A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms relate...A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.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
Deep hydrodesulfurization (HDS) is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/...Deep hydrodesulfurization (HDS) is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/or new types of reactors. In this work, the kinetics of dibenzothiophene (DBT) hydrodesulfurization over Ni-P/SBA-15/ cordierite catalyst was investigated at 340-380 ℃ and 3.0-5.0 MPa. The first-order reaction model with respect to both DBT and H2 was used to fit the kinetics data in a batch recycle operation system. It is found that both the activation energy and rate constant over the Ni-P monolithic catalyst under our operating conditions are close to those over conventionally used HDS catalysts. Comparative performance studies of two types of reactors, i.e., trickle bed reactor and monolithic reactor, were performed based on reactor modeling and simulation. The results indicate that the productivity of the monolithic reactor is 3 times higher than that of the trickle bed reactor on a catalyst weight basis since effective utilization of the catalyst is higher in the monolithic reactor, but the volumetric productivity of the monolithic reactor is lower for HDS of DBT. Based on simulation results, a two- reactor-in-series configuration for hydrodesulfurization is proposed, in which a monolithic reactor is followed by a tickled bed reactor so as to attain intensified performance of the system converting fuel oil of different sulfur-containing compounds. It is illustrated that the two reactor scheme outperforms the trickle bed reactor both on reactor volume and catalyst mass bases while the content of sulfur is reduced from 200 μg·g-1 to about 10 μ·g-1.展开更多
The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations . To two-loop...The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations . To two-loop order, the asymptotic scaling laws and the critical exponents are studied in the frame of a double expansion with ρ of order . In , it is argued that the initial slip exponent θ = 0 together with the dynamic exponent is exact in this kind of random system.展开更多
The purpose of thepresent study is to determine whether a long range correlation is present in BZ (Belousov-Zhabotinskii) reaction and how this correlation varies with the change in concentration of the solution. To...The purpose of thepresent study is to determine whether a long range correlation is present in BZ (Belousov-Zhabotinskii) reaction and how this correlation varies with the change in concentration of the solution. To explore the dynamics of the system with change in concentration, phase space plot and power spectrum are studied. Hurst exponent is estimated using log log plot and R/S technique. We discuss the results which uncover how the system changes from an excitable steady stateto a limit cycle,展开更多
Solid oxide fuel cell (SOFC) has been identified as an effective and clean alternative choice for marine power system.This paper emphasizes on the dynamic modeling of SOFC power system and its performance based upon m...Solid oxide fuel cell (SOFC) has been identified as an effective and clean alternative choice for marine power system.This paper emphasizes on the dynamic modeling of SOFC power system and its performance based upon marine operating circumstance.A SOFC power system model has been provided considering thermodynamic and electrochemical reaction mechanism.Subcomponents of lithium ion battery, power conditioning unit, stack structure and controller are integrated in the model.The dynamic response of the system is identified according to the inertia of its subcomponent and controller.Validation of the whole system simulation at steady state and transit period are presented, concerning the effects of thermo inertia, control strategy and seagoing environment.The simulation results show reasonable accuracy compare with lab test.The models can be used to predict performance of a SOFC power system and identify the system response when part of the component parameter is adjusted.展开更多
Like in other sectors of activity, the sustainability in refrigeration systems is a mandatory goal to achieve, namely at house holdings, bars and restaurants, where small-scale refrigerators and freezers are widely us...Like in other sectors of activity, the sustainability in refrigeration systems is a mandatory goal to achieve, namely at house holdings, bars and restaurants, where small-scale refrigerators and freezers are widely used. The aim of this work is to demonstrate experimentally, trough measurements carried out in these equipments, the improvement that can be achieved if several modifications are implemented in traditional household refrigeration systems. In addition, it was also simulated and analysed experimentally a slightly different equipment, a refrigeration system used for draught beverages. Both systems work on a single vapour compression refrigeration with R-134a as working fluid. In the end, by implemented the modifications tested in the virtual model, it was possible to improve their thermal behaviour, a decrease in electrical energy consumption, as well as, the associated CO2 emissions reduction can be attained. In this project, the CFD (Computational Fluid Dynamics) soffware--ANSYS Fluent was used to simulate the ambient temperature and velocity fields inside the refrigerator and in that way to validate the measured results.展开更多
Multibody musculoskeletal modeling of human gait has been proved helpful in investigating the pathology of musculoskeletal disorders.However,conventional inverse dynamics methods rely on external force sensors and can...Multibody musculoskeletal modeling of human gait has been proved helpful in investigating the pathology of musculoskeletal disorders.However,conventional inverse dynamics methods rely on external force sensors and cannot capture the nonlinear muscle behaviors.Meanwhile,the forward dynamics approach is computationally demanding and only suited for relatively simple tasks.This study proposed an integrated simulation methodology to fulfill the requirements of estimating foot-ground reaction force,tendon elasticity,and muscle recruitment optimization.A hybrid motion capture system,which combines the marker-based infrared device and markerless tracking through deep convolutional neural networks,was developed to track lower limb movements.The foot-ground reaction forces were determined by a contact model for soft materials,and its parameters were estimated using a two-step optimization method.The muscle recruitment problem was first resolved via a static optimization algorithm,and the obtained muscle activations were used as initial values for further simulation.A torque tracking procedure was then performed by minimizing the errors of joint torques calculated by musculotendon equilibrium equations and inverse dynamics.The proposed approach was validated against the electromyography measurements of a healthy subject during gait.The simulation framework provides a robust way of predicting joint torques,musculotendon forces,and muscle activations,which can be beneficial for understanding the biomechanics of normal and pathological gait.展开更多
In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeli...In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.展开更多
The eight datasets of the summer (June-August) surface sensible heat (SH) flux over the Tibetan Plateau (TP) are compared on the time scales of the climatology,interannual variability and linear trend during 1980-2006...The eight datasets of the summer (June-August) surface sensible heat (SH) flux over the Tibetan Plateau (TP) are compared on the time scales of the climatology,interannual variability and linear trend during 1980-2006.These data sets include five reanalyses (National Center for Environmental Prediction reanalysis,NCEPR1 and NCEPR2,NCEP climate forecast system reanalysis,CFSR,Japanese 25-year reanalysis,JRA,and European Centre for Medium Range Weather Forecasts reanalysis,ERA40),two land surface model outputs (Noah model data of Global Land Data Assimilation System version 2,G2_Noah,and Simple Biosphere version 2 output by Yang et al.,YSiB2),and estimated SH based on China Meteorological Administration (CMA) station observations,ObCh.The results suggest that the summer SH on the TP differs from one dataset to another due to different inputs and calculations.Climatologically,the ERA40 and JRA distribute rather uniformly while the other six products show similar regional disparities,that is,larger in the west than in the east and stronger in the north and the south than in the middle of the plateau.The mean magnitude of the SH averaged over the 76 stations above the TP varies considerably among each dataset with the difference of more than 20 W m?2 between the maximum (G2_Noah) and minimum (ObCh).Nevertheless,they are consistent in the interannual variability and mostly show a significant decreasing trend corresponding to the weakening surface wind speed,in spite of the distinct trend for the ground-air temperature difference among the different data sets.These two consistencies indicate the particular availability of the SH products,which is helpful to the relevant climate dynamics research.展开更多
With the combination of engine and two electric machines, the power split device allows higher efficiency of the engine. The operation modes of a power split HEV are analyzed, and the system dynamic model is establish...With the combination of engine and two electric machines, the power split device allows higher efficiency of the engine. The operation modes of a power split HEV are analyzed, and the system dynamic model is established for HEV forward simulation and controller design. Considering the fact that the operation modes of the HEV are event-driven and the system dynamics is continuous time-driven for each mode, the structure of the controller is built and described with the hybrid automaton control theory. In this control structure, the mode selection process is depicted by the finite state machine (FSM). The multi-mode switch controller is designed to realize power distribution. Furthermore, the vehicle mode operations are optimized, and the nonlinear model predictive control (NMPC) strategy is applied by implementing dynamic programming (DP) in the finite pre- diction horizon. Comparative simulation results demonstrate that the hybrid control structure is effective and feasible for HEV energy management design. The NMPC optimal strategy is superior in improving fuel economy.展开更多
Energy flow drives the complex systems to evolve.The allometric scaling as the universalenergy flow pattern has been found in different scales of ecological systems.It reflects the generalpower law relationship betwee...Energy flow drives the complex systems to evolve.The allometric scaling as the universalenergy flow pattern has been found in different scales of ecological systems.It reflects the generalpower law relationship between flow and store.The underlying mechanisms of energy flow patterns areexplained as the branching transportation networks which can be regarded as the result of systematicoptimization of a biological target under constraints.Energy flows in the ecological system may bemodelled by the food web model and population dynamics on the network.This paper reviews thelatest progress on the energy flow patterns,explanatory models for the allometric scaling and modellingapproach of flow and network evolution dynamics in ecology.Furthermore,the possibility of generalizingthese flow patterns,modelling approaches to other complex systems is discussed.展开更多
In the past twenty years,great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems.Most of the results have been generalized to the relative...In the past twenty years,great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems.Most of the results have been generalized to the relative case in the sense of a given factor map.In this survey we offer an overview of these developments.展开更多
Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of...Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schr¨odinger(NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.展开更多
For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under t...For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.展开更多
基金Project(10772113) supported by the National Natural Science Foundation of China
文摘A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.
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 State Key Development Program for Basic Research of China(2006CB202503)
文摘Deep hydrodesulfurization (HDS) is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/or new types of reactors. In this work, the kinetics of dibenzothiophene (DBT) hydrodesulfurization over Ni-P/SBA-15/ cordierite catalyst was investigated at 340-380 ℃ and 3.0-5.0 MPa. The first-order reaction model with respect to both DBT and H2 was used to fit the kinetics data in a batch recycle operation system. It is found that both the activation energy and rate constant over the Ni-P monolithic catalyst under our operating conditions are close to those over conventionally used HDS catalysts. Comparative performance studies of two types of reactors, i.e., trickle bed reactor and monolithic reactor, were performed based on reactor modeling and simulation. The results indicate that the productivity of the monolithic reactor is 3 times higher than that of the trickle bed reactor on a catalyst weight basis since effective utilization of the catalyst is higher in the monolithic reactor, but the volumetric productivity of the monolithic reactor is lower for HDS of DBT. Based on simulation results, a two- reactor-in-series configuration for hydrodesulfurization is proposed, in which a monolithic reactor is followed by a tickled bed reactor so as to attain intensified performance of the system converting fuel oil of different sulfur-containing compounds. It is illustrated that the two reactor scheme outperforms the trickle bed reactor both on reactor volume and catalyst mass bases while the content of sulfur is reduced from 200 μg·g-1 to about 10 μ·g-1.
文摘The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations . To two-loop order, the asymptotic scaling laws and the critical exponents are studied in the frame of a double expansion with ρ of order . In , it is argued that the initial slip exponent θ = 0 together with the dynamic exponent is exact in this kind of random system.
文摘The purpose of thepresent study is to determine whether a long range correlation is present in BZ (Belousov-Zhabotinskii) reaction and how this correlation varies with the change in concentration of the solution. To explore the dynamics of the system with change in concentration, phase space plot and power spectrum are studied. Hurst exponent is estimated using log log plot and R/S technique. We discuss the results which uncover how the system changes from an excitable steady stateto a limit cycle,
文摘Solid oxide fuel cell (SOFC) has been identified as an effective and clean alternative choice for marine power system.This paper emphasizes on the dynamic modeling of SOFC power system and its performance based upon marine operating circumstance.A SOFC power system model has been provided considering thermodynamic and electrochemical reaction mechanism.Subcomponents of lithium ion battery, power conditioning unit, stack structure and controller are integrated in the model.The dynamic response of the system is identified according to the inertia of its subcomponent and controller.Validation of the whole system simulation at steady state and transit period are presented, concerning the effects of thermo inertia, control strategy and seagoing environment.The simulation results show reasonable accuracy compare with lab test.The models can be used to predict performance of a SOFC power system and identify the system response when part of the component parameter is adjusted.
文摘Like in other sectors of activity, the sustainability in refrigeration systems is a mandatory goal to achieve, namely at house holdings, bars and restaurants, where small-scale refrigerators and freezers are widely used. The aim of this work is to demonstrate experimentally, trough measurements carried out in these equipments, the improvement that can be achieved if several modifications are implemented in traditional household refrigeration systems. In addition, it was also simulated and analysed experimentally a slightly different equipment, a refrigeration system used for draught beverages. Both systems work on a single vapour compression refrigeration with R-134a as working fluid. In the end, by implemented the modifications tested in the virtual model, it was possible to improve their thermal behaviour, a decrease in electrical energy consumption, as well as, the associated CO2 emissions reduction can be attained. In this project, the CFD (Computational Fluid Dynamics) soffware--ANSYS Fluent was used to simulate the ambient temperature and velocity fields inside the refrigerator and in that way to validate the measured results.
基金the National Natural Science Foundations of China(Grant Nos.12102035 and 12125201)the China Postdoctoral Science Foundation(Grant No.2020TQ0042)the Beijing Natural Science Foundation(Grant No.L212008).
文摘Multibody musculoskeletal modeling of human gait has been proved helpful in investigating the pathology of musculoskeletal disorders.However,conventional inverse dynamics methods rely on external force sensors and cannot capture the nonlinear muscle behaviors.Meanwhile,the forward dynamics approach is computationally demanding and only suited for relatively simple tasks.This study proposed an integrated simulation methodology to fulfill the requirements of estimating foot-ground reaction force,tendon elasticity,and muscle recruitment optimization.A hybrid motion capture system,which combines the marker-based infrared device and markerless tracking through deep convolutional neural networks,was developed to track lower limb movements.The foot-ground reaction forces were determined by a contact model for soft materials,and its parameters were estimated using a two-step optimization method.The muscle recruitment problem was first resolved via a static optimization algorithm,and the obtained muscle activations were used as initial values for further simulation.A torque tracking procedure was then performed by minimizing the errors of joint torques calculated by musculotendon equilibrium equations and inverse dynamics.The proposed approach was validated against the electromyography measurements of a healthy subject during gait.The simulation framework provides a robust way of predicting joint torques,musculotendon forces,and muscle activations,which can be beneficial for understanding the biomechanics of normal and pathological gait.
基金supported by the National Natural Science Foundation of China(Grant Nos.11372068 and 11572350)the National Basic Research Program of China(Grant No.2014CB744104)
文摘In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.
基金supported by Major Projects of the Knowledge Innovation Program of Chinese Academy of Sciences (Grant No. KZCX2-YW-Q11-01)the National Basic Research Program of China (Grant No. 2010CB950403)National Natural Science Foundation of China (Grant Nos. 40925015,40810059005 and 40821092)
文摘The eight datasets of the summer (June-August) surface sensible heat (SH) flux over the Tibetan Plateau (TP) are compared on the time scales of the climatology,interannual variability and linear trend during 1980-2006.These data sets include five reanalyses (National Center for Environmental Prediction reanalysis,NCEPR1 and NCEPR2,NCEP climate forecast system reanalysis,CFSR,Japanese 25-year reanalysis,JRA,and European Centre for Medium Range Weather Forecasts reanalysis,ERA40),two land surface model outputs (Noah model data of Global Land Data Assimilation System version 2,G2_Noah,and Simple Biosphere version 2 output by Yang et al.,YSiB2),and estimated SH based on China Meteorological Administration (CMA) station observations,ObCh.The results suggest that the summer SH on the TP differs from one dataset to another due to different inputs and calculations.Climatologically,the ERA40 and JRA distribute rather uniformly while the other six products show similar regional disparities,that is,larger in the west than in the east and stronger in the north and the south than in the middle of the plateau.The mean magnitude of the SH averaged over the 76 stations above the TP varies considerably among each dataset with the difference of more than 20 W m?2 between the maximum (G2_Noah) and minimum (ObCh).Nevertheless,they are consistent in the interannual variability and mostly show a significant decreasing trend corresponding to the weakening surface wind speed,in spite of the distinct trend for the ground-air temperature difference among the different data sets.These two consistencies indicate the particular availability of the SH products,which is helpful to the relevant climate dynamics research.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the National Natural Science Foundation of China(Grant Nos.51475213&51305167)the Scientific Research Innovation Projects of Jiangsu Province(Grant No.KYLX_1022)
文摘With the combination of engine and two electric machines, the power split device allows higher efficiency of the engine. The operation modes of a power split HEV are analyzed, and the system dynamic model is established for HEV forward simulation and controller design. Considering the fact that the operation modes of the HEV are event-driven and the system dynamics is continuous time-driven for each mode, the structure of the controller is built and described with the hybrid automaton control theory. In this control structure, the mode selection process is depicted by the finite state machine (FSM). The multi-mode switch controller is designed to realize power distribution. Furthermore, the vehicle mode operations are optimized, and the nonlinear model predictive control (NMPC) strategy is applied by implementing dynamic programming (DP) in the finite pre- diction horizon. Comparative simulation results demonstrate that the hybrid control structure is effective and feasible for HEV energy management design. The NMPC optimal strategy is superior in improving fuel economy.
基金supported by Guozhi Xu Post Doctoral Research Foundationthe National Natural Science Foundation of China under Grant No. 60574068.
文摘Energy flow drives the complex systems to evolve.The allometric scaling as the universalenergy flow pattern has been found in different scales of ecological systems.It reflects the generalpower law relationship between flow and store.The underlying mechanisms of energy flow patterns areexplained as the branching transportation networks which can be regarded as the result of systematicoptimization of a biological target under constraints.Energy flows in the ecological system may bemodelled by the food web model and population dynamics on the network.This paper reviews thelatest progress on the energy flow patterns,explanatory models for the allometric scaling and modellingapproach of flow and network evolution dynamics in ecology.Furthermore,the possibility of generalizingthese flow patterns,modelling approaches to other complex systems is discussed.
基金supported by Foundation for the Authors of National Excellent Doctoral Dissertation of China (Grant No.201018)National Natural Science Foundation of China (Grant No. 10801035)Ministry of Education of China (Grant No. 200802461004)
文摘In the past twenty years,great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems.Most of the results have been generalized to the relative case in the sense of a given factor map.In this survey we offer an overview of these developments.
基金Supported by the Research Grants Council contract HKU17200815
文摘Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schr¨odinger(NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.
基金supported by National Natural Science Foundation of China (Grant No. 11001100)China Postdoctoral Science Foundation (Grant No.20100470645)+3 种基金Shanghai Postdoctoral Science Foundation (Grant No. 11R21412100)the Young Fund of the College of Mathematics at Jilin Universitysupported by National Natural Science Foundation of China(Grant No. 10971093)National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)
文摘For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.