An unequal time interval sequence or a sequence with blanks is usually completed with average generation in grey system theory. This paper discovers that there exists obvious errors when using average generation to ge...An unequal time interval sequence or a sequence with blanks is usually completed with average generation in grey system theory. This paper discovers that there exists obvious errors when using average generation to generate internal points of non-consecutive neighbours. The average generation and the preference generation of the sequence are discussed, the concave and convex properties show the status of local sequence and propose a new idea for using the status to build up the criteria of choosing generation coefficient. Compared with the general average method of the one-dimensional data sequence, the two-dimensional data sequence is defined and its average generation is discussed, and the coefficient decision method for the preference generation is presented.展开更多
The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory （MFT）. The dependence of th...The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory （MFT）. The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and trieritical line.展开更多
The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We ...The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We divide a given difficult random K-SAT formula into two easy sub-formulas and let the two corresponding solution spaces to interact with each other through a coupling field x. We investigate the statistical mechanical property of this coupled system by mean field theory and computer simulations. The coupled system has an ergodicity-breaking （clustering） transition at certain critical value Xd of the coupling field. At this transition point, the mean overlap value between the solutions of the two solution spaces is very close to 1. The mean energy density of the coupled system at its clustering transition point is less than the mean energy density of the original K-SAT problem at the temperature-induced clustering transition point. The implications of this work for designing new heuristic K-SAT solvers are discussed.展开更多
The atom fidelity is investigated in a system consisting of Mtwo-level atoms and M single-mode fields by use of complete quantum theory and numerical evaluation method. The influences of various system parameters on t...The atom fidelity is investigated in a system consisting of Mtwo-level atoms and M single-mode fields by use of complete quantum theory and numerical evaluation method. The influences of various system parameters on the evolution of atomic fidelity are studied. The results show that the atomic fidelity evolves in a Rabi oscillation manner. The oscillation frequency is mainly modulated by the coupling strength between atoms and light field, the atomic transition probabilities and the average photon numbers. Other factors hardly impact on the atomic fidelity. The present results may provide a useful approach to the maintenance of the atomic fidelity in the atom cavity field systems.展开更多
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.展开更多
文摘An unequal time interval sequence or a sequence with blanks is usually completed with average generation in grey system theory. This paper discovers that there exists obvious errors when using average generation to generate internal points of non-consecutive neighbours. The average generation and the preference generation of the sequence are discussed, the concave and convex properties show the status of local sequence and propose a new idea for using the status to build up the criteria of choosing generation coefficient. Compared with the general average method of the one-dimensional data sequence, the two-dimensional data sequence is defined and its average generation is discussed, and the coefficient decision method for the preference generation is presented.
文摘The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory （MFT）. The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and trieritical line.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences under Grant No.KJCX2-EW-J02the Natural National Science Foundation of China under Grant Nos.11121403 and 11225526
文摘The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We divide a given difficult random K-SAT formula into two easy sub-formulas and let the two corresponding solution spaces to interact with each other through a coupling field x. We investigate the statistical mechanical property of this coupled system by mean field theory and computer simulations. The coupled system has an ergodicity-breaking （clustering） transition at certain critical value Xd of the coupling field. At this transition point, the mean overlap value between the solutions of the two solution spaces is very close to 1. The mean energy density of the coupled system at its clustering transition point is less than the mean energy density of the original K-SAT problem at the temperature-induced clustering transition point. The implications of this work for designing new heuristic K-SAT solvers are discussed.
基金Supported by the National Nature Science Foundation of China under Grant No.11304230Nature Science Foundation of Shaanxi Province under Grant No.2013JM1006+1 种基金the Project of Education Department of Shaanxi Provincial Government under Grant No.2013JK0634the Special Subject Construction of Weinan Normal University under Grant Nos.14TSXK06 and 15ZRRC14
文摘The atom fidelity is investigated in a system consisting of Mtwo-level atoms and M single-mode fields by use of complete quantum theory and numerical evaluation method. The influences of various system parameters on the evolution of atomic fidelity are studied. The results show that the atomic fidelity evolves in a Rabi oscillation manner. The oscillation frequency is mainly modulated by the coupling strength between atoms and light field, the atomic transition probabilities and the average photon numbers. Other factors hardly impact on the atomic fidelity. The present results may provide a useful approach to the maintenance of the atomic fidelity in the atom cavity field systems.
基金supported by National Natural Science Foundation of China(Grant No.91130005)the US Army Research Office(Grant No.W911NF-11-1-0101)
文摘This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
