The fast dynamic properties of the surface of metallic glasses(MGs) play a critical role in determining their potential applications. However, due to the significant difference in thermal history between atomic simula...The fast dynamic properties of the surface of metallic glasses(MGs) play a critical role in determining their potential applications. However, due to the significant difference in thermal history between atomic simulation models and laboratory-made samples, the atomic-scale behaviors of the fast surface dynamics of MGs in experiments remain uncertain. Herein, we prepared model MG films with notable variations in thermal stability using a recently developed efficient annealing protocol, and investigated their atomic-scale dynamics systematically. We found that the dynamics of surface atoms remain invariant, whereas the difference in dynamical heterogeneity between surface and interior regions increases with the improvement of thermal stability. This can be associated with the more pronounced correlation between atomic activation energy spectra and depth from the surface in samples with higher thermal stability. In addition, dynamic anisotropy appears for surface atoms, and their transverse dynamics are faster than normal components, which can also be interpreted by activation energy spectra. Our results reveal the presence of strong liquid-like atomic dynamics confined to the surface of laboratory-made MGs, illuminating the underlying mechanisms for surface engineering design, such as cold joining by ultrasonic vibrations and superlattice growth.展开更多
In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial di...In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.展开更多
Consider a three-dimensional system having an invariant surface. By using bifurca- tion techniques and analyzing the solutions of bifurcation equations, the authors study the spacial bifurcation phenomena of a k multi...Consider a three-dimensional system having an invariant surface. By using bifurca- tion techniques and analyzing the solutions of bifurcation equations, the authors study the spacial bifurcation phenomena of a k multiple closed orbit in the invariant surface. The su?cient conditions of the existence of many closed orbits bifurcate from the k multiple closed orbit are obtained.展开更多
If T is an isomorphism of L<sub>∞</sub>（A,μ）into L<sub>∞</sub>（B,v）which satisfies the condition ||T|| ||T<sup>-1</sup>||≤1+ε,where（A,μ）is a σ-finite measure space then...If T is an isomorphism of L<sub>∞</sub>（A,μ）into L<sub>∞</sub>（B,v）which satisfies the condition ||T|| ||T<sup>-1</sup>||≤1+ε,where（A,μ）is a σ-finite measure space then T/||T||is close to an isometry with an error less than 4ε1.展开更多
A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n ...A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n - 1）-dimensional invariant surface called carrying simplex E as a globe attractor, hence the long term dynamics of the system is com- pletely determined by the dynamics on E. For the three-dimensional system, the whole dynamical behavior was presented. It has a unique positive equilibrium point and any limit set is either an equilibrium point or a limit cycle. The system is permanent and it is proved that the number of periodic orbits is finite and non-periodic oscillation the May Leonard phenomenon does not exist. A criterion for the positive equilibrium to be globally asymptotically stable is provided. Whether there exist limit cycles or not remains open.展开更多
We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its...We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.展开更多
基金sponsored by the National Natural Science Foundation of China (Grant No. 52101201)supported by the National Natural Science Foundation of China (Grant No.T2325004)+2 种基金sponsored by the National Natural Science Foundation of China(Grant No. 51801046)the Natural Science Foundation of Chongqing,China (Grant No. cstc2021jcyj-msxm X0369)the Science Fund for Scientific and Technological Innovation Team of Shaanxi Province (Grant No. 2021TD-14)。
文摘The fast dynamic properties of the surface of metallic glasses(MGs) play a critical role in determining their potential applications. However, due to the significant difference in thermal history between atomic simulation models and laboratory-made samples, the atomic-scale behaviors of the fast surface dynamics of MGs in experiments remain uncertain. Herein, we prepared model MG films with notable variations in thermal stability using a recently developed efficient annealing protocol, and investigated their atomic-scale dynamics systematically. We found that the dynamics of surface atoms remain invariant, whereas the difference in dynamical heterogeneity between surface and interior regions increases with the improvement of thermal stability. This can be associated with the more pronounced correlation between atomic activation energy spectra and depth from the surface in samples with higher thermal stability. In addition, dynamic anisotropy appears for surface atoms, and their transverse dynamics are faster than normal components, which can also be interpreted by activation energy spectra. Our results reveal the presence of strong liquid-like atomic dynamics confined to the surface of laboratory-made MGs, illuminating the underlying mechanisms for surface engineering design, such as cold joining by ultrasonic vibrations and superlattice growth.
基金supported by the NNSF of China (11171191 and 11201266)
文摘In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.
基金Project supported by the Ministry of Education of China (No.20010248019, No.20020248010) and theNational Natural Science Foundation of China (No.10371072).
文摘Consider a three-dimensional system having an invariant surface. By using bifurca- tion techniques and analyzing the solutions of bifurcation equations, the authors study the spacial bifurcation phenomena of a k multiple closed orbit in the invariant surface. The su?cient conditions of the existence of many closed orbits bifurcate from the k multiple closed orbit are obtained.
文摘If T is an isomorphism of L<sub>∞</sub>（A,μ）into L<sub>∞</sub>（B,v）which satisfies the condition ||T|| ||T<sup>-1</sup>||≤1+ε,where（A,μ）is a σ-finite measure space then T/||T||is close to an isometry with an error less than 4ε1.
文摘A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n - 1）-dimensional invariant surface called carrying simplex E as a globe attractor, hence the long term dynamics of the system is com- pletely determined by the dynamics on E. For the three-dimensional system, the whole dynamical behavior was presented. It has a unique positive equilibrium point and any limit set is either an equilibrium point or a limit cycle. The system is permanent and it is proved that the number of periodic orbits is finite and non-periodic oscillation the May Leonard phenomenon does not exist. A criterion for the positive equilibrium to be globally asymptotically stable is provided. Whether there exist limit cycles or not remains open.
基金partially supported by a MINECO-FEDER(Grant No.MTM2016-77278-P)a MINECO(Grant No.MTM2013-40998-P)+1 种基金an AGAUR(Grant No.2014SGR-568)partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
