Standard treatments of thermodynamic equilibrium are incomplete. They do not take account of all factors determining equilibrium, cannot explain why many systems do not reach equilibrium and do not discuss the questio...Standard treatments of thermodynamic equilibrium are incomplete. They do not take account of all factors determining equilibrium, cannot explain why many systems do not reach equilibrium and do not discuss the questions of reaching and maintaining equilibrium. The arguments presented here provide a single physical definition of thermodynamic equilibrium that accounts for all factors determining thermodynamic equilibrium for mixtures of combustible gases and air. Based on the standard delrmition of thermodynamic equilibrium, the MBD （Maxwell Boltzmann distribution） and a simple molecular model lead to three possible types of equilibrium. The regions of temperature pressure and composition for each type of equilibrium are defined by the measured values of ignition temperatures and the explosive and flammability limits. How this definition of thermodynamic equilibrium can be extended to all molecular systems is discussed in the following papers.展开更多
Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the propose...Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.展开更多
In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific exam...In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/kBT, kB is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.展开更多
文摘Standard treatments of thermodynamic equilibrium are incomplete. They do not take account of all factors determining equilibrium, cannot explain why many systems do not reach equilibrium and do not discuss the questions of reaching and maintaining equilibrium. The arguments presented here provide a single physical definition of thermodynamic equilibrium that accounts for all factors determining thermodynamic equilibrium for mixtures of combustible gases and air. Based on the standard delrmition of thermodynamic equilibrium, the MBD （Maxwell Boltzmann distribution） and a simple molecular model lead to three possible types of equilibrium. The regions of temperature pressure and composition for each type of equilibrium are defined by the measured values of ignition temperatures and the explosive and flammability limits. How this definition of thermodynamic equilibrium can be extended to all molecular systems is discussed in the following papers.
基金Supported by the National Natural Science Foundations of China under Grant Nos.61202051,11272132the Special Fund for Basic Scientific Research of Central CollegesChina University of Geosciences Wuhan under Grant Nos.CUG110828 and CUG130416
文摘Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.
基金supported by the Natural Science Foundation of Yunnan Province (Grant No. 2010CD031)the National Natural Science Foun-dation of China (Grant Nos. 50906035, 51066002 and U0937604)
文摘In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/kBT, kB is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.
