The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics...The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.展开更多
Although several strategies(including grain refinement,texture adjustment,precipitation hardening,etc.)have been verified to effectively improve the mechanical properties of lightweight magnesium(Mg)alloys,considerabl...Although several strategies(including grain refinement,texture adjustment,precipitation hardening,etc.)have been verified to effectively improve the mechanical properties of lightweight magnesium(Mg)alloys,considerable efforts are still needed to be made to comprehensively understand the potential mechanisms controlling complex microstructures and deformation behaviors exhibited by the hexagonal close-packed host lattice of Mg,thus assisting the rational design of materials at a more physical level.As the cornerstone of this review,a universal rule,the so-called synergy of thermodynamics and kinetics(i.e.,thermo-kinetic diversity,correlation and connectivity),including a recently proposed theory of generalized stability(GS),is introduced to deepen our understanding on common behaviors in Mg alloys(i.e.,deformations(slip and twining modes),phase transformations(especially for precipitations)and interactions in between)at a new perspective.Guided by the GS theory,typical cases for Mg alloys design are qualitatively evaluated to reemphasize the traditional strengthening and toughening strategies mentioned above and to illuminate their exquisite coordination for breaking through the trade-off relationship between strength and ductility,corresponding to a typical thermo-kinetic pair(i.e.,high driving force(ΔG)-high GS).To produce the Mg alloys with superior strength-ductility balances,the potential capacity of this GS theory for guiding processing path design is discussed,finally。展开更多
By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact...By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.展开更多
The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer progra...The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer program, are presented graphically. An example of the computer program with all physicochemical knowledge involved in the related algorithm is attached herewith.展开更多
This work obtains the disguise version of exact solitary wave solutions of the generalized(2+1)-dimensk>nal Zakharov-Kuznetsov-Benjamin-Bona-Mahony and the regularized long wave equation with some free parame...This work obtains the disguise version of exact solitary wave solutions of the generalized(2+1)-dimensk>nal Zakharov-Kuznetsov-Benjamin-Bona-Mahony and the regularized long wave equation with some free parameters via modified simple equation method(MSE).Usually the method does not give any solution if the balance number is more than one,but we apply MSE method successfully in different way to carry out the solutions of nonlinear evolution equation with balance number two.Finally some graphical results of the velocity profiles are presented for different values of the material constants.It is shown that this method,without help of any symbolic computation,provide a straightforward and powerful mathematical tool for solving nonlinear evolution equation.展开更多
The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were ob...The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were obtained according to Approach II to GEB, i.e., on the basis of the equation 2?f(O) ? f(H) obtained from elemental balances: f(H) for H, and f(O) for O. Equivalency of the Approach II and the Approach I to GEB was proved for an aqueous solution and a binary-solvent system. On this basis, a compact form of GEB was derived.展开更多
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear tran...A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.展开更多
A complex example of electrolytic redox system involving 47 species, 3 electron-active elements and five (3 am-phiprotic + 2 aprotic) co-solvents, is presented. Mixed solvates of the species thus formed are admitted i...A complex example of electrolytic redox system involving 47 species, 3 electron-active elements and five (3 am-phiprotic + 2 aprotic) co-solvents, is presented. Mixed solvates of the species thus formed are admitted in the system considered. It is proved that the Generalized Electron Balance (GEB) in its simplest form obtained according to the Approach II to GEB is identical with the one obtained for aqueous media and binary-solvent system, and is equivalent to the Approach I to GEB.展开更多
基金The project supported in part by USA NIH Grant under HG002894
文摘The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
基金the Natural Science Foundation of China(Nos.52130110,52171013 and 51790481)the Research Fund of the State Key Laboratory of Solidification Processing(Nos.2019-TZ-01 and 2019-BJ-02)+1 种基金the Fundamental Research Funds for the Central Universities(No.3102020QD0412)“2020-2022 Youth Talent Promotion Project”of China Association for Science and Technology.
文摘Although several strategies(including grain refinement,texture adjustment,precipitation hardening,etc.)have been verified to effectively improve the mechanical properties of lightweight magnesium(Mg)alloys,considerable efforts are still needed to be made to comprehensively understand the potential mechanisms controlling complex microstructures and deformation behaviors exhibited by the hexagonal close-packed host lattice of Mg,thus assisting the rational design of materials at a more physical level.As the cornerstone of this review,a universal rule,the so-called synergy of thermodynamics and kinetics(i.e.,thermo-kinetic diversity,correlation and connectivity),including a recently proposed theory of generalized stability(GS),is introduced to deepen our understanding on common behaviors in Mg alloys(i.e.,deformations(slip and twining modes),phase transformations(especially for precipitations)and interactions in between)at a new perspective.Guided by the GS theory,typical cases for Mg alloys design are qualitatively evaluated to reemphasize the traditional strengthening and toughening strategies mentioned above and to illuminate their exquisite coordination for breaking through the trade-off relationship between strength and ductility,corresponding to a typical thermo-kinetic pair(i.e.,high driving force(ΔG)-high GS).To produce the Mg alloys with superior strength-ductility balances,the potential capacity of this GS theory for guiding processing path design is discussed,finally。
基金Supported by the Natural Science Foundation of Education Committee of Henan Province（2003110003）
文摘By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.
文摘The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer program, are presented graphically. An example of the computer program with all physicochemical knowledge involved in the related algorithm is attached herewith.
文摘This work obtains the disguise version of exact solitary wave solutions of the generalized(2+1)-dimensk>nal Zakharov-Kuznetsov-Benjamin-Bona-Mahony and the regularized long wave equation with some free parameters via modified simple equation method(MSE).Usually the method does not give any solution if the balance number is more than one,but we apply MSE method successfully in different way to carry out the solutions of nonlinear evolution equation with balance number two.Finally some graphical results of the velocity profiles are presented for different values of the material constants.It is shown that this method,without help of any symbolic computation,provide a straightforward and powerful mathematical tool for solving nonlinear evolution equation.
文摘The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were obtained according to Approach II to GEB, i.e., on the basis of the equation 2?f(O) ? f(H) obtained from elemental balances: f(H) for H, and f(O) for O. Equivalency of the Approach II and the Approach I to GEB was proved for an aqueous solution and a binary-solvent system. On this basis, a compact form of GEB was derived.
文摘A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.
文摘A complex example of electrolytic redox system involving 47 species, 3 electron-active elements and five (3 am-phiprotic + 2 aprotic) co-solvents, is presented. Mixed solvates of the species thus formed are admitted in the system considered. It is proved that the Generalized Electron Balance (GEB) in its simplest form obtained according to the Approach II to GEB is identical with the one obtained for aqueous media and binary-solvent system, and is equivalent to the Approach I to GEB.
