Let B1 С RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical ...Let B1 С RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients：{-div（｜△u｜p-2△u）=｜x｜s｜u｜p＊（s）-2u＋λ｜x｜t｜u｜p-2u, x∈B1, u｜σB1 =0, where t, s〉-p, 2≤p〈N, p＊（s）= （N＋s）pN-p andλ is a real parameter. We show particularly that the above problem exists infinitely many radial solutions if the space dimension N 〉p（p-1）t＋p（p2-p＋1） andλ∈（0,λ1,t）, whereλ1,t is the first eigenvalue of-△p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ （ps＋p） min{1, p＋t/p＋s}＋p2p-（p-1） min{1, p＋tp＋s} andλ〉0 is small.展开更多
We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with t...We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.展开更多
Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers,e.g.static safety of factor(static FoS)or the critical seismic acceleration coefficient,while little att...Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers,e.g.static safety of factor(static FoS)or the critical seismic acceleration coefficient,while little attention has been given to the relationship between the slope stability numbers and the critical seismic acceleration coefficient.This study aims to investigate the relationship between the static FoS and the critical seismic acceleration coefficient of soil slopes in the framework of the upper-bound limit analysis.Based on the 3D rotational failure mechanism,the critical seismic acceleration coefficient using the pseudo-static method and the static FoS using the strength reduction technique are first determined.Then,the relationship between the static FoS and the critical seismic acceleration coefficient is presented under considering the slope angleβ,the frictional angleφ,and the dimensionless coefficients B/H and c/γH.Finally,a fitting formula between the static FoS and the critical seismic acceleration coefficient is proposed and validated by analytical and numerical results.展开更多
The relation between the critical radius and the particle size distribution for generalized Ostwald type ripening processes whereby the mass transfer coefficient is modelled by a power law was derived. The critical ra...The relation between the critical radius and the particle size distribution for generalized Ostwald type ripening processes whereby the mass transfer coefficient is modelled by a power law was derived. The critical radius is determined by the growth rate, the mass transfer coefficient and the mass balance, and is independent of whether the limiting stationary growth regime has been obtained.展开更多
We study the critical slowing down phenomenon in deformation and groundwater observations before the Nilka-Gongliu MS6. 0 earthquake on November 1, 2011 and Xinyuan-Hejing M S6. 6 earthquake on June 30,2012. Firstly,w...We study the critical slowing down phenomenon in deformation and groundwater observations before the Nilka-Gongliu MS6. 0 earthquake on November 1, 2011 and Xinyuan-Hejing M S6. 6 earthquake on June 30,2012. Firstly,we remove the annual variation and tendency change of basic data by means of wavelet transform analysis.Secondly,we calculate the autocorrelation coefficients and variance of the critical slowing down phenomenon. Lastly,we try to verify the critical slowing down phenomenon before an earthquake. The result indicates that there was obvious critical slowing down of the records at different stations before earthquakes.展开更多
To provide information for amendment to Technical Specifications for Power Transmission Towers (SDGJ94-90), the critical loads of typical compressed angle steels was calculated. The correlation of buckling loads and ...To provide information for amendment to Technical Specifications for Power Transmission Towers (SDGJ94-90), the critical loads of typical compressed angle steels was calculated. The correlation of buckling loads and slenderness of compressed angle steels was obtained with regression. A new slenderness coefficient equation was proposed based on the result of the correlation. A practical measure to ensure good result in nonlinear solution using Arch-length method is put forward.展开更多
In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coef...In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence.展开更多
基金supported by the National Natural Science Foundation of China(11326139,11326145)Tian Yuan Foundation(KJLD12067)Hubei Provincial Department of Education(Q20122504)
文摘Let B1 С RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients：{-div（｜△u｜p-2△u）=｜x｜s｜u｜p＊（s）-2u＋λ｜x｜t｜u｜p-2u, x∈B1, u｜σB1 =0, where t, s〉-p, 2≤p〈N, p＊（s）= （N＋s）pN-p andλ is a real parameter. We show particularly that the above problem exists infinitely many radial solutions if the space dimension N 〉p（p-1）t＋p（p2-p＋1） andλ∈（0,λ1,t）, whereλ1,t is the first eigenvalue of-△p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ （ps＋p） min{1, p＋t/p＋s}＋p2p-（p-1） min{1, p＋tp＋s} andλ〉0 is small.
基金supported by the National Natural Science Foundation of China (Grant No. 51076128)the National High Technology Research and Development Program of China (Grant No. 2009AA05Z107)
文摘We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.
基金Project(2017YFB1201204)supported by the National Key R&D Program of ChinaProject(1053320190957)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers,e.g.static safety of factor(static FoS)or the critical seismic acceleration coefficient,while little attention has been given to the relationship between the slope stability numbers and the critical seismic acceleration coefficient.This study aims to investigate the relationship between the static FoS and the critical seismic acceleration coefficient of soil slopes in the framework of the upper-bound limit analysis.Based on the 3D rotational failure mechanism,the critical seismic acceleration coefficient using the pseudo-static method and the static FoS using the strength reduction technique are first determined.Then,the relationship between the static FoS and the critical seismic acceleration coefficient is presented under considering the slope angleβ,the frictional angleφ,and the dimensionless coefficients B/H and c/γH.Finally,a fitting formula between the static FoS and the critical seismic acceleration coefficient is proposed and validated by analytical and numerical results.
基金Project (No. 20076039) supported by the National Science Founda-tion of China
文摘The relation between the critical radius and the particle size distribution for generalized Ostwald type ripening processes whereby the mass transfer coefficient is modelled by a power law was derived. The critical radius is determined by the growth rate, the mass transfer coefficient and the mass balance, and is independent of whether the limiting stationary growth regime has been obtained.
基金sponsored by the Earthquake Science Foundation of Xinjiang,China(201105)
文摘We study the critical slowing down phenomenon in deformation and groundwater observations before the Nilka-Gongliu MS6. 0 earthquake on November 1, 2011 and Xinyuan-Hejing M S6. 6 earthquake on June 30,2012. Firstly,we remove the annual variation and tendency change of basic data by means of wavelet transform analysis.Secondly,we calculate the autocorrelation coefficients and variance of the critical slowing down phenomenon. Lastly,we try to verify the critical slowing down phenomenon before an earthquake. The result indicates that there was obvious critical slowing down of the records at different stations before earthquakes.
文摘To provide information for amendment to Technical Specifications for Power Transmission Towers (SDGJ94-90), the critical loads of typical compressed angle steels was calculated. The correlation of buckling loads and slenderness of compressed angle steels was obtained with regression. A new slenderness coefficient equation was proposed based on the result of the correlation. A practical measure to ensure good result in nonlinear solution using Arch-length method is put forward.
基金supported by National Natural Science Foundation of China (Grant No. 10728101)National Basic Research Program of China+3 种基金Doctoral Program Foundation of the Ministry of Education of Chinathe "111" projectSGST 09DZ2272900supported by the Outstanding Doctoral Science Foundation Program of Fudan University
文摘In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence.
