The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and th...The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.展开更多
In the spirit of Morse homology initiated by Witten and Floer,we construct two∞-categories A and B.The weak one A comes out of the Morse-Smale pairs and their higher homotopies,and the strict one B concerns the chain...In the spirit of Morse homology initiated by Witten and Floer,we construct two∞-categories A and B.The weak one A comes out of the Morse-Smale pairs and their higher homotopies,and the strict one B concerns the chain complexes of the Morse functions.Based on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters,we build up a weak∞-functor F:A→B.Higher algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory.展开更多
Let MR<sup>n+1</sup> be a compact connected smooth hypersurface, and WR<sup>n+1</sup> be the area bounded by M. We study the question: Does W contain a principal centre of curvature for some po...Let MR<sup>n+1</sup> be a compact connected smooth hypersurface, and WR<sup>n+1</sup> be the area bounded by M. We study the question: Does W contain a principal centre of curvature for some point of M?展开更多
This paper studies the Gauss map of submanifolds in space forms defined by Willmore andSaleemi. By using Morse functions,it is proved that the degree of Gauss map is the Eulernumber of the submanifold.The tight immers...This paper studies the Gauss map of submanifolds in space forms defined by Willmore andSaleemi. By using Morse functions,it is proved that the degree of Gauss map is the Eulernumber of the submanifold.The tight immersions are also studied.展开更多
We construct explicit Morse functions on Grassmannian manifolds, and use them to find explicit taut embeddings of the quadratic hypersurfaces in complex projective spaces into Euclidean spaces.
基金Support provided by Department of Science and Technology(DST),Government of India vide Grant No.DST/INSPIRE Fellowship/2020/IF200538。
文摘The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.
基金Supported by National Key R&D Program of China(Grant No.2020YFA0713300)NSFC(Grant Nos.11771303,12171327,11911530092,11871045)。
文摘In the spirit of Morse homology initiated by Witten and Floer,we construct two∞-categories A and B.The weak one A comes out of the Morse-Smale pairs and their higher homotopies,and the strict one B concerns the chain complexes of the Morse functions.Based on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters,we build up a weak∞-functor F:A→B.Higher algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory.
文摘Let MR<sup>n+1</sup> be a compact connected smooth hypersurface, and WR<sup>n+1</sup> be the area bounded by M. We study the question: Does W contain a principal centre of curvature for some point of M?
文摘This paper studies the Gauss map of submanifolds in space forms defined by Willmore andSaleemi. By using Morse functions,it is proved that the degree of Gauss map is the Eulernumber of the submanifold.The tight immersions are also studied.
文摘We construct explicit Morse functions on Grassmannian manifolds, and use them to find explicit taut embeddings of the quadratic hypersurfaces in complex projective spaces into Euclidean spaces.
