A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square ...A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.展开更多
The chaotic system is sensitive to the initial value, and this can be applied in the weak signal detection. There are periodic, critical and chaotic states in a chaotic system. When the system is in the critical stat...The chaotic system is sensitive to the initial value, and this can be applied in the weak signal detection. There are periodic, critical and chaotic states in a chaotic system. When the system is in the critical state, a small perturbation of system,n parameter may lead to a qualitative change of the system＇s state. This paper introduces a new method to detect weak signals by the way of disturbing the damping ratio. The authors choose the duffing equation, using MATLAB to carry on the simulation, to study the changes of the system when the signal to be measured is added to the damping ratio. By means of observing the phase loots chart and time damin chart, the weak signal will be detected.展开更多
Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The princi...Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λn(L, t) = Lγ/νf n(t L^(1/ν)), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ1, λ2 and λ6, we get the finite-size scaling form of the second moment correlation length ξ(L, t) = Lξ(tL^(1/ν)).It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.展开更多
文摘A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.
文摘The chaotic system is sensitive to the initial value, and this can be applied in the weak signal detection. There are periodic, critical and chaotic states in a chaotic system. When the system is in the critical state, a small perturbation of system,n parameter may lead to a qualitative change of the system＇s state. This paper introduces a new method to detect weak signals by the way of disturbing the damping ratio. The authors choose the duffing equation, using MATLAB to carry on the simulation, to study the changes of the system when the signal to be measured is added to the damping ratio. By means of observing the phase loots chart and time damin chart, the weak signal will be detected.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11121403 and 11504384
文摘Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λn(L, t) = Lγ/νf n(t L^(1/ν)), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ1, λ2 and λ6, we get the finite-size scaling form of the second moment correlation length ξ(L, t) = Lξ(tL^(1/ν)).It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.
