in terms of the multiple variable expansion method. The changes of the temperature and concentration fields, the morphology of the interface, the normalization parameter and the Peclet number of the system induced by uniform external flow are derived. The results show that, compared with the system of dendritic growth from undercooled pure melt, the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface. Nevertheless, the shape of the interface still remains nearly a paraboloid.展开更多
This paper presents an approach to synthesis of gold nanoparticles with different morphologies and investigation of the relationship between morphologies and their optical properties.Spherical gold nanoparticles with ...This paper presents an approach to synthesis of gold nanoparticles with different morphologies and investigation of the relationship between morphologies and their optical properties.Spherical gold nanoparticles with different sizes are synthesized via reduction method.Using seed-mediated solution growth method,gold nanoparticles with shuttle,star and stick shapes can be obtained.The sizes and morphologies of the gold nanoparticles are characterized by transmission electron microscopy （TEM）.The characterization results illustrate the growth process of the gold nanoparticles with different morphologies.Absorption spectroscopy and Raman spectroscopy measurements are performed to demonstrate the relationship between the morphologies and optical properties.The results of Raman characterization show that the gold nanoparticles with different morphologies can be used to probe molecules with different concentrations.展开更多
基金Supported by National Natural Science Foundation of China(11471267)the Doctoral Scientific Research Funds of China West Normal University(15D006 and 16E014)+1 种基金Meritocracy Research Funds of China West Normal University(17YC383)Natural Science Foundation of Education of Guizhou Province(KY[2016]046)
文摘In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.
基金supported by the MKE (The Ministry of Knowledge Economy)Korea Under the ITRC (Information Technology Research Centre) support program supervised by the NIPA (National IT industry Promotion Agency) (NIPA-2012-H0301-12-2009)+1 种基金supported by the Ministry of Education, Science and Technology (MEST)National Research Foundation of Korea (NRF) through the Human Resource Training Project for Regional Innovation (2012H1B8A2026212)
文摘A convenient and scalable technique for the synthesis of rutile titanium dioxide(TiO2) nano-rods was presented by using bulk TiO2 powder, sodium hydroxide(NaOH) and distilled water as raw materials. X-ray diffraction(XRD) and field emission scanning electron microscopy(FESEM) studies indicate that the prepared sample is crystalline and free from any impurities, however, it has no distinct shape and possesses a huge degree of agglomeration, and the average crystal size is around 40 nm. After annealing the sample at 600 °C for 2 h, it is observed through FESEM that nano-rods are formed. And XRD analysis shows that the nano-rods are single crystalline with distinct and smooth surfaces in different sizes with average length of about 1 μm and diameter of about 80 nm. Further UV-visible spectroscopy and Raman studies were conducted for the prepared sample and the band gap of the final product is found to be 3.40 eV.
基金the National Natural Science Foundation of China(No.50702029)Shandong Provincial Education Department(No.J05D08)Natural Science Foundation of Qingdao(No.05-1-JC-89)
文摘Ordered zinc oxide （ZnO） rod arrays with very high orientation were fabricated on Si substrates by using a solution method. The substrate surfaces were functionalized by Self-Assembly Monolayers （SAMs）. In the very early growth stage, the oriented ZnO crystals had already grown, which appeared to be the main reason why ZnO nanorods showed very high orientation. The un-dense and un-uniform SAMs provided a surface that was heterogeneous to ZnO nucleation. Consequently, highly oriented ZnO rods were selectively grown on the ＂coin-like＂ SAM-uncovered regions. The route developed here can provide some helpful information to control the nucleation and orientation of ZnO in aqueous solution. Also, the site-selective growth mechanisms can indicate a clue to grow patterned highly oriented ZnO nanorod arrays by the organic template.
文摘A new model of dendritic growth and solute distribution of Fe-0.04%C binary alloys was developed, which is based on the sharp interface model of dendritic growth. This innovative model improved the cellular automaton method, combined with the finite difference method, considered concentration field, temperature field and the shape of molten pool. This model simulated the growth morphologies of single equiaxial crystal, the relationship between tip growth velocity and time, multi-equiaxed crystals’ growth morphologies and solute distribution, the growth of columnar crystals, columnar-to-equiaxed transition after coupling temperature field, and compared with experimental results. The results indicate that crystallographic orientation has certain influence on dendritic morphologies, that the tip growth velocity tends to be stable with the extension of time in the end, that the shape of molten pool influences the growth morphologies of columnar crystals and that the solute mainly concentrates in dendritic roots and among grain boundaries. The simulated results are in accord with experimental results.
基金Supported by the National Basic Research Program of China (Grant No. 2006CB605205)the National Natural Science Foundation of China (Grant No. 10672019)
文摘The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the steady-state solution for the case of the large Schmidt number, in terms of the multiple variable expansion method. The changes of the temperature and concentration fields, the morphology of the interface, the normalization parameter and the Peclet number of the system induced by uniform external flow are derived. The results show that, compared with the system of dendritic growth from undercooled pure melt, the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface. Nevertheless, the shape of the interface still remains nearly a paraboloid.
基金Merit-funded Science and Technology Project for Returned Oversea Scholars from Ministry of Human and Social Security of Shanxi provinceNatural Science Foundation for Young Scientists of Shanxi province(No.2011011020-2)Shanxi Province Foundation for Returness(No.2008062)
文摘This paper presents an approach to synthesis of gold nanoparticles with different morphologies and investigation of the relationship between morphologies and their optical properties.Spherical gold nanoparticles with different sizes are synthesized via reduction method.Using seed-mediated solution growth method,gold nanoparticles with shuttle,star and stick shapes can be obtained.The sizes and morphologies of the gold nanoparticles are characterized by transmission electron microscopy （TEM）.The characterization results illustrate the growth process of the gold nanoparticles with different morphologies.Absorption spectroscopy and Raman spectroscopy measurements are performed to demonstrate the relationship between the morphologies and optical properties.The results of Raman characterization show that the gold nanoparticles with different morphologies can be used to probe molecules with different concentrations.
