After the investigation on partial remelting of thixotropic magnesium serial alloys (ZK60) by near non-equilibrium liquidus casting (NNLC), the primary solid grains of ZK60-2Ca alloy spheroidized notably during pa...After the investigation on partial remelting of thixotropic magnesium serial alloys (ZK60) by near non-equilibrium liquidus casting (NNLC), the primary solid grains of ZK60-2Ca alloy spheroidized notably during partial remelting processing, however, coarsening and polygonization as occurred holding time prolonged. The refining and globularity of the thixotropic alloys are promoted after further alloyed by Y, RE, Nd and/or Ag, and the results vary with those addition. The remelting structure of ZK60-2Ca-1Y alloy is finer than its base alloy. And the effect of RE, especially Ag, on the refinement of microstrueture is notable, but Nd does nothing on it. There is little impact of remelting temperature fluctuation on partial remelted microstrueture as holding time in general. On the contrary, it is more sensitive at longer holding time. The quality thixotropic silver-contained alloy can be achieved by remelted partially at 600℃ for 10 min.展开更多
Ericson formula represents the first formula, which was suggested to describe the partial level density (PLD) formula in pre-equilibrium region of the nuclear reactions. Then a number of corrections were added to this...Ericson formula represents the first formula, which was suggested to describe the partial level density (PLD) formula in pre-equilibrium region of the nuclear reactions. Then a number of corrections were added to this formula in order to make it more suitable to physical meaning. In this paper, there are two aims to be done: the first aim is to study the correspondence between one and two-components formulae in Ericson, Pauli, and pairing corrections;the second aim is to compare and study the results of Comprehensive formula, which contents with all corrections, with Ericson, Pauli, and pairing formulae. The Comprehensive formula was suggested to simulate the reality. To achieve these aims the 56Fe and 90Zr nuclei were chosen and the results showed that the difference between one and two-components formulae was too small which can be neglected. Furthermore, the results strongly recommended that for cross section calculations of the nuclear reaction, one must use Comprehensive formula rather than Pauli formula.展开更多
A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate system.Compared with the existin...A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate system.Compared with the existing approaches,the pGHQ scheme has the following advantages:extremely concise algorithm,unifies the constructing procedure for symmetric and asymmetric on-node lattices,and covers a full-range quadrature degree of a given discrete velocity set.We employ the pGHQ scheme to search the local optimal and asymmetric lattices for{n=3,4,5,6,7}moment degree equilibrium distribution discretization on the range[-10,10].The search reveals a surprising abundance of available lattices.Through a brief analysis,the discrete velocity set shows a significant influence on the positivity of equilibrium distributions,which is considered as one of the major impacts of the numerical stability of the LB method.Hence,the results of the p GHQ scheme lay a foundation for further investigations to improve the numerical stability of the LB method by modifying the discrete velocity set.It is also worth noting that pGHQ can be extended into the entropic LB model,even though it was proposed for the Hermite polynomial expansion LB theory.展开更多
Ultrahigh-pressure(UHP) metamorphic rocks are distinctive products of crustal deep subduction,and are mainly exposed in continental subduction-collision terranes. UHP slices of continental crust are usually involved...Ultrahigh-pressure(UHP) metamorphic rocks are distinctive products of crustal deep subduction,and are mainly exposed in continental subduction-collision terranes. UHP slices of continental crust are usually involved in multistage exhumation and partial melting, which has obvious influence on the rheological features of the rocks, and thus significantly affect the dynamic behavior of subducted slices. Moreover,partial melting of UHP rocks have significant influence on element mobility and related isotope behavior within continental subduction zones, which is in turn crucial to chemical differentiation of the continental crust and to crust-mantle interaction.Partial melting can occur before, during or after the peak metamorphism of UHP rocks. Post-peak decompression melting has been better constrained by remelting experiments; however, because of multiple stages of decompression, retrogression and deformation, evidence of former melts in UHP rocks is often erased. Field evidence is among the most reliable criteria to infer partial melting. Glass and nanogranitoid inclusions are generally considered conclusive petrographic evidence. The residual assemblages after melt extraction are also significant to indicate partial melting in some cases. Besides field and petrographic evidence, bulk-rock and zircon trace-element geochemical features are also effective tools for recognizing partial melting of UHP rocks. Phase equilibrium modeling is an important petrological tool that is becoming more and more popular in P-T estimation of the evolution of metamorphic rocks; by taking into account the activity model of silicate melt, it can predict when partial melting occurred if the P-T path of a given rock is provided.UHP silicate melt is commonly leucogranitic and peraluminous in composition with high SiO_2,low MgO, FeO, MnO, TiO_2 and CaO, and variable K_2 O and Na_2 O contents. Mineralogy of nanogranites found in UHP rocks mainly consists of plagioclase + K-feldspar + quartz, plagioclase being commonly albite-rich.Trace element pattern of the melt is characterized by significant enrichment of large ion lithophile elements(LILE), depletion of heavy rare earth elements(HREE) and high field strength elements(HFSE),indicating garnet and rutile stability in the residual assemblage. In eclogites, significant Mg-isotope fractionation occurs between garnet and phengite; therefore, Mg isotopes may become an effective indicator for partial melting of eclogites.展开更多
The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principl...The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.展开更多
In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasico...In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, and Ci(x)-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.展开更多
A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems...A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings展开更多
This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and ph...This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game G<sub>C</sub> has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game G<sub>Q</sub> with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γ<sub>c</sub> such that for γγ<sub>c</sub> there is a pure strategy Nash equilibrium and for γ≥γ<sub>c </sub>there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.展开更多
文摘After the investigation on partial remelting of thixotropic magnesium serial alloys (ZK60) by near non-equilibrium liquidus casting (NNLC), the primary solid grains of ZK60-2Ca alloy spheroidized notably during partial remelting processing, however, coarsening and polygonization as occurred holding time prolonged. The refining and globularity of the thixotropic alloys are promoted after further alloyed by Y, RE, Nd and/or Ag, and the results vary with those addition. The remelting structure of ZK60-2Ca-1Y alloy is finer than its base alloy. And the effect of RE, especially Ag, on the refinement of microstrueture is notable, but Nd does nothing on it. There is little impact of remelting temperature fluctuation on partial remelted microstrueture as holding time in general. On the contrary, it is more sensitive at longer holding time. The quality thixotropic silver-contained alloy can be achieved by remelted partially at 600℃ for 10 min.
文摘Ericson formula represents the first formula, which was suggested to describe the partial level density (PLD) formula in pre-equilibrium region of the nuclear reactions. Then a number of corrections were added to this formula in order to make it more suitable to physical meaning. In this paper, there are two aims to be done: the first aim is to study the correspondence between one and two-components formulae in Ericson, Pauli, and pairing corrections;the second aim is to compare and study the results of Comprehensive formula, which contents with all corrections, with Ericson, Pauli, and pairing formulae. The Comprehensive formula was suggested to simulate the reality. To achieve these aims the 56Fe and 90Zr nuclei were chosen and the results showed that the difference between one and two-components formulae was too small which can be neglected. Furthermore, the results strongly recommended that for cross section calculations of the nuclear reaction, one must use Comprehensive formula rather than Pauli formula.
基金Project supported by the National Science and Technology Major Project,China(Grant No.2017ZX06002002)
文摘A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate system.Compared with the existing approaches,the pGHQ scheme has the following advantages:extremely concise algorithm,unifies the constructing procedure for symmetric and asymmetric on-node lattices,and covers a full-range quadrature degree of a given discrete velocity set.We employ the pGHQ scheme to search the local optimal and asymmetric lattices for{n=3,4,5,6,7}moment degree equilibrium distribution discretization on the range[-10,10].The search reveals a surprising abundance of available lattices.Through a brief analysis,the discrete velocity set shows a significant influence on the positivity of equilibrium distributions,which is considered as one of the major impacts of the numerical stability of the LB method.Hence,the results of the p GHQ scheme lay a foundation for further investigations to improve the numerical stability of the LB method by modifying the discrete velocity set.It is also worth noting that pGHQ can be extended into the entropic LB model,even though it was proposed for the Hermite polynomial expansion LB theory.
基金financially supported by the National Basic Research Program of China (Grant No. 2015CB856104)the National Natural Science Foundation of China (Grant No. 41273036)
文摘Ultrahigh-pressure(UHP) metamorphic rocks are distinctive products of crustal deep subduction,and are mainly exposed in continental subduction-collision terranes. UHP slices of continental crust are usually involved in multistage exhumation and partial melting, which has obvious influence on the rheological features of the rocks, and thus significantly affect the dynamic behavior of subducted slices. Moreover,partial melting of UHP rocks have significant influence on element mobility and related isotope behavior within continental subduction zones, which is in turn crucial to chemical differentiation of the continental crust and to crust-mantle interaction.Partial melting can occur before, during or after the peak metamorphism of UHP rocks. Post-peak decompression melting has been better constrained by remelting experiments; however, because of multiple stages of decompression, retrogression and deformation, evidence of former melts in UHP rocks is often erased. Field evidence is among the most reliable criteria to infer partial melting. Glass and nanogranitoid inclusions are generally considered conclusive petrographic evidence. The residual assemblages after melt extraction are also significant to indicate partial melting in some cases. Besides field and petrographic evidence, bulk-rock and zircon trace-element geochemical features are also effective tools for recognizing partial melting of UHP rocks. Phase equilibrium modeling is an important petrological tool that is becoming more and more popular in P-T estimation of the evolution of metamorphic rocks; by taking into account the activity model of silicate melt, it can predict when partial melting occurred if the P-T path of a given rock is provided.UHP silicate melt is commonly leucogranitic and peraluminous in composition with high SiO_2,low MgO, FeO, MnO, TiO_2 and CaO, and variable K_2 O and Na_2 O contents. Mineralogy of nanogranites found in UHP rocks mainly consists of plagioclase + K-feldspar + quartz, plagioclase being commonly albite-rich.Trace element pattern of the melt is characterized by significant enrichment of large ion lithophile elements(LILE), depletion of heavy rare earth elements(HREE) and high field strength elements(HFSE),indicating garnet and rutile stability in the residual assemblage. In eclogites, significant Mg-isotope fractionation occurs between garnet and phengite; therefore, Mg isotopes may become an effective indicator for partial melting of eclogites.
基金Project supported by the National Natural Science Foundation of China(No.10771173)
文摘The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.
基金supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, and Ci(x)-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.
基金Project supported by the Natural Science Foundation of Sichuan Educational Commission (No.2003A081)
文摘A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings
文摘This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game G<sub>C</sub> has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game G<sub>Q</sub> with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γ<sub>c</sub> such that for γγ<sub>c</sub> there is a pure strategy Nash equilibrium and for γ≥γ<sub>c </sub>there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.