Based on theory of three-dimensional hydrodynamics, an Euler-Lagrangian particle model is established to study the transport and water exchange capability in the Jiaozhou Bay. The three-dimensional hydrodynamic model,...Based on theory of three-dimensional hydrodynamics, an Euler-Lagrangian particle model is established to study the transport and water exchange capability in the Jiaozhou Bay. The three-dimensional hydrodynamic model, driven by tide and wind, is used to study the effects of wetting and drying of estuarine intertidal flats by the dry-wet grid technology based on the Estuarine, Coastal and Ocean Model （ECOM）. The particle model includes the advection and the diffusion processes, of which the advection process is simulated with a certain method, and the diffusion process is simulated with the random walk method. The effect of the intertidal zone, the turbulent diffusion and the timescales of the water exchange are also discussed. The results show that a moving boundary model can simulate the transport process of the particle in the intertidal zone, where the particles are transported for a longer distance than that of the stationary result. Simulations with and without the turbulent random walk show that the effect of turbulent diffusion is very effective at spreading particles throughout the estuary and speeding up the particle movement. The spatial distribution of residence time is given to quantify the water exchange capability that has very important ramifications to water quality. The effect of wind on the water exchange is also examined and the southeasterly wind in summer tends to block the water exchange near the northeast coast, while the northerly wind in winter speeds up the transport process. These results indicate that the Lagrangian particle model is applicable and has a large potential to help understanding the water exchange capability in estuaries, which can also be useful to simulate the transport process of contaminant.展开更多
In this paper, we develop a unique time-varying forecasting model for dynamic demand of medical resources based on a susceptible-exposed-infected-recovered （SEIR） influenza diffusion model. In this forecasting mecha...In this paper, we develop a unique time-varying forecasting model for dynamic demand of medical resources based on a susceptible-exposed-infected-recovered （SEIR） influenza diffusion model. In this forecasting mechanism, medical resources allocated in the early period will take effect in subduing the spread of influenza and thus impact the demand in the later period. We adopt a discrete time-space network to describe the medical resources allocation process following a hypothetical influenza outbreak in a region. The entire medical resources allocation process is constructed as a multi-stage integer programming problem. At each stage, we solve a cost minimization sub-problem subject to the time-varying demand. The corresponding optimal allocation result is then used as an input to the control process of influenza spread, which in turn determines the demand for the next stage. In addition, we present a comparison between the proposed model and an empirical model. Our results could help decision makers prepare for a pandemic, including how to allocate limited resources dynamically.展开更多
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obta...A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.展开更多
A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is const...A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.展开更多
In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but...In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.展开更多
Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form...Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.展开更多
基金Supported by the National Natural Science Foundation of China(No.40676016)the National Key Project for Basics Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004).
基金supported by the Special Fund for Public Welfare Industry(Oceanography)(Grant No.20080511)
文摘Based on theory of three-dimensional hydrodynamics, an Euler-Lagrangian particle model is established to study the transport and water exchange capability in the Jiaozhou Bay. The three-dimensional hydrodynamic model, driven by tide and wind, is used to study the effects of wetting and drying of estuarine intertidal flats by the dry-wet grid technology based on the Estuarine, Coastal and Ocean Model （ECOM）. The particle model includes the advection and the diffusion processes, of which the advection process is simulated with a certain method, and the diffusion process is simulated with the random walk method. The effect of the intertidal zone, the turbulent diffusion and the timescales of the water exchange are also discussed. The results show that a moving boundary model can simulate the transport process of the particle in the intertidal zone, where the particles are transported for a longer distance than that of the stationary result. Simulations with and without the turbulent random walk show that the effect of turbulent diffusion is very effective at spreading particles throughout the estuary and speeding up the particle movement. The spatial distribution of residence time is given to quantify the water exchange capability that has very important ramifications to water quality. The effect of wind on the water exchange is also examined and the southeasterly wind in summer tends to block the water exchange near the northeast coast, while the northerly wind in winter speeds up the transport process. These results indicate that the Lagrangian particle model is applicable and has a large potential to help understanding the water exchange capability in estuaries, which can also be useful to simulate the transport process of contaminant.
基金partially supported by the National Natural Science Foundation of China (No.71301076,71401075)Natural Science Foundation of Jiangsu Province(BK20130771)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(20133219120037)the Zijin Intelligent Program(No. 2013-ZJ0211) of Nanjing University of Science and Technology
文摘In this paper, we develop a unique time-varying forecasting model for dynamic demand of medical resources based on a susceptible-exposed-infected-recovered （SEIR） influenza diffusion model. In this forecasting mechanism, medical resources allocated in the early period will take effect in subduing the spread of influenza and thus impact the demand in the later period. We adopt a discrete time-space network to describe the medical resources allocation process following a hypothetical influenza outbreak in a region. The entire medical resources allocation process is constructed as a multi-stage integer programming problem. At each stage, we solve a cost minimization sub-problem subject to the time-varying demand. The corresponding optimal allocation result is then used as an input to the control process of influenza spread, which in turn determines the demand for the next stage. In addition, we present a comparison between the proposed model and an empirical model. Our results could help decision makers prepare for a pandemic, including how to allocate limited resources dynamically.
文摘A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.
基金the National Natural Science Foundation of China (Nos.40676016 and 40876010)the National Basic Research Program (973) of China (Nos.2003CB415101-03 and 2004CB418304)+2 种基金the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)LASG State Key Laboratory Special FundE-Institutes of Shanghai Municipal Education Commission (No.E03004)
文摘A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.
基金This work is supported by the Foundation of Ability Person of Fuzhou University under the grant 0030824228 andthe Foundation of Developing Science and Technology of Fuzhou University under the grant 2003-QX-21 and the Foundation of Fujian Education Bur
文摘In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.
基金Acknowledgements The authors thank the anonymous referees for helpful comments. Yingqiu Li＇s work was supported by the National Natural Science Foundation of China （Grant No. 11171044） und the Natural Science Foundation of Hunan Province （Grant No. llJ32001） Suxin Wang＇s work was supported by the Natural Sciences and Engineering Research Council of Canada.
文摘Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.
