Wc show that there is no localization for the 4-order Schrodinger operator Jt,Af and Bearn operator 38%more precisely,on the one hand,we show that the 4-order Schrodinger operator Atf, does not converge pointwise to z...Wc show that there is no localization for the 4-order Schrodinger operator Jt,Af and Bearn operator 38%more precisely,on the one hand,we show that the 4-order Schrodinger operator Atf, does not converge pointwise to zero as t→0 provided f∈H^s(R)with compact support and 0<s<1/4 by constructing a counterexample in R.On the other hand,we show that the Beam operator Btf also has the same property with the 4-order Schrodinger operator Jt,4f.Hence,we find that the Hausdorff dimension of the divergence set for Jt,4f and Btf is a1,J4(s)=a1,B(s)=1 as 0<s<1/4.展开更多
This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</...This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. Previous works showed that the third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections are far larger than the corresponding 1<sup>st</sup>-order and 2<sup>nd</sup>-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4<sup>th</sup>-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4<sup>th</sup>-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross sections, and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.展开更多
Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refrac...Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.11761131002).
文摘Wc show that there is no localization for the 4-order Schrodinger operator Jt,Af and Bearn operator 38%more precisely,on the one hand,we show that the 4-order Schrodinger operator Atf, does not converge pointwise to zero as t→0 provided f∈H^s(R)with compact support and 0<s<1/4 by constructing a counterexample in R.On the other hand,we show that the Beam operator Btf also has the same property with the 4-order Schrodinger operator Jt,4f.Hence,we find that the Hausdorff dimension of the divergence set for Jt,4f and Btf is a1,J4(s)=a1,B(s)=1 as 0<s<1/4.
文摘This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. Previous works showed that the third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections are far larger than the corresponding 1<sup>st</sup>-order and 2<sup>nd</sup>-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4<sup>th</sup>-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4<sup>th</sup>-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross sections, and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.
文摘Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.
