In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me...In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.展开更多
In this paper,on the basis of Ref.[1],the author studies the boundary value problems of the second-order differential equations,the highest order derivatives of which contain the small parameters.The numerical example...In this paper,on the basis of Ref.[1],the author studies the boundary value problems of the second-order differential equations,the highest order derivatives of which contain the small parameters.The numerical examples show that the calculating process of this method is quite simple and its accuracy is even higher than that of the multiple scales method.展开更多
Soil-rock mixture(S-RM)is a widely distributed geotechnical medium composed of "soil" and "rock block" different both in size and strength. Internal rock blocks form special and variable meso-struc...Soil-rock mixture(S-RM)is a widely distributed geotechnical medium composed of "soil" and "rock block" different both in size and strength. Internal rock blocks form special and variable meso-structural characteristics of S-RM. The objective of this work was to study the control mechanism of meso-structural characteristics on mechanical properties of S-RM. For S-RM containing randomly generated polygonal rock blocks, a series of biaxial tests based on DEM were conducted. On the basis of research on the effects of rock blocks' breakability and sample lateral boundary type(rigid, flexible) on macroscopic mechanical behavior of S-RM, an expanded Mohr-Coulomb criterion in power function form was proposed to represent the strength envelop. At the mesoscopic level, the variations of meso-structure such as rotation of rock block, and the formation mechanism and evolution process of the shear band during tests were investigated. The results show that for S-RM with a high content of rock block, translation, rotating and breakage of rock blocks have crucial effects on mechanical behavior of S-RM. The formation and location of the shear band inside S-RM sample are also controlled by breakability and arrangement of rock blocks.展开更多
In this paper,an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary ...In this paper,an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary value methods.In order to efficiently solve the generated linear large-scale system,the generalized minimal residual(GMRES)algorithm is applied.For accelerating the convergence rate of the it erative,the St rang-type,Chantype and P-type preconditioners are introduced.The suggested met hod can reach higher order accuracy both in space and in time than the existing met hods.When the used boundary value method is Ak1,K2-stable,it is proven that Strang-type preconditioner is invertible and the spectra of preconditioned matrix is clustered around 1.It implies that the iterative solution is convergent rapidly.Numerical experiments with the absorbing boundary condition and the generalized Dirichlet type further verify the efficiency.展开更多
文摘In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.
文摘In this paper,on the basis of Ref.[1],the author studies the boundary value problems of the second-order differential equations,the highest order derivatives of which contain the small parameters.The numerical examples show that the calculating process of this method is quite simple and its accuracy is even higher than that of the multiple scales method.
基金Projects(51323014,51479095)supported by the National Natural Science Foundation of ChinaProject(20111081125)supported by Independent Research Plan of Tsinghua University,ChinaProject(2013-KY-4)supported by the State Key Laboratory of Hydroscience and Engineering Project,China
文摘Soil-rock mixture(S-RM)is a widely distributed geotechnical medium composed of "soil" and "rock block" different both in size and strength. Internal rock blocks form special and variable meso-structural characteristics of S-RM. The objective of this work was to study the control mechanism of meso-structural characteristics on mechanical properties of S-RM. For S-RM containing randomly generated polygonal rock blocks, a series of biaxial tests based on DEM were conducted. On the basis of research on the effects of rock blocks' breakability and sample lateral boundary type(rigid, flexible) on macroscopic mechanical behavior of S-RM, an expanded Mohr-Coulomb criterion in power function form was proposed to represent the strength envelop. At the mesoscopic level, the variations of meso-structure such as rotation of rock block, and the formation mechanism and evolution process of the shear band during tests were investigated. The results show that for S-RM with a high content of rock block, translation, rotating and breakage of rock blocks have crucial effects on mechanical behavior of S-RM. The formation and location of the shear band inside S-RM sample are also controlled by breakability and arrangement of rock blocks.
基金National Natural Science Foundation of China under grants 11801389 and 11571128.
文摘In this paper,an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary value methods.In order to efficiently solve the generated linear large-scale system,the generalized minimal residual(GMRES)algorithm is applied.For accelerating the convergence rate of the it erative,the St rang-type,Chantype and P-type preconditioners are introduced.The suggested met hod can reach higher order accuracy both in space and in time than the existing met hods.When the used boundary value method is Ak1,K2-stable,it is proven that Strang-type preconditioner is invertible and the spectra of preconditioned matrix is clustered around 1.It implies that the iterative solution is convergent rapidly.Numerical experiments with the absorbing boundary condition and the generalized Dirichlet type further verify the efficiency.
