Piezoelectric actuator has high stiffness, high frequency and infinite control precision, but a short output displacement which is often 1/1 000 of its length. In order to meet the requirements that tools feeding shou...Piezoelectric actuator has high stiffness, high frequency and infinite control precision, but a short output displacement which is often 1/1 000 of its length. In order to meet the requirements that tools feeding should be long-travel, high-frequency and high-precision in non-circular precision turning, a new one-freedom flexure hinge structure is put forward to amplify the output displacement of piezoelectric actuator. Theoretical analysis is done on the static and dynamic characteristics of the structure, differential equations are presented, and it is also verified by the finite element method. It's proved by experiments that the output displacement of the structure is 293 μm and its resonant frequency is 312 Hz.展开更多
An unique mask moving method is developed for forming effective micro-optical structures with continuous profile. The mechanism for forming different micro-optical profiles is disclosed, and the designed approach for ...An unique mask moving method is developed for forming effective micro-optical structures with continuous profile. The mechanism for forming different micro-optical profiles is disclosed, and the designed approach for binary moving mask is described. Finally some concrete micro-optical components with typical microstructures are presented for demonstrating the validity of the method.展开更多
This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place onl...This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.展开更多
Based on micro-displacement measurement principles of the spherical differential capacitance sensor, the relationship between the capacitance variation and the micro-displacement of each pair of detecting electrodes f...Based on micro-displacement measurement principles of the spherical differential capacitance sensor, the relationship between the capacitance variation and the micro-displacement of each pair of detecting electrodes for the superconducting gyroscope (SCG) with eight detecting electrodes is analyzed. The model of the SCG rotor drift is established through dimensionless processing, linearization within micro-displacement and the least-square approach. Both the measurement scheme of the SCG rotor drift based on the model and its parameter relationship are presented. To guarantee the potential of the suspension rotor to be zero, the distributing scheme of four pairs of detecting electrodes is presented. The scheme can measure the magnitude and the direction of the rotor drift. The negative factors for affecting the measurement precision of .the SCG rotor drift and simulation results of the total effects are given. Simulation results show that the distributing capacitance of these differential capacitance sensors, the zero potential of the rotor and the model error are the major negative factors. The methods for eliminating those negative factors and the application range of the model are given. The model ensures the relationship between the output voltage and the rotor drift be linear.展开更多
A simple and compact microstrip-fed ultra wideband (UWB) printed monopole antenna is presented. The antenna is composed of a circular radiator and a finitely grounded plane. The antenna occupies about 16.62 GHz abso...A simple and compact microstrip-fed ultra wideband (UWB) printed monopole antenna is presented. The antenna is composed of a circular radiator and a finitely grounded plane. The antenna occupies about 16.62 GHz absolute bandwidth and 142.7% relative bandwidth covering from 3.38 GHz to 20 GHz with voltage standing wave ratio (VSWR) below two. A quasi-omnidirectional and quasi-symmetrical radiation pattern in H plane is obtained in the whole bandwidth. The high performance of the antenna is validated with measured and simulated results given. The antenna can be applied for the system design of UWB wireless communication.展开更多
In order to improve the bias stability of the micro-electro mechanical system(MEMS) gyroscope and reduce the impact on the bias from environmental temperature,a digital signal processing method is described for impr...In order to improve the bias stability of the micro-electro mechanical system(MEMS) gyroscope and reduce the impact on the bias from environmental temperature,a digital signal processing method is described for improving the accuracy of the drive phase in the gyroscope drive mode.Through the principle of bias signal generation,it can be concluded that the deviation of the drive phase is the main factor affecting the bias stability.To fulfill the purpose of precise drive phase control,a digital signal processing circuit based on the field-programmable gate array(FPGA) with the phase-lock closed-loop control method is described and a demodulation method for phase error suppression is given.Compared with the analog circuit,the bias drift is largely reduced in the new digital circuit and the bias stability is improved from 60 to 19 °/h.The new digital control method can greatly increase the drive phase accuracy,and thus improve the bias stability.展开更多
Ti/TiN multilayer film was deposited on uranium surface by arc ion plating technique to improve fretting wear behavior. The morphology, structure and element distribution of the film were measured by scanning electric...Ti/TiN multilayer film was deposited on uranium surface by arc ion plating technique to improve fretting wear behavior. The morphology, structure and element distribution of the film were measured by scanning electric microscopy(SEM), X-ray diffractometry(XRD) and Auger electron spectroscopy(AES). Fretting wear tests of uranium and Ti/TiN multilayer film were carried out using pin-on-disc configuration. The fretting tests of uranium and Ti/TiN multilayer film were carried out under normal load of 20 N and various displacement amplitudes ranging from 5 to 100 μm. With the increase of the displacement amplitude, the fretting changed from partial slip regime(PSR) to slip regime(SR). The coefficient of friction(COF) increased with the increase of displacement amplitude. The results indicated that the displacement amplitude had a strong effect on fretting wear behavior of the film. The damage of the film was very slight when the displacement amplitude was below 20 μm. The observations indicated that the delamination was the main wear mechanism of Ti/TiN multilayer film in PSR. The main wear mechanism of Ti/TiN multilayer film in SR was delamination and abrasive wear.展开更多
Laser Doppler Anemometer has been used to measure the flow field characteristics near the interface around a moving bubble in the presence of ultrafine particles. In order to model a moving bubble, the bubble was fixe...Laser Doppler Anemometer has been used to measure the flow field characteristics near the interface around a moving bubble in the presence of ultrafine particles. In order to model a moving bubble, the bubble was fixed into the counter flow liquid by a metal mesh. Experimental materials are air and water, and the particles are complex oxidate powder. Experiments were carried out under the operating conditions: the liquid flow velocity u 0 is 12.6 cm/s, the equivalent diameter d e is 0.6 cm, the mass concentration of particle is 0.2 0 0 ,the average particle diameter is about 10 nm and the density is 2 g/cm 3. The velocity profiles of both frontal and tail vortex areas were measured respectively. The experimental results show that the velocity fields are obviously changed in the existence of particles. In the frontal area of the bubble, both tangential and normal velocities decrease due to the presence of particles, but in tail vortex area, the tangential velocities increase remarkably, and normal velocities rise gradually from the center towards the fringe in the opposite tendency to that of no particles. The influences of flow field change in the presence of particles on gas liquid mass transfer are analyzed and discussed.展开更多
A lattice Boltzmann model of two dimensions is used to simulate the movement of a single rigid particle suspended in a pulsating flow in micro vessel The particle is as big as a red blood cell, and the micro vessel is...A lattice Boltzmann model of two dimensions is used to simulate the movement of a single rigid particle suspended in a pulsating flow in micro vessel The particle is as big as a red blood cell, and the micro vessel is four times as wide as the diameter of the particle. It is found that Segrd-Silberberg effect will not respond to the pulsation of the flow when the Reynolds number is relatively high. However, when the Reynolds number is low enough, Segrd-Silberberg effect disappears. In the steady flow, different initial position leads to different equilibrium positions. In a pulsating flow, different frequencies of pulsation also cause different equilibrium positions. Particularly, when the frequency of pulsation is closed to the human heart rate, Segrd-Silberberg effect presents again. The evolutions of velocity, rotation, and trajectory of the particle are investigated to find the dynamics of such abnormal phenomenon.展开更多
Laboratory incubation was conducted to investigate transformation of straw 14 C in Ultisol and Vertisol under aerobic condition for 112 d at 30 oC. Dried and ground 14 C labeled rice and maize...Laboratory incubation was conducted to investigate transformation of straw 14 C in Ultisol and Vertisol under aerobic condition for 112 d at 30 oC. Dried and ground 14 C labeled rice and maize straws were mixed with the soils at the rate of 2.5 g kg -1 . Decomposition of the straw C and native soil C both revealed two stages, being faster during the initial days, and slower thereafter. About 37.33%~48.80% of the straw C and 4.22%~6.83% of the native soil C decomposed by the end of the incubation. The kinds of the straws only slightly influenced the rates of their decomposition in soils, however, some retardation was found in Ultisol at the initial decomposition stage due to its lower pH. Positive priming effects were observed in the soils applied with straw, and the rate of priming effect ranged from 7.23% to 13.80%. Net losses of native soil C were found under such incubation conditions, except Ultisol with rice straw. Soil biomass C and 14 C decreased gradually with incubation time, and seemed to be consistent with the decomposition patterns of straw C and native soil C. The ratio of biomass 12 C to biomass 14 C ranged from 1.35 to 3.37. Soil biomass C occupied 1.17%~2.32% of the total soil organic C, and the proportion of biomass 14 C to the residual 14 C varied from 7.3% to 14.3%.展开更多
With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS a...With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.展开更多
Nitrogen pollution is an increasingly severe worldwide problem because of drainage of nitrogen-containing wastewater and intensive application of nitrogen-containing fertilizers. Denitrification, a key process in nitr...Nitrogen pollution is an increasingly severe worldwide problem because of drainage of nitrogen-containing wastewater and intensive application of nitrogen-containing fertilizers. Denitrification, a key process in nitrogen cycles, is commonly employed for nitrogen removal in engineered wastewater treatment systems. Biological denitrification is performed by denitrifying microbes(bacteria) that use nitrate as terminal electron acceptor. Better understanding the functions of diverse microbial populations in denitrification-based wastewater treatment systems, and the interactions of these populations with operating environments, is essential for improving both treatment performance and system stability. Recent advances in "meta-omics"(e.g., genomics, transcriptomics, proteomics, metabolomics), other molecular biology tools, and microbiome analysis have greatly enhanced such understanding. This minireview summarizes recent findings regarding microbial community structure and composition, key functional microbes and their physiology, functional genes involved in nitrogen cycle, and responses of microbes and their genes to changes of environmental factors or operating parameters, in denitrification processes in wastewater treatment systems. Of particular interest are heterotrophic denitrification systems(which require alternative organic carbon sources) and the autotrophic denitrification systems(which do not require an external carbon source). Integrated microbiome and-omics approaches have great future potential for determination of optimal environmental and biotechnological parameters,novel process development, and improvement of nitrogen removal efficiency and system stability.展开更多
In this paper, steady incompressible micropolar fluid flow through a non-uniform channel with multiple stenoses is considered. Assuming the stenoses to be mild and using the slip boundary condition, the equations gove...In this paper, steady incompressible micropolar fluid flow through a non-uniform channel with multiple stenoses is considered. Assuming the stenoses to be mild and using the slip boundary condition, the equations governing the flow of the proposed model are solved, and closed-form expressions for the flow characteristics (resistance to flow and wall shear stress) are derived. The effects of different parameters on these flow characteristics are analyzed. It is observed that both the resistance to the flow and the wall shear stress increase with the heights of the stenoses and the slip parameter; but decrease with the Darcy number, b^rthermore, the effects of the wall exponent parameter, the cross-viscosity coefficient and the micropolar parameter on the flow characteristics are discussed.展开更多
This paper presents a new control strategy based on current differential feedback to accelerate the dynamic response of electromagnetic actuators, instead of traditional closed-loop control based on displacement feedb...This paper presents a new control strategy based on current differential feedback to accelerate the dynamic response of electromagnetic actuators, instead of traditional closed-loop control based on displacement feedback. The method mainly includes a differentiator, proportioner and signal synthesizer. Analysis and simulation on the step characteristics of an electromagnetic actuator were discussed, and all the results show that the approach can improve the actuator's step response greatly. Finally, the control method is applied to a real gravure system which verifies the control performance.展开更多
With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equatio...With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations (FPDEs). The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.展开更多
In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A pract...In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A practical example based on a simplified model is given to analyze the dynamical process of Sichuan economy growth.展开更多
文摘Piezoelectric actuator has high stiffness, high frequency and infinite control precision, but a short output displacement which is often 1/1 000 of its length. In order to meet the requirements that tools feeding should be long-travel, high-frequency and high-precision in non-circular precision turning, a new one-freedom flexure hinge structure is put forward to amplify the output displacement of piezoelectric actuator. Theoretical analysis is done on the static and dynamic characteristics of the structure, differential equations are presented, and it is also verified by the finite element method. It's proved by experiments that the output displacement of the structure is 293 μm and its resonant frequency is 312 Hz.
文摘An unique mask moving method is developed for forming effective micro-optical structures with continuous profile. The mechanism for forming different micro-optical profiles is disclosed, and the designed approach for binary moving mask is described. Finally some concrete micro-optical components with typical microstructures are presented for demonstrating the validity of the method.
基金Supported by the Innovation Project for University Prominent Research Talents of Henan (2003KJCX008)
文摘This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.
文摘Based on micro-displacement measurement principles of the spherical differential capacitance sensor, the relationship between the capacitance variation and the micro-displacement of each pair of detecting electrodes for the superconducting gyroscope (SCG) with eight detecting electrodes is analyzed. The model of the SCG rotor drift is established through dimensionless processing, linearization within micro-displacement and the least-square approach. Both the measurement scheme of the SCG rotor drift based on the model and its parameter relationship are presented. To guarantee the potential of the suspension rotor to be zero, the distributing scheme of four pairs of detecting electrodes is presented. The scheme can measure the magnitude and the direction of the rotor drift. The negative factors for affecting the measurement precision of .the SCG rotor drift and simulation results of the total effects are given. Simulation results show that the distributing capacitance of these differential capacitance sensors, the zero potential of the rotor and the model error are the major negative factors. The methods for eliminating those negative factors and the application range of the model are given. The model ensures the relationship between the output voltage and the rotor drift be linear.
文摘A simple and compact microstrip-fed ultra wideband (UWB) printed monopole antenna is presented. The antenna is composed of a circular radiator and a finitely grounded plane. The antenna occupies about 16.62 GHz absolute bandwidth and 142.7% relative bandwidth covering from 3.38 GHz to 20 GHz with voltage standing wave ratio (VSWR) below two. A quasi-omnidirectional and quasi-symmetrical radiation pattern in H plane is obtained in the whole bandwidth. The high performance of the antenna is validated with measured and simulated results given. The antenna can be applied for the system design of UWB wireless communication.
基金The National Natural Science Foundation of China (No.60974116)the Research Fund of Aeronautics Science (No. 20090869007)Specialized Research Fund for the Doctoral Program of Higher Education(No. 200802861063)
文摘In order to improve the bias stability of the micro-electro mechanical system(MEMS) gyroscope and reduce the impact on the bias from environmental temperature,a digital signal processing method is described for improving the accuracy of the drive phase in the gyroscope drive mode.Through the principle of bias signal generation,it can be concluded that the deviation of the drive phase is the main factor affecting the bias stability.To fulfill the purpose of precise drive phase control,a digital signal processing circuit based on the field-programmable gate array(FPGA) with the phase-lock closed-loop control method is described and a demodulation method for phase error suppression is given.Compared with the analog circuit,the bias drift is largely reduced in the new digital circuit and the bias stability is improved from 60 to 19 °/h.The new digital control method can greatly increase the drive phase accuracy,and thus improve the bias stability.
基金Projects(U1530136,51375407) supported by the National Natural Science Foundation of ChinaProject(2017TD0017) supported by the Young Scientific Innovation Team of Science and Technology of Sichuan Province,China
文摘Ti/TiN multilayer film was deposited on uranium surface by arc ion plating technique to improve fretting wear behavior. The morphology, structure and element distribution of the film were measured by scanning electric microscopy(SEM), X-ray diffractometry(XRD) and Auger electron spectroscopy(AES). Fretting wear tests of uranium and Ti/TiN multilayer film were carried out using pin-on-disc configuration. The fretting tests of uranium and Ti/TiN multilayer film were carried out under normal load of 20 N and various displacement amplitudes ranging from 5 to 100 μm. With the increase of the displacement amplitude, the fretting changed from partial slip regime(PSR) to slip regime(SR). The coefficient of friction(COF) increased with the increase of displacement amplitude. The results indicated that the displacement amplitude had a strong effect on fretting wear behavior of the film. The damage of the film was very slight when the displacement amplitude was below 20 μm. The observations indicated that the delamination was the main wear mechanism of Ti/TiN multilayer film in PSR. The main wear mechanism of Ti/TiN multilayer film in SR was delamination and abrasive wear.
文摘Laser Doppler Anemometer has been used to measure the flow field characteristics near the interface around a moving bubble in the presence of ultrafine particles. In order to model a moving bubble, the bubble was fixed into the counter flow liquid by a metal mesh. Experimental materials are air and water, and the particles are complex oxidate powder. Experiments were carried out under the operating conditions: the liquid flow velocity u 0 is 12.6 cm/s, the equivalent diameter d e is 0.6 cm, the mass concentration of particle is 0.2 0 0 ,the average particle diameter is about 10 nm and the density is 2 g/cm 3. The velocity profiles of both frontal and tail vortex areas were measured respectively. The experimental results show that the velocity fields are obviously changed in the existence of particles. In the frontal area of the bubble, both tangential and normal velocities decrease due to the presence of particles, but in tail vortex area, the tangential velocities increase remarkably, and normal velocities rise gradually from the center towards the fringe in the opposite tendency to that of no particles. The influences of flow field change in the presence of particles on gas liquid mass transfer are analyzed and discussed.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10747004,11065006,and 81060307
文摘A lattice Boltzmann model of two dimensions is used to simulate the movement of a single rigid particle suspended in a pulsating flow in micro vessel The particle is as big as a red blood cell, and the micro vessel is four times as wide as the diameter of the particle. It is found that Segrd-Silberberg effect will not respond to the pulsation of the flow when the Reynolds number is relatively high. However, when the Reynolds number is low enough, Segrd-Silberberg effect disappears. In the steady flow, different initial position leads to different equilibrium positions. In a pulsating flow, different frequencies of pulsation also cause different equilibrium positions. Particularly, when the frequency of pulsation is closed to the human heart rate, Segrd-Silberberg effect presents again. The evolutions of velocity, rotation, and trajectory of the particle are investigated to find the dynamics of such abnormal phenomenon.
文摘Laboratory incubation was conducted to investigate transformation of straw 14 C in Ultisol and Vertisol under aerobic condition for 112 d at 30 oC. Dried and ground 14 C labeled rice and maize straws were mixed with the soils at the rate of 2.5 g kg -1 . Decomposition of the straw C and native soil C both revealed two stages, being faster during the initial days, and slower thereafter. About 37.33%~48.80% of the straw C and 4.22%~6.83% of the native soil C decomposed by the end of the incubation. The kinds of the straws only slightly influenced the rates of their decomposition in soils, however, some retardation was found in Ultisol at the initial decomposition stage due to its lower pH. Positive priming effects were observed in the soils applied with straw, and the rate of priming effect ranged from 7.23% to 13.80%. Net losses of native soil C were found under such incubation conditions, except Ultisol with rice straw. Soil biomass C and 14 C decreased gradually with incubation time, and seemed to be consistent with the decomposition patterns of straw C and native soil C. The ratio of biomass 12 C to biomass 14 C ranged from 1.35 to 3.37. Soil biomass C occupied 1.17%~2.32% of the total soil organic C, and the proportion of biomass 14 C to the residual 14 C varied from 7.3% to 14.3%.
基金the National Natural Science Foundation of China (Grant No. 11171208)Shanghai Leading Academic Discipline Project (Grant No. S30106)
文摘With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.
基金supported by the projects of National Key Research and Development Program of China (2016YFD0501409)
文摘Nitrogen pollution is an increasingly severe worldwide problem because of drainage of nitrogen-containing wastewater and intensive application of nitrogen-containing fertilizers. Denitrification, a key process in nitrogen cycles, is commonly employed for nitrogen removal in engineered wastewater treatment systems. Biological denitrification is performed by denitrifying microbes(bacteria) that use nitrate as terminal electron acceptor. Better understanding the functions of diverse microbial populations in denitrification-based wastewater treatment systems, and the interactions of these populations with operating environments, is essential for improving both treatment performance and system stability. Recent advances in "meta-omics"(e.g., genomics, transcriptomics, proteomics, metabolomics), other molecular biology tools, and microbiome analysis have greatly enhanced such understanding. This minireview summarizes recent findings regarding microbial community structure and composition, key functional microbes and their physiology, functional genes involved in nitrogen cycle, and responses of microbes and their genes to changes of environmental factors or operating parameters, in denitrification processes in wastewater treatment systems. Of particular interest are heterotrophic denitrification systems(which require alternative organic carbon sources) and the autotrophic denitrification systems(which do not require an external carbon source). Integrated microbiome and-omics approaches have great future potential for determination of optimal environmental and biotechnological parameters,novel process development, and improvement of nitrogen removal efficiency and system stability.
文摘In this paper, steady incompressible micropolar fluid flow through a non-uniform channel with multiple stenoses is considered. Assuming the stenoses to be mild and using the slip boundary condition, the equations governing the flow of the proposed model are solved, and closed-form expressions for the flow characteristics (resistance to flow and wall shear stress) are derived. The effects of different parameters on these flow characteristics are analyzed. It is observed that both the resistance to the flow and the wall shear stress increase with the heights of the stenoses and the slip parameter; but decrease with the Darcy number, b^rthermore, the effects of the wall exponent parameter, the cross-viscosity coefficient and the micropolar parameter on the flow characteristics are discussed.
基金Project supported by the Science and Technology Plan of Zhejiang Province (No. 2008C11028), China
文摘This paper presents a new control strategy based on current differential feedback to accelerate the dynamic response of electromagnetic actuators, instead of traditional closed-loop control based on displacement feedback. The method mainly includes a differentiator, proportioner and signal synthesizer. Analysis and simulation on the step characteristics of an electromagnetic actuator were discussed, and all the results show that the approach can improve the actuator's step response greatly. Finally, the control method is applied to a real gravure system which verifies the control performance.
基金supported by National Natural Science Foundation of China (Grant Nos.10901027 and 11171274)Foundation of Hunan Educational Committee (Grant No. 10C0370)
文摘With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations (FPDEs). The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.
基金This research is supported by the National Natural Science Foundation of China(No.70171021)
文摘In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A practical example based on a simplified model is given to analyze the dynamical process of Sichuan economy growth.