This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and...This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.展开更多
Based on the hyperbolic mild-slope equations derived by Copeland (1985), a numerical model is established in unstag- gered grids. A composite 4 th-order Adam-Bashforth-Moulton (ABM) scheme is used to solve the model i...Based on the hyperbolic mild-slope equations derived by Copeland (1985), a numerical model is established in unstag- gered grids. A composite 4 th-order Adam-Bashforth-Moulton (ABM) scheme is used to solve the model in the time domain. Terms involving the first order spatial derivatives are differenced to O ( Δx )4accuracy utilizing a five-point formula. The nonlinear dispersion relationship proposed by Kirby and Dalrymple (1986) is used to consider the nonlinear effect. A numerical test is performed upon wave propagating over a typical shoal. The agreement between the numerical and the experimental results validates the present model. Biodistribution and applications are also summarized.展开更多
This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the ...This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.展开更多
基金Supported by the Chinese Academy of Sciences (No. KJ 951-B1-704), the National Natural Science Foundation of China (No. 59736130) and the State Key Fundamental Research Plan of China (No. G2000026305).
文摘This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.
基金This work is financially supported by the National Natural Science Foundation of China （50409015）.
文摘Based on the hyperbolic mild-slope equations derived by Copeland (1985), a numerical model is established in unstag- gered grids. A composite 4 th-order Adam-Bashforth-Moulton (ABM) scheme is used to solve the model in the time domain. Terms involving the first order spatial derivatives are differenced to O ( Δx )4accuracy utilizing a five-point formula. The nonlinear dispersion relationship proposed by Kirby and Dalrymple (1986) is used to consider the nonlinear effect. A numerical test is performed upon wave propagating over a typical shoal. The agreement between the numerical and the experimental results validates the present model. Biodistribution and applications are also summarized.
基金supported by the National Natural Science Foundation of China under Grant Nos.11101025,11071080,11171113the National Natural Science Foundation of China under Grant No.11126279+1 种基金the Fundamental Research Funds for the Central Universitiesthe Youth Foundation of Tianyuan Mathematics
文摘This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.
