In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theore...In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.展开更多
Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and ...Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and pseudomorphic conversion to SrC2 O4·H2O occurs. In the second step, SrC2 O4·H2O reacts with H2C2O4 to form H[Sr(C2 O4)1.5(H2O)]. Sr(HC2 O4)(C2 O4)0.5·H2 O crystallizes during cooling of the reaction mixture to room temperature if the solution reaches the saturation concentration of (H[Sr(C2O4)1.5(H2O)]. The aims of this study are the derivation of reaction rate equations and the determination of the kinetic parameters such as pre-exponential factor, apparent activation energy and order of H2C2O4 concentration for each reaction step.Fractional conversions of SrSO4 were calculated using the quantitative amounts of dissolved S and Sr. It was determined that the reaction rate increased at the initial time of reaction by increasing the temperature using solutions with approximately same H2C2O4 concentrations. The reaction extends very slowly after a certain time in solutions with low H2C2O4 concentration and ends by the formation of a protective layer of SrC2O4-H2O around the surfaces of solid particles. Fractional conversion of SrSO4 is increased by increasing concentration of H2C2O4 at constant temperature. Kinetic model equations were derived using shrinking core model for each step.展开更多
The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are sol...The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.展开更多
By employing three typical equations of states （EOSs） of the crust matter, the effect of the crust on the structure and properties are investigated, where the core matter is described by the MDIxl model and the non-...By employing three typical equations of states （EOSs） of the crust matter, the effect of the crust on the structure and properties are investigated, where the core matter is described by the MDIxl model and the non-Newtonian gravity （described by the Yukawa contribution） is considered. It is shown that the EOSs of the crust matter have a notable effect on the mass-radius relation and the moment of inertia.展开更多
Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive for...Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.展开更多
文摘In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.
基金the financial support of the Scientific Research Projects Coordination Unit of Istanbul University (Project number: 17344 and 31088)
文摘Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and pseudomorphic conversion to SrC2 O4·H2O occurs. In the second step, SrC2 O4·H2O reacts with H2C2O4 to form H[Sr(C2 O4)1.5(H2O)]. Sr(HC2 O4)(C2 O4)0.5·H2 O crystallizes during cooling of the reaction mixture to room temperature if the solution reaches the saturation concentration of (H[Sr(C2O4)1.5(H2O)]. The aims of this study are the derivation of reaction rate equations and the determination of the kinetic parameters such as pre-exponential factor, apparent activation energy and order of H2C2O4 concentration for each reaction step.Fractional conversions of SrSO4 were calculated using the quantitative amounts of dissolved S and Sr. It was determined that the reaction rate increased at the initial time of reaction by increasing the temperature using solutions with approximately same H2C2O4 concentrations. The reaction extends very slowly after a certain time in solutions with low H2C2O4 concentration and ends by the formation of a protective layer of SrC2O4-H2O around the surfaces of solid particles. Fractional conversion of SrSO4 is increased by increasing concentration of H2C2O4 at constant temperature. Kinetic model equations were derived using shrinking core model for each step.
基金Funded by the National Natural Science Foundation of China (No.40574004).
文摘The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.
基金Supported by the National Natural Science Foundation of China under Grant No.10947023the Fundamental Research Funds for the Central Universities under Grant No.2009ZM0193the SRP of SCUT under Grant No.D210632w
文摘By employing three typical equations of states （EOSs） of the crust matter, the effect of the crust on the structure and properties are investigated, where the core matter is described by the MDIxl model and the non-Newtonian gravity （described by the Yukawa contribution） is considered. It is shown that the EOSs of the crust matter have a notable effect on the mass-radius relation and the moment of inertia.
基金National Natural Science Foundation of China(No.10272046)
文摘Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.
