We consider the diffusion process Xt on Rn with radial diffusion and drift coefficients. We prove that once the one-dimensional diffusion ｜Xt｜ has algebraic L2-convergence, so does Xt. And some classical examples ar...We consider the diffusion process Xt on Rn with radial diffusion and drift coefficients. We prove that once the one-dimensional diffusion ｜Xt｜ has algebraic L2-convergence, so does Xt. And some classical examples are discussed.展开更多
In this paper,the coupling method is used to study the ergodicity for infinite dimensional diffusion processes on manifolos The result presented here improves,in some interesting cases,the results obtained by Deuschel...In this paper,the coupling method is used to study the ergodicity for infinite dimensional diffusion processes on manifolos The result presented here improves,in some interesting cases,the results obtained by Deuschel and Stroock (1990) by using the logarithmic Sobolev inequality.展开更多
The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statisti...The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statistical physics and consist of an important class of interacting particle systems which is currently an active research field in probability and mathematical physics. The models are concrete but as a part of the infinite-dimensional mathematics, the topic is quite hard. It is explained how new problems arise, and how some new ideas and new mathematical tools are introduced. Surprisingly, the mathematical tools produced from the study on the simple models then turn to have a lot of powerful applications not only in probability theory but also in other branches of mathematics. Nevertheless, the story is still far from finished, and some important open problems are proposed for further study.展开更多
A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model,we extend the th...A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model,we extend the theory of the broadening exponent of critical fluctuations to cover the chemical reaction-heat conduction coupling systems as an asymptotic property of the corresponding Markovian master equation (ME),and establish a valid stochastic thermodynamics for such systems. As an illustration,the non-isothermal and inhomogeneous Schl-gl model is explicitly studied. Through an order analysis of the contributions from both the drift and diffusion to the evolution of the probability distribution in the corresponding Fokker-Planck equation(FPE) in the approach to bifurcation,we have identified the critical transition rule for the broadening exponent of the fluctuations due to the coupling between chemical reaction and heat conduction. It turns out that the dissipation induced by the critical fluctuations reaches a deterministic level,leading to a thermodynamic effect on the nonequilibrium physico-chemical processes.展开更多
This work is concerned with successful couplings for a class of multidimensional diffusion processes with state-dependent switching. We construct a type of couplings for this class of processes, and give some sufficie...This work is concerned with successful couplings for a class of multidimensional diffusion processes with state-dependent switching. We construct a type of couplings for this class of processes, and give some sufficient conditions to guarantee this type of couplings to be successful. Besides, two illustrative examples are provided.展开更多
The absorption of CO2 in insoluble organic amine is crucial for understanding the mechanism of coupled reaction-extraction-crystallization process between aqueous chloride and CO2. In this study, the solubility and di...The absorption of CO2 in insoluble organic amine is crucial for understanding the mechanism of coupled reaction-extraction-crystallization process between aqueous chloride and CO2. In this study, the solubility and diffusivity of CO2 in n-butanol＋ N235 system were measured and reported. The absorption of CO2 in the system is a physical absorption behavior and the solubility of CO2 decreases with the increase of the mass fraction of N235. The diffusivity of CO2 increases firstly and then decreases with the increase in the mass fraction of N235. Moreover, the absorption mechanism of CO2 in the coupled reaction-extraction-crystallization process was investigated and identified by experiments. The results indicated that in the coupled reaction-extraction-crystallization process, CO2 is absorbed by the aqueous phase rather than by the organic phase and further transferred into the aqueous phase.展开更多
We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative...We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11101040, 11371283, 11431014）, YETP0264, 985 Projects, and the Fundamental Research Funds for the Central Universities.
文摘We consider the diffusion process Xt on Rn with radial diffusion and drift coefficients. We prove that once the one-dimensional diffusion ｜Xt｜ has algebraic L2-convergence, so does Xt. And some classical examples are discussed.
文摘In this paper,the coupling method is used to study the ergodicity for infinite dimensional diffusion processes on manifolos The result presented here improves,in some interesting cases,the results obtained by Deuschel and Stroock (1990) by using the logarithmic Sobolev inequality.
文摘The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statistical physics and consist of an important class of interacting particle systems which is currently an active research field in probability and mathematical physics. The models are concrete but as a part of the infinite-dimensional mathematics, the topic is quite hard. It is explained how new problems arise, and how some new ideas and new mathematical tools are introduced. Surprisingly, the mathematical tools produced from the study on the simple models then turn to have a lot of powerful applications not only in probability theory but also in other branches of mathematics. Nevertheless, the story is still far from finished, and some important open problems are proposed for further study.
基金supported by the National Natural Science Foundation of China (20673074 & 20973119)
文摘A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model,we extend the theory of the broadening exponent of critical fluctuations to cover the chemical reaction-heat conduction coupling systems as an asymptotic property of the corresponding Markovian master equation (ME),and establish a valid stochastic thermodynamics for such systems. As an illustration,the non-isothermal and inhomogeneous Schl-gl model is explicitly studied. Through an order analysis of the contributions from both the drift and diffusion to the evolution of the probability distribution in the corresponding Fokker-Planck equation(FPE) in the approach to bifurcation,we have identified the critical transition rule for the broadening exponent of the fluctuations due to the coupling between chemical reaction and heat conduction. It turns out that the dissipation induced by the critical fluctuations reaches a deterministic level,leading to a thermodynamic effect on the nonequilibrium physico-chemical processes.
基金supported by National Natural Science Foundation of China(Grant No.11171024)Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200917)
文摘This work is concerned with successful couplings for a class of multidimensional diffusion processes with state-dependent switching. We construct a type of couplings for this class of processes, and give some sufficient conditions to guarantee this type of couplings to be successful. Besides, two illustrative examples are provided.
文摘The absorption of CO2 in insoluble organic amine is crucial for understanding the mechanism of coupled reaction-extraction-crystallization process between aqueous chloride and CO2. In this study, the solubility and diffusivity of CO2 in n-butanol＋ N235 system were measured and reported. The absorption of CO2 in the system is a physical absorption behavior and the solubility of CO2 decreases with the increase of the mass fraction of N235. The diffusivity of CO2 increases firstly and then decreases with the increase in the mass fraction of N235. Moreover, the absorption mechanism of CO2 in the coupled reaction-extraction-crystallization process was investigated and identified by experiments. The results indicated that in the coupled reaction-extraction-crystallization process, CO2 is absorbed by the aqueous phase rather than by the organic phase and further transferred into the aqueous phase.
文摘We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.
