A model of liquid ZA27 cast alloy is established according to molecular dynamics theory and an atomic structural model of co-existent a phase and liquid is also presented by means of computer programming. Recursion me...A model of liquid ZA27 cast alloy is established according to molecular dynamics theory and an atomic structural model of co-existent a phase and liquid is also presented by means of computer programming. Recursion method is adopted to calculate the electronic structure of RE (rare earth) in grains and around phase boundaries respectively. The calculation shows that RE is more stable around phase boundaries than in grains, which explains the fact that the solution of RE in a phase is less, and RE mainly aggregates in front of phase boundary. The calculations of bonding order integrals also show that RE in front of phases hardly solidify onto the grain surfaces as active element so as to prevent grains growth and refine the grains. As a result, the modification mechanism of RE may be explained from the view of electronic structure.展开更多
The model of dislocations was used to construct the model of grain boundary (GB) with pure rare earths, and rare earth elements and impurities. The influence of the interaction between rare earth elements and impuriti...The model of dislocations was used to construct the model of grain boundary (GB) with pure rare earths, and rare earth elements and impurities. The influence of the interaction between rare earth elements and impurities on the cohesive properties of 5.3° low angle GB of Fe was investigated by the recursion method. The calculated results of environment sensitive embeding energy( E ESE ) show that the preferential segregation of rare earth elements towards GBs exists. Calculations of bond order integrals (BOI) show that rare earth elements increase the cohesive strength of low angle GB, and impurities such as S, P weaken the intergranular cohesion of the GB. So rare earth element of proper quantity added in steel not only cleanses other harmful impurities off the GBs, but also enhances the intergranular cohesion. This elucidates the action mechanism of rare earth elements in steel from electronic level and offers theoretical evidence for applications of rare earth elements in steels.展开更多
The model of the liquid-phase ZA27 alloys was set up by molecular dynamics theory. The atomic structure of phase, RE-compounds, and the phase-liquid interface in ZA27 alloys were constructed by computer programming. E...The model of the liquid-phase ZA27 alloys was set up by molecular dynamics theory. The atomic structure of phase, RE-compounds, and the phase-liquid interface in ZA27 alloys were constructed by computer programming. Electronic structures of phase with rare earth elements dissolved and of phase-liquid interfaces with rare earth elements enrichment in ZA27 casting alloys were investigated by using the Recursion method. The ESE energy of RE elements and the structure energy of RE-compounds, phase, and the liquid-phase ZA27 alloys were calculated. The results show that rare earth elements are more stable to be in the phase interface than in phase, which explains the fact of very small solid solubility of rare earth elements in phase, and the enrichment in the solid-liquid growth front. This makes dendrite melt and break down, dissociate and propagate. RE-compounds can act as heterogeneous nuclei for phase, leading to phase refinement. All above elucidates the modification mechanism of rare earth elements in zinc-aluminum casting alloys at electronic level.展开更多
An atomic group model of the disordered binary alloy Rhx-Pt1-x has been constructed to investigate surface segregation. According to the model, we have calculated the electronic structure of the Rhx-Pt1-x alloy surfac...An atomic group model of the disordered binary alloy Rhx-Pt1-x has been constructed to investigate surface segregation. According to the model, we have calculated the electronic structure of the Rhx-Pt1-x alloy surface by using the recursion method when O atoms are adsorbed on the Rhx-Pt1-x （110） surface under the condition of coverage 0.5. The calculation results indicate that the chemical adsorption of O changes greatly the density of states near the Fermi level, and the surface segregation exhibits a reversal behaviour. In addition, when x 〈 0.3, the surface on which O is adsorbed displays the property of Pt; whereas when x 〉 0.3 it displays the property of Rh.展开更多
Recursion leads to automatic matrix blocking in the computation of dense linear algebra. It makes a good use of memory hierarchies of today's high-performance computers and hence improves the efficiency of the alg...Recursion leads to automatic matrix blocking in the computation of dense linear algebra. It makes a good use of memory hierarchies of today's high-performance computers and hence improves the efficiency of the algorithm. The recursive algorithm for LU factorization of matrix that is used to solve linear systems of equations is studied in this paper. A detailed derivation of the recursive algorithm is presented. FORTRAN90 language, which supports recursion as a language feature, is used to implement the algorithm. Experimental results show that the recursive algorithm is near 20% faster than the currently used block algorithm.展开更多
Arnoldi’s method and the incomplete orthogonalization method (IOM) for large non-Hermitian linear systerns are studied. It is shown that the inverse of a general nonsingular j × j Hessenberg matrir can be update...Arnoldi’s method and the incomplete orthogonalization method (IOM) for large non-Hermitian linear systerns are studied. It is shown that the inverse of a general nonsingular j × j Hessenberg matrir can be updated in O(j2) flops from that of its (j -1) × (j - 1) principal submatrir. The updating recursion of inverses of the Hessenberg matrices does not need any QR or LU decompostion as commonly used in the literature. Some updating recursions of the residual norms and the approximate solutions obtained by these two methods are derived. These results are appealing because they allow one to decide when the methods converge and show one how to compute approximate solutions very cheaply and easily.展开更多
The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal de...The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.展开更多
基金Authors deeply appreciate the support from the National Natural Science Foundation of China(No.50275098)the Natural Science Foundation of Liaoning Province(No.20022031)
文摘A model of liquid ZA27 cast alloy is established according to molecular dynamics theory and an atomic structural model of co-existent a phase and liquid is also presented by means of computer programming. Recursion method is adopted to calculate the electronic structure of RE (rare earth) in grains and around phase boundaries respectively. The calculation shows that RE is more stable around phase boundaries than in grains, which explains the fact that the solution of RE in a phase is less, and RE mainly aggregates in front of phase boundary. The calculations of bonding order integrals also show that RE in front of phases hardly solidify onto the grain surfaces as active element so as to prevent grains growth and refine the grains. As a result, the modification mechanism of RE may be explained from the view of electronic structure.
文摘The model of dislocations was used to construct the model of grain boundary (GB) with pure rare earths, and rare earth elements and impurities. The influence of the interaction between rare earth elements and impurities on the cohesive properties of 5.3° low angle GB of Fe was investigated by the recursion method. The calculated results of environment sensitive embeding energy( E ESE ) show that the preferential segregation of rare earth elements towards GBs exists. Calculations of bond order integrals (BOI) show that rare earth elements increase the cohesive strength of low angle GB, and impurities such as S, P weaken the intergranular cohesion of the GB. So rare earth element of proper quantity added in steel not only cleanses other harmful impurities off the GBs, but also enhances the intergranular cohesion. This elucidates the action mechanism of rare earth elements in steel from electronic level and offers theoretical evidence for applications of rare earth elements in steels.
文摘The model of the liquid-phase ZA27 alloys was set up by molecular dynamics theory. The atomic structure of phase, RE-compounds, and the phase-liquid interface in ZA27 alloys were constructed by computer programming. Electronic structures of phase with rare earth elements dissolved and of phase-liquid interfaces with rare earth elements enrichment in ZA27 casting alloys were investigated by using the Recursion method. The ESE energy of RE elements and the structure energy of RE-compounds, phase, and the liquid-phase ZA27 alloys were calculated. The results show that rare earth elements are more stable to be in the phase interface than in phase, which explains the fact of very small solid solubility of rare earth elements in phase, and the enrichment in the solid-liquid growth front. This makes dendrite melt and break down, dissociate and propagate. RE-compounds can act as heterogeneous nuclei for phase, leading to phase refinement. All above elucidates the modification mechanism of rare earth elements in zinc-aluminum casting alloys at electronic level.
基金Project supported by the National Natural Science Foundation of China （Grant No 50571071）.
文摘An atomic group model of the disordered binary alloy Rhx-Pt1-x has been constructed to investigate surface segregation. According to the model, we have calculated the electronic structure of the Rhx-Pt1-x alloy surface by using the recursion method when O atoms are adsorbed on the Rhx-Pt1-x （110） surface under the condition of coverage 0.5. The calculation results indicate that the chemical adsorption of O changes greatly the density of states near the Fermi level, and the surface segregation exhibits a reversal behaviour. In addition, when x 〈 0.3, the surface on which O is adsorbed displays the property of Pt; whereas when x 〉 0.3 it displays the property of Rh.
文摘Recursion leads to automatic matrix blocking in the computation of dense linear algebra. It makes a good use of memory hierarchies of today's high-performance computers and hence improves the efficiency of the algorithm. The recursive algorithm for LU factorization of matrix that is used to solve linear systems of equations is studied in this paper. A detailed derivation of the recursive algorithm is presented. FORTRAN90 language, which supports recursion as a language feature, is used to implement the algorithm. Experimental results show that the recursive algorithm is near 20% faster than the currently used block algorithm.
文摘Arnoldi’s method and the incomplete orthogonalization method (IOM) for large non-Hermitian linear systerns are studied. It is shown that the inverse of a general nonsingular j × j Hessenberg matrir can be updated in O(j2) flops from that of its (j -1) × (j - 1) principal submatrir. The updating recursion of inverses of the Hessenberg matrices does not need any QR or LU decompostion as commonly used in the literature. Some updating recursions of the residual norms and the approximate solutions obtained by these two methods are derived. These results are appealing because they allow one to decide when the methods converge and show one how to compute approximate solutions very cheaply and easily.
基金Supported by the National Natural Science Foundation of China (61862033, 61762049, 61902162)Jiangxi Provincial Natural Science Foundation (20202BABL202026, 20202BABL202025, 20202BAB202015)。
文摘The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.
