In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on...In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.展开更多
The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coeffici...The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α（v,μ）,γ（v,μ）and the scattering-fission kernel k（x,v,v′,μ,μ′）are boundedmeasurable,and the total collision frequency v∑（x,v）is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i（?）|β<sub>1</sub>（?）β（?）β<sub>2</sub>},where β<sub>2</sub>】β<sub>1</sub>】-λ<sup>*</sup>,with λ<sup>*</sup> the essential infimum of v∑（x,v）.Fi-nally,the asymptotic expansion of the solution for the time-dependent equation（dN）/（dt）=AN,N（0）=N<sub>0</sub> is given as a corollary.展开更多
The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yield...The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yields a robust Absorbing Boundary Condition(ABC) independent of the angle of incidence and the frequency of outgoing waves. In this paper, the principle of the PML technique is briefly presented. Then some problems in the application and their settlements are discussed emphatically. Finally three numerical tests and a measured result are devoted to examine the accuracy and effectiveness of this approach.展开更多
This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C<sub>0</sub>-semigroup theory,we have proved that this problemhas a un...This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C<sub>0</sub>-semigroup theory,we have proved that this problemhas a unique nonnegative solution and found the spectral property of the corresponding transportoperator.Finally we give the asymptotic behavior of the solution for this equation.展开更多
This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak so...This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.展开更多
文摘In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.
基金Project supported by the National Natural Science Foundation of China
文摘The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α（v,μ）,γ（v,μ）and the scattering-fission kernel k（x,v,v′,μ,μ′）are boundedmeasurable,and the total collision frequency v∑（x,v）is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i（?）|β<sub>1</sub>（?）β（?）β<sub>2</sub>},where β<sub>2</sub>】β<sub>1</sub>】-λ<sup>*</sup>,with λ<sup>*</sup> the essential infimum of v∑（x,v）.Fi-nally,the asymptotic expansion of the solution for the time-dependent equation（dN）/（dt）=AN,N（0）=N<sub>0</sub> is given as a corollary.
基金Supported by the National Natural Science Foundation of China
文摘The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yields a robust Absorbing Boundary Condition(ABC) independent of the angle of incidence and the frequency of outgoing waves. In this paper, the principle of the PML technique is briefly presented. Then some problems in the application and their settlements are discussed emphatically. Finally three numerical tests and a measured result are devoted to examine the accuracy and effectiveness of this approach.
基金Project supported by the science Fund of the Chinese Academy of Sciences
文摘This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C<sub>0</sub>-semigroup theory,we have proved that this problemhas a unique nonnegative solution and found the spectral property of the corresponding transportoperator.Finally we give the asymptotic behavior of the solution for this equation.
文摘This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.
