B2-ordered Fe3Al single crystals with various orientations were deformed in tension at room temperature in vacuum. The shape of shear stress-strain curves and work hardening rates were found to be strongly dependent o...B2-ordered Fe3Al single crystals with various orientations were deformed in tension at room temperature in vacuum. The shape of shear stress-strain curves and work hardening rates were found to be strongly dependent on the orientation. The formation of the five different work hardening stages were considered to be related to the number of operative slip systems, the effect of secondary slip systems and the dissociation of the twofold superdislocation. Stage I is an easy glide stage corresponding to single slip. Stage II, with high hardening rate, often corresponds to the existence of conjugate slip systems. Stage III, with relatively low hardening rate, corresponds to the weaker hardening of secondary slip systems. Stage IV, with the highest hardening rate, is not only related to multiple slip but also the dissociation of twofold superdislocations and the moving of superpartials with an antiphase boundary (APB) trap. Stages V, with a negative hardening rate, may be caused by the cross slip of single dissociated superdislocation. The number of stages and the work hardening rate of the same stage were also found to change significantly, when the tensile orientation lies in different orientation regions.展开更多
The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional and higher-order extension of the famous KdV equation in fluid dynamics. In this paper, by constructing new test functions, we invest...The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional and higher-order extension of the famous KdV equation in fluid dynamics. In this paper, by constructing new test functions, we investigate the periodic solitary wave solutions for the (2 + 1)-dimensional fifth-order KdV equation by virtue of the Hirota bilinear form. Several novel analytic solutions for such a model are obtained and verified with the help of symbolic computation.展开更多
In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth mani...In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.展开更多
This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a mathematical model that can simulate the evolution and/or tr...This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2<sup>nd</sup>-CASAM.展开更多
This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a benchmark mathematical model that can simulate th...This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.展开更多
基金This work was supported by the China Research and Development Fund (No. 59681005)
文摘B2-ordered Fe3Al single crystals with various orientations were deformed in tension at room temperature in vacuum. The shape of shear stress-strain curves and work hardening rates were found to be strongly dependent on the orientation. The formation of the five different work hardening stages were considered to be related to the number of operative slip systems, the effect of secondary slip systems and the dissociation of the twofold superdislocation. Stage I is an easy glide stage corresponding to single slip. Stage II, with high hardening rate, often corresponds to the existence of conjugate slip systems. Stage III, with relatively low hardening rate, corresponds to the weaker hardening of secondary slip systems. Stage IV, with the highest hardening rate, is not only related to multiple slip but also the dissociation of twofold superdislocations and the moving of superpartials with an antiphase boundary (APB) trap. Stages V, with a negative hardening rate, may be caused by the cross slip of single dissociated superdislocation. The number of stages and the work hardening rate of the same stage were also found to change significantly, when the tensile orientation lies in different orientation regions.
文摘The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional and higher-order extension of the famous KdV equation in fluid dynamics. In this paper, by constructing new test functions, we investigate the periodic solitary wave solutions for the (2 + 1)-dimensional fifth-order KdV equation by virtue of the Hirota bilinear form. Several novel analytic solutions for such a model are obtained and verified with the help of symbolic computation.
文摘In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.
文摘This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2<sup>nd</sup>-CASAM.
文摘This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.
