Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending ext...Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.展开更多
The Sommerfeld electrical conductivity is calculated in d dimensions following Boltzmann kinetic approach.At T = 0,the mathematical form of the electrical conductivity is found to remain invariant in any generalised s...The Sommerfeld electrical conductivity is calculated in d dimensions following Boltzmann kinetic approach.At T = 0,the mathematical form of the electrical conductivity is found to remain invariant in any generalised spatial(d)dimensions.展开更多
Crimped ribbon flame arresters are important safety devices in the chemical industry, especially for the danger- ous situations. Although proper design of arresters by the numerical simulation method is promising, its...Crimped ribbon flame arresters are important safety devices in the chemical industry, especially for the danger- ous situations. Although proper design of arresters by the numerical simulation method is promising, its reliabil- ity and accuracy are dependent upon the mathematical model. In this work, an integrated mathematical model for the microchannel in the crimped ribbon flame attesters was set up; the fluid flow behavior and the sensitiv- ities of four chemical kinetics mechanisms of propane-air on the accuracy were analysed. It is shown that turbu- lence is predominant in the microchannel of the crimped ribbon flame arresters under the defiagration and detonation conditions, and a new quenching criterion for the numerical simulation is proposed. The kinetics mechanism of Mansouri et al. among the four ones is the most accurate due to the best agreement of the pre- dicted outlet temperature at the experimental flameproof velocity with the autoignition temperature of propane-air. The species mass fraction profiles and the temperature distribution, which are too difficult to mea- sure due to the tiny dimension of the microchannel in experiments, are captured. The fundamental insights into chemical reactions and heat loss are well portrayed. It can be concluded that the integrated mathematical model established in this work can be used as a reliable tool for modeling, selecting and designing such type of crimped ribbon flame attesters with the propane-air medium in the future.展开更多
The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods.Weibull distribution function was adopted to de...The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods.Weibull distribution function was adopted to describe the mesoscopic heterogeneity of rocks.The failure process of heterogeneous rock specimen under uniaxial loading was simulated using FLAC 3D software.Five schemes were adopted to investigate the influence of heterogeneity.The results demonstrate that as the homogeneity increases,the peak strength and brittleness of rocks increase,and the macro elastic modulus improves as well.Heterogeneity has great influence on macro elastic modulus and strength when the homogeneity coefficient is less than 20.0.The volume expansion is not so obvious when the homogeneity increases.As the homogeneity coefficient increases the acoustic emissions modes change from swarm shock to main shock.When the homogeneity coefficient is high,the cumulative acoustic emission events-axial strain curve is gentle before the rock failure.The numerical results agree with the previously numerical results and earlier experimental measurements.展开更多
A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the...A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.展开更多
A direct feedback control system based on fuzzy recurrent neural network is proposed, and a method of training weights of fuzzy recurrent neural network was designed by applying modified contract mapping genetic algor...A direct feedback control system based on fuzzy recurrent neural network is proposed, and a method of training weights of fuzzy recurrent neural network was designed by applying modified contract mapping genetic algorithm. Computer simulation results indicate that fuzzy recurrent neural network controller has perfect dynamic and static performances .展开更多
Through the experiment of coal spontaneous combustion and relationship particle size with oxidation character of loose coal, some calculation formula of characteristic parameters is got in the process of coal spontane...Through the experiment of coal spontaneous combustion and relationship particle size with oxidation character of loose coal, some calculation formula of characteristic parameters is got in the process of coal spontaneous combustion. According to these theories of porous medium hydrodynamics, mass transfer and heat transfer, mathematical models of air leak field, oxygen concentration field and temperature field are set up. Through experimental and theoretical analysis, 3 D dynamic mathematical model of coal spontaneous combustion is set up. The method of ascertaining boundary condition of model is analyzed, and finite difference method is adopted to solve 2 D mathematical model.展开更多
This paper, having made systematic trend analysis on the front and rear segments of Xintan landslide for space and time respectively by using matbematical statistical principles,discovered that there is obvious trend ...This paper, having made systematic trend analysis on the front and rear segments of Xintan landslide for space and time respectively by using matbematical statistical principles,discovered that there is obvious trend displacement Of the monitoring points in the rear margin area of the slope and the rates of trend displacement gradually increase with time whereas there is no trend displacement of the monitoring points in the front margin area. This result suggests that the rear margin area of segment is an area of overall sliding and is transforming towards destabilization whereas the front margin area is an area of relative stability. This analytical result well coincides with the conclusion of evaluation on dynamic stability. The analytical result mentioned above shows that the medium to short term forecast and prediction of slope stability can be made by using trend displacement analysis technique in order to achieve the goal of timely evaluation and prevention.展开更多
A mathematical model of the kinetics of thin-layer separation of granular materials by size stacked sieve classifiers based on the theory of Markov processes is constructed. The probability of screening in a cell in t...A mathematical model of the kinetics of thin-layer separation of granular materials by size stacked sieve classifiers based on the theory of Markov processes is constructed. The probability of screening in a cell in the shape and size of the holes and particle sieve material shared with the influence of the relative speed of their movement was determined. Residues on whole meal with sieves were identified by a kinetic model and numerical calculations, the efficacy of separation.展开更多
Let u=u（x,t,uo）represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt＋δux＋γHuxx＋βuxxx＋f（u）x=αuxx,u（x,0）=uo（x）, whereα〉0,β〉0,γ〉0,δ〉0...Let u=u（x,t,uo）represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt＋δux＋γHuxx＋βuxxx＋f（u）x=αuxx,u（x,0）=uo（x）, whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f（0）=0,｜f（u）｜→∞as ｜u｜→∞,and f∈C^1（R）,and there exist the following limits Lo=lim sup/u→o f（u）/u^3 and L∞=lim sup/u→∞ f（u）/u^5 Suppose that the initial function u0∈L^I（R）∩H^2（R）.By using energy estimates,Fourier transform,Plancherel＇s identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv（xxt）＋δvx＋γHv（xx）＋βv（xxx）=αv（xx）,v（x,0）=vo（x）, the author justifies the following limits（with sharp rates of decay） lim t→∞[（1＋t）^（m＋1/2）∫｜uxm（x,t）｜^2dx]=1/2π（π/2α）^（1/2）m!!/（4α）^m[∫R uo（x）dx]^2, if∫R uo（x）dx≠0, where 0!!=1,1!!=1 and m!!=1·3…（2m-3）…（2m-1）.Moreover lim t→∞[（1＋t）^（m＋3/2）∫R｜uxm（x,t）｜^2dx]=1/2π（x/2α）^（1/2）（m＋1）!!/（4α）^（m＋1）[∫Rρo（x）dx]^2, if the initial function uo（x）=ρo′（x）,for some functionρo∈C^1（R）∩L^1（R）and∫Rρo（x）dx≠0.展开更多
Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQ...Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.展开更多
文摘Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.
文摘The Sommerfeld electrical conductivity is calculated in d dimensions following Boltzmann kinetic approach.At T = 0,the mathematical form of the electrical conductivity is found to remain invariant in any generalised spatial(d)dimensions.
基金Supported by the National Key Research and Development Program of China(2016YFB0301701)the National Natural Science Foundation of China(21706268+4 种基金9143411421376254)the Postdoctoral Science Foundation of Qingdao Municipal Government(Y7330419DM)the Instrument Developing Project of the Chinese Academy of Sciences(YZ201641)State Key Laboratory of Safety and Control for Chemicals of China
文摘Crimped ribbon flame arresters are important safety devices in the chemical industry, especially for the danger- ous situations. Although proper design of arresters by the numerical simulation method is promising, its reliabil- ity and accuracy are dependent upon the mathematical model. In this work, an integrated mathematical model for the microchannel in the crimped ribbon flame attesters was set up; the fluid flow behavior and the sensitiv- ities of four chemical kinetics mechanisms of propane-air on the accuracy were analysed. It is shown that turbu- lence is predominant in the microchannel of the crimped ribbon flame arresters under the defiagration and detonation conditions, and a new quenching criterion for the numerical simulation is proposed. The kinetics mechanism of Mansouri et al. among the four ones is the most accurate due to the best agreement of the pre- dicted outlet temperature at the experimental flameproof velocity with the autoignition temperature of propane-air. The species mass fraction profiles and the temperature distribution, which are too difficult to mea- sure due to the tiny dimension of the microchannel in experiments, are captured. The fundamental insights into chemical reactions and heat loss are well portrayed. It can be concluded that the integrated mathematical model established in this work can be used as a reliable tool for modeling, selecting and designing such type of crimped ribbon flame attesters with the propane-air medium in the future.
基金Project(2007CB209407) supported by the National Basic Research Program of ChinaProject(50729904) supported by the National Natural Science Foundation of China
文摘The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods.Weibull distribution function was adopted to describe the mesoscopic heterogeneity of rocks.The failure process of heterogeneous rock specimen under uniaxial loading was simulated using FLAC 3D software.Five schemes were adopted to investigate the influence of heterogeneity.The results demonstrate that as the homogeneity increases,the peak strength and brittleness of rocks increase,and the macro elastic modulus improves as well.Heterogeneity has great influence on macro elastic modulus and strength when the homogeneity coefficient is less than 20.0.The volume expansion is not so obvious when the homogeneity increases.As the homogeneity coefficient increases the acoustic emissions modes change from swarm shock to main shock.When the homogeneity coefficient is high,the cumulative acoustic emission events-axial strain curve is gentle before the rock failure.The numerical results agree with the previously numerical results and earlier experimental measurements.
基金The project supported by National Natural Science Foundation of China under Grant No. 90403019
文摘A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.
文摘A direct feedback control system based on fuzzy recurrent neural network is proposed, and a method of training weights of fuzzy recurrent neural network was designed by applying modified contract mapping genetic algorithm. Computer simulation results indicate that fuzzy recurrent neural network controller has perfect dynamic and static performances .
文摘Through the experiment of coal spontaneous combustion and relationship particle size with oxidation character of loose coal, some calculation formula of characteristic parameters is got in the process of coal spontaneous combustion. According to these theories of porous medium hydrodynamics, mass transfer and heat transfer, mathematical models of air leak field, oxygen concentration field and temperature field are set up. Through experimental and theoretical analysis, 3 D dynamic mathematical model of coal spontaneous combustion is set up. The method of ascertaining boundary condition of model is analyzed, and finite difference method is adopted to solve 2 D mathematical model.
文摘This paper, having made systematic trend analysis on the front and rear segments of Xintan landslide for space and time respectively by using matbematical statistical principles,discovered that there is obvious trend displacement Of the monitoring points in the rear margin area of the slope and the rates of trend displacement gradually increase with time whereas there is no trend displacement of the monitoring points in the front margin area. This result suggests that the rear margin area of segment is an area of overall sliding and is transforming towards destabilization whereas the front margin area is an area of relative stability. This analytical result well coincides with the conclusion of evaluation on dynamic stability. The analytical result mentioned above shows that the medium to short term forecast and prediction of slope stability can be made by using trend displacement analysis technique in order to achieve the goal of timely evaluation and prevention.
文摘A mathematical model of the kinetics of thin-layer separation of granular materials by size stacked sieve classifiers based on the theory of Markov processes is constructed. The probability of screening in a cell in the shape and size of the holes and particle sieve material shared with the influence of the relative speed of their movement was determined. Residues on whole meal with sieves were identified by a kinetic model and numerical calculations, the efficacy of separation.
文摘Let u=u（x,t,uo）represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt＋δux＋γHuxx＋βuxxx＋f（u）x=αuxx,u（x,0）=uo（x）, whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f（0）=0,｜f（u）｜→∞as ｜u｜→∞,and f∈C^1（R）,and there exist the following limits Lo=lim sup/u→o f（u）/u^3 and L∞=lim sup/u→∞ f（u）/u^5 Suppose that the initial function u0∈L^I（R）∩H^2（R）.By using energy estimates,Fourier transform,Plancherel＇s identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv（xxt）＋δvx＋γHv（xx）＋βv（xxx）=αv（xx）,v（x,0）=vo（x）, the author justifies the following limits（with sharp rates of decay） lim t→∞[（1＋t）^（m＋1/2）∫｜uxm（x,t）｜^2dx]=1/2π（π/2α）^（1/2）m!!/（4α）^m[∫R uo（x）dx]^2, if∫R uo（x）dx≠0, where 0!!=1,1!!=1 and m!!=1·3…（2m-3）…（2m-1）.Moreover lim t→∞[（1＋t）^（m＋3/2）∫R｜uxm（x,t）｜^2dx]=1/2π（x/2α）^（1/2）（m＋1）!!/（4α）^（m＋1）[∫Rρo（x）dx]^2, if the initial function uo（x）=ρo′（x）,for some functionρo∈C^1（R）∩L^1（R）and∫Rρo（x）dx≠0.
基金supported by the National Natural Science Foundation of China (20973077, 20303007)the Program for New Century Excellent Talents in University (NCET)
文摘Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.
