For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the metho...For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.展开更多
Determination of the optimal model parameters for biochemical systems is a time consuming iterative process. In this study, a novel hybrid differential evolution （DE） algorithm based on the differential evolution te...Determination of the optimal model parameters for biochemical systems is a time consuming iterative process. In this study, a novel hybrid differential evolution （DE） algorithm based on the differential evolution technique and a local search strategy is developed for solving kinetic parameter estimation problems. By combining the merits of DE with Gauss-Newton method, the proposed hybrid approach employs a DE algorithm for identifying promising regions of the solution space followed by use of Gauss-Newton method to determine the optimum in the identified regions. Some well-known benchmark estimation problems are utilized to test the efficiency and the robustness of the proposed algorithm compared to other methods in literature. The comparison indicates that the present hybrid algorithm outperforms other estimation techniques in terms of the global searching ability and the con- vergence speed. Additionally, the estimation of kinetic model parameters for a feed batch fermentor is carried out to test the applicability of the proposed algorithm. The result suggests that the method can be used to estimate suitable values of model oarameters for a comolex mathematical model.展开更多
A reduced mechanism for propane/air combustion and its flame inhibition by phosphorus-containing compounds (PCCs) is constructed with the level of importance (LOI) method. The analysis is performed on solutions of fre...A reduced mechanism for propane/air combustion and its flame inhibition by phosphorus-containing compounds (PCCs) is constructed with the level of importance (LOI) method. The analysis is performed on solutions of freely propagating premixed flames with detailed chemical kinetics involving 121 species and 682 reactions proposed by Jayaweera et al. For the non-homogeneous reaction-diffusion system, the chemical lifetime of each species is weighted by its diffusion timescale, and the characteristic flame timescale is used to normalize the chemical lifetime. The definition of sensitivity in LOI is extended so that multi-parameters can be used as sensitivity targets. Propane, oxygen, dimethyl methylphosphonate (DMMP), and flame speed are selected to be perturbed for sensitivity analysis, the species with low LOI index are removed, and reactions involving the redundant species are excluded from the mechanism. A skeletal mechanism is obtained, which consists of 57 species and 268 elementary reactions. Calculations for laminar flame speeds, key flame radicals and catalytic cycles using the skeletal mechanism are in good agreement with those by using the detailed mechanism over a wide range of equivalence ratio undoped and doped with DMMP.展开更多
We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death （ES...We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death （ESD） is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the ease with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways.展开更多
In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval nu...In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parame- ters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present dif- ferent characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.展开更多
This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of...This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.展开更多
A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary diff...A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations （ODEs） of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.展开更多
基金Supported by the Natural Science Foundation of Ningbo under Grant No. 2008A610029
文摘For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.
基金Supported by the National Natural Science Foundation of China （60804027, 61064003） and Fuzhou University Research Foundation （FZU-02335, 600338 and 600567）.
文摘Determination of the optimal model parameters for biochemical systems is a time consuming iterative process. In this study, a novel hybrid differential evolution （DE） algorithm based on the differential evolution technique and a local search strategy is developed for solving kinetic parameter estimation problems. By combining the merits of DE with Gauss-Newton method, the proposed hybrid approach employs a DE algorithm for identifying promising regions of the solution space followed by use of Gauss-Newton method to determine the optimum in the identified regions. Some well-known benchmark estimation problems are utilized to test the efficiency and the robustness of the proposed algorithm compared to other methods in literature. The comparison indicates that the present hybrid algorithm outperforms other estimation techniques in terms of the global searching ability and the con- vergence speed. Additionally, the estimation of kinetic model parameters for a feed batch fermentor is carried out to test the applicability of the proposed algorithm. The result suggests that the method can be used to estimate suitable values of model oarameters for a comolex mathematical model.
基金Supported by the National Natural Science Foundation of China （50876097） the Program for New Century Excellent Talents in University of China （NCET-06-0546）
文摘A reduced mechanism for propane/air combustion and its flame inhibition by phosphorus-containing compounds (PCCs) is constructed with the level of importance (LOI) method. The analysis is performed on solutions of freely propagating premixed flames with detailed chemical kinetics involving 121 species and 682 reactions proposed by Jayaweera et al. For the non-homogeneous reaction-diffusion system, the chemical lifetime of each species is weighted by its diffusion timescale, and the characteristic flame timescale is used to normalize the chemical lifetime. The definition of sensitivity in LOI is extended so that multi-parameters can be used as sensitivity targets. Propane, oxygen, dimethyl methylphosphonate (DMMP), and flame speed are selected to be perturbed for sensitivity analysis, the species with low LOI index are removed, and reactions involving the redundant species are excluded from the mechanism. A skeletal mechanism is obtained, which consists of 57 species and 268 elementary reactions. Calculations for laminar flame speeds, key flame radicals and catalytic cycles using the skeletal mechanism are in good agreement with those by using the detailed mechanism over a wide range of equivalence ratio undoped and doped with DMMP.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10974020 and 11174039,NCET-11-0031the Fundamental Research Funds for the Central Universities
文摘We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death （ESD） is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the ease with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways.
文摘In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parame- ters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present dif- ferent characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.
文摘This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.
基金This research was supported by the National Natural Science Foundation of China （No. 30870397） and the State Key Laboratory of Vegetation and Environmental Change.
文摘A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations （ODEs） of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.
