A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncatio...A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncation error is O（△t^2 ＋ △x^4）.展开更多
In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability c...In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.展开更多
In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition...In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function. As its application, the approximate solutions are constructed.展开更多
Reference [1] deals with the uniqueness of solution to problem （A） and solution of problem （A） is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of ...Reference [1] deals with the uniqueness of solution to problem （A） and solution of problem （A） is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of problem （A） is continuously dependent on boundary value on the basis of references [2] and [3].展开更多
We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the lo...We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.展开更多
In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depen...In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.展开更多
Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes （SWNTs） is studied by the nonequilibrium molecular dynamics （MD） method with Brenner Ⅱ potential. The thermal co...Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes （SWNTs） is studied by the nonequilibrium molecular dynamics （MD） method with Brenner Ⅱ potential. The thermal conductivities are calculated for （5, 5） and （7, 7） SWNTs with lengths ranging from 22 to 155nm. The results show that the thermal conductivity of SWNTs is sensitive to the length and it does not converge to a finite value when the tube length increases up to 155nm, however it obeys a power law relation.展开更多
Using the scattering matrix method, we investigate the thermal transport m a nanostructure at low temperarures. It is found that phonon transport exhibits some novel and interesting features： resonant transmission, r...Using the scattering matrix method, we investigate the thermal transport m a nanostructure at low temperarures. It is found that phonon transport exhibits some novel and interesting features： resonant transmission, resonant reflection, and small thermal conductance. A comparison between thermal conductances is performed when stress-free and hard-wall boundary conditions are applied for acoustic modes, respectively. The result indicates that the characteristics of the thermal conductance versus temperature for different types of boundary conditions are qualitatively different.展开更多
基金NSF of the Education Department of Henan Province(20031100010)
文摘A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncation error is O（△t^2 ＋ △x^4）.
基金Supported by NSF of the Education Department of Henan Province(20031100010)
文摘In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.
文摘In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function. As its application, the approximate solutions are constructed.
文摘Reference [1] deals with the uniqueness of solution to problem （A） and solution of problem （A） is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of problem （A） is continuously dependent on boundary value on the basis of references [2] and [3].
基金supported by the China Postdoctoral Science Foundation (20090450333)supported by the National Basic Research Program (2005CB321700)NSFC (40890154)
文摘We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.
基金supported by NSFC (11171228,10801111,10971171)the fundamental Research Funds for the Central University (2010121006)the Natural Science Foundation of Fujian Province of China (2010J05011)
文摘In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.
文摘Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes （SWNTs） is studied by the nonequilibrium molecular dynamics （MD） method with Brenner Ⅱ potential. The thermal conductivities are calculated for （5, 5） and （7, 7） SWNTs with lengths ranging from 22 to 155nm. The results show that the thermal conductivity of SWNTs is sensitive to the length and it does not converge to a finite value when the tube length increases up to 155nm, however it obeys a power law relation.
基金Supported by the National Natural Science Foundation of China under Grant No 10547132, and the Young Teacher Foundation of Tianjin University under Grant No 5110117.
文摘Using the scattering matrix method, we investigate the thermal transport m a nanostructure at low temperarures. It is found that phonon transport exhibits some novel and interesting features： resonant transmission, resonant reflection, and small thermal conductance. A comparison between thermal conductances is performed when stress-free and hard-wall boundary conditions are applied for acoustic modes, respectively. The result indicates that the characteristics of the thermal conductance versus temperature for different types of boundary conditions are qualitatively different.
