The movement mode of snakes is crawling,and the living environment of snakes with numerous branches and stones will cause plenty of wear for the snake scales.There are plenty of surface structures and morphology on sn...The movement mode of snakes is crawling,and the living environment of snakes with numerous branches and stones will cause plenty of wear for the snake scales.There are plenty of surface structures and morphology on snake scales to avoid severe wear.Among them,the research towards the keeled structure on snake scales is missing.Therefore,in this research,the wear resistance improvement of the keeled structure on the snake scales and the overlapped distribution of snake scales are investigated.The keeled and smooth snake scales were 3D printed and they were distributed on the substrate in the overlapped or paralleled ways.Besides these four samples with keeled/smooth scales and overlapped/paralleled distributed,there is also a reference sample with the same thickness.Based on the tribology test,the number of grooves of samples with the keeled structures is higher than that of samples with smooth surfaces,which indicates that the keeled structure dramatically enhances the wear resistance of snake scales,especially during the wear in the vertical direction.The experiment on surface morphology greatly compromised the result of the tribology test.In addition,the bottom portion of the keeled snake scales can be protected by the keeled structure.Besides,the overlapped distribution can protect the central region of snake scales and provide double-layer protection of the snake body.Overall,the keeled structure and the overlapped distribution play a significant part in the improvement of wear resistance of the snake skin.These findings can enhance the knowledge of the reptiles-mimic surface structure and facilitate the application of military uniforms under high-wear conditions.展开更多
With the rapid development in advanced industries,such as microelectronics and optics sectors,the functional feature size of devises/components has been decreasing from micro to nanometric,and even ACS for higher perf...With the rapid development in advanced industries,such as microelectronics and optics sectors,the functional feature size of devises/components has been decreasing from micro to nanometric,and even ACS for higher performance,smaller volume and lower energy consumption.By this time,a great many quantum structures are proposed,with not only an extreme scale of several or even single atom,but also a nearly ideal lattice structure with no material defect.It is almost no doubt that such structures play critical role in the next generation products,which shows an urgent demand for the ACSM.Laser machining is one of the most important approaches widely used in engineering and scientific research.It is high-efficient and applicable for most kinds of materials.Moreover,the processing scale covers a huge range from millimeters to nanometers,and has already touched the atomic level.Laser–material interaction mechanism,as the foundation of laser machining,determines the machining accuracy and surface quality.It becomes much more sophisticated and dominant with a decrease in processing scale,which is systematically reviewed in this article.In general,the mechanisms of laser-induced material removal are classified into ablation,CE and atomic desorption,with a decrease in the scale from above microns to angstroms.The effects of processing parameters on both fundamental material response and machined surface quality are discussed,as well as theoretical methods to simulate and understand the underlying mechanisms.Examples at nanometric to atomic scale are provided,which demonstrate the capability of laser machining in achieving the ultimate precision and becoming a promising approach to ACSM.展开更多
With the development of carbon electricity,achieving a low-carbon economy has become a prevailing and inevitable trend.Improving low-carbon expansion generation planning is critical for carbon emission mitigation and ...With the development of carbon electricity,achieving a low-carbon economy has become a prevailing and inevitable trend.Improving low-carbon expansion generation planning is critical for carbon emission mitigation and a lowcarbon economy.In this paper,a two-layer low-carbon expansion generation planning approach considering the uncertainty of renewable energy at multiple time scales is proposed.First,renewable energy sequences considering the uncertainty in multiple time scales are generated based on the Copula function and the probability distribution of renewable energy.Second,a two-layer generation planning model considering carbon trading and carbon capture technology is established.Specifically,the upper layer model optimizes the investment decision considering the uncertainty at a monthly scale,and the lower layer one optimizes the scheduling considering the peak shaving at an hourly scale and the flexibility at a 15-minute scale.Finally,the results of different influence factors on low-carbon generation expansion planning are compared in a provincial power grid,which demonstrate the effectiveness of the proposed model.展开更多
There are millimeter, micron and nanometer scales of pores and fractures in coal to describe different scales of coal pores and fissures communicating path and to quantitatively characterize their permeability. Such i...There are millimeter, micron and nanometer scales of pores and fractures in coal to describe different scales of coal pores and fissures communicating path and to quantitatively characterize their permeability. Such information provides an important basis for studying coalbed methane output mechanism. The pores and fissures in a large number of coal samples were observed and counted by scanning electron microscopy and optical microscopy. The probability distribution models of pore-fissure network were then established. Different scales of pore-fissures 2D network models were reconstructed by Monte Carlo method. The 2D seepage models were obtained through assignment zero method and using Matlab software. The effect of permeability on different scale pore-fractures network was obtained by two-dimensional seepage equation. Predicted permeability is compared with the measured ones. The results showed that the dominant order of different scale pore-fractures connected path from high to low is millimeter-sized fractures, seepage pores and micron-size fractures. The contribution of coal reservoir permeability from large to small is millimeter-size fractures, micron-size fractures and seepage pores. Different parameters in different scale pore-fractures are of different influence permeability.Reconstruction of different scale pore-fractures network can clearly display the connectivity of porefractures, which can provide a basis for selecting migration path and studying gas flow pattern.展开更多
Evaluation of the quality of small-bowel cleansing is required to assess the reliability of findings in capsule endoscopy(CE). Moreover, consensus regarding the need of intestinal preparation for CE remains to be achi...Evaluation of the quality of small-bowel cleansing is required to assess the reliability of findings in capsule endoscopy(CE). Moreover, consensus regarding the need of intestinal preparation for CE remains to be achieved. The presence of multiple grading scales for smallbowel preparation in CE, which are time-consuming and complicated, adds difficulty to the comparison of different small-bowel cleansing regimens and their application in clinical practice. Nowadays, a validated scale universally accepted for grading small-bowel cleansing is lacking. In fact, there are numerous grading systems with very different technical characteristics, namely, the parameters and the portion of the CE video that are analyzed, the objectivity of the analysis, the lesser or greater dependency on the operator, and the validation of the score. The authors performed a review which aims to systematize and summarize currently available smallbowel grading scales in CE.展开更多
The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati techniq...The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
This paper is concerned with the oscillatory behavior of a class of third-order nonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequali...This paper is concerned with the oscillatory behavior of a class of third-order nonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.展开更多
We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems a...We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s principle.Secondly,the definitions of Mei symmetry on time scales are given and its criterions are deduced.Finally,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are obtained.Results are illustrated with two examples.展开更多
The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems o...The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.展开更多
With the increasing proportion of wind power integration, the volatility of wind power brings huge challenges to the safe and stable operation of the electric power system. At present, the indexes commonly used to eva...With the increasing proportion of wind power integration, the volatility of wind power brings huge challenges to the safe and stable operation of the electric power system. At present, the indexes commonly used to evaluate the volatility of wind power only consider its overall characteristics, such as the standard deviation of wind power, the average of power variables, etc., while ignoring the detailed volatility of wind power, that is, the features of the frequency distribution of power variables. However, how to accurately describe the detailed volatility of wind power is the key foundation to reduce its adverse influences. To address this, a quantitative method for evaluating the detailed volatility of wind power at multiple temporal-spatial scales is proposed. First, the volatility indexes which can evaluate the detailed fluctuation characteristics of wind power are presented, including the upper confidence limit, lower confidence limit and confidence interval of power variables under the certain confidence level. Then, the actual wind power data from a location in northern China is used to illustrate the application of the proposed indexes at multiple temporal(year–season–month–day) and spatial scales(wind turbine–wind turbines–wind farm–wind farms) using the calculation time windows of 10 min, 30 min, 1 h, and 4 h. Finally, the relationships between wind power forecasting accuracy and its corresponding detailed volatility are analyzed to further verify the effectiveness of the proposed indexes. The results show that the proposed volatility indexes can effectively characterize the detailed fluctuations of wind power at multiple temporal-spatial scales. It is anticipated that the results of this study will serve as an important reference for the reserve capacity planning and optimization dispatch in the electric power system which with a high proportion of renewable energy.展开更多
A fast-slow coupled model of the hydro-turbine governing system(HTGS)is established by introducing frequency disturbance in this paper.Based on the proposed model,the performances of two time scales for bursting oscil...A fast-slow coupled model of the hydro-turbine governing system(HTGS)is established by introducing frequency disturbance in this paper.Based on the proposed model,the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams,time waveforms and phase portraits.We find that stability and operational characteristics of the HTGS change with the value of system parameter k_d.Furthermore,the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out.Meanwhile,we obtain that the relative deviation of the mechanical torque mt rises with the increase of a.These methods and results of the study,combined with the performance of two time scales and the fast-slow coupled engineering model,provide some theoretical bases for investigating interesting physical phenomena of the engineering system.展开更多
In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales...In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.展开更多
This paper, divided into three parts (Part II-A, Part II-B and Part II-C), contains the detailed factorizational theory of asymptotic expansions of type (?)?, , , where the asymptotic scale?, , is assumed to be an ext...This paper, divided into three parts (Part II-A, Part II-B and Part II-C), contains the detailed factorizational theory of asymptotic expansions of type (?)?, , , where the asymptotic scale?, , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of . It follows two pre-viously published papers: the first, labelled as Part I, contains the complete (elementary but non-trivial) theory for;the second is a survey highlighting only the main results without proofs. All the material appearing in §2 of the survey is here reproduced in an expanded form, as it contains all the preliminary formulas necessary to understand and prove the results. The remaining part of the survey—especially the heuristical considerations and consequent conjectures in §3—may serve as a good introduction to the complete theory.展开更多
A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term ...A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.展开更多
The aims of this study were to prepare natural hydroxyapatite from fish scales(FsHAp)for potential use as a filler in polymer.The FsHAp was prepared from Tilapia fish scales using thermal method.The FsHAp was milled f...The aims of this study were to prepare natural hydroxyapatite from fish scales(FsHAp)for potential use as a filler in polymer.The FsHAp was prepared from Tilapia fish scales using thermal method.The FsHAp was milled for 48 h and dried by spray method.The morphology was characterized using field emission scanning electron microscope(FESEM)which showed irregular shape of FsHAp particles with particle size around 7μm.The analysis of FsHAp was carried out using Fourier transform infrared spectroscopy(FTIR)and X-ray diffraction(XRD)to confirm chemical structure of FsHAp.展开更多
In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are o...In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are obtained for the oscillation of the dynamic equations.The main result is illustrated by an example.展开更多
In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error esti...In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori bound of exact solution are not needed for the choice rule. Numerical tests show that the proposed method is effective and stable.展开更多
-In this paper, the factors for SSTA development in finite sea area of low latitudes are discussed with simpler linearized equations, According to the coupling conditions at the interface of atmosphere and ocean, we s...-In this paper, the factors for SSTA development in finite sea area of low latitudes are discussed with simpler linearized equations, According to the coupling conditions at the interface of atmosphere and ocean, we studied the horizontal scale relations of air-sea coupled system satisfying the dynamical and thermodynamical requirements, From the fluctuation viewpoint, the relation of horizontal scales and wave numbers are presented for a linear atmosphere-ocean coupled system with the same time scales. At last part of the paper, the state of fluctuations is examined for different sea scales under certain given atmospheric scale with a simpler two-layer coupled model, and some significant results obtained.展开更多
Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. Wh...Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger,the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.展开更多
基金funded By Key Scientific And Technological Program Of Ningbo City(No.2021Z108)Yongjiang Talent Introduction Programme(No.2021A-154-G).
文摘The movement mode of snakes is crawling,and the living environment of snakes with numerous branches and stones will cause plenty of wear for the snake scales.There are plenty of surface structures and morphology on snake scales to avoid severe wear.Among them,the research towards the keeled structure on snake scales is missing.Therefore,in this research,the wear resistance improvement of the keeled structure on the snake scales and the overlapped distribution of snake scales are investigated.The keeled and smooth snake scales were 3D printed and they were distributed on the substrate in the overlapped or paralleled ways.Besides these four samples with keeled/smooth scales and overlapped/paralleled distributed,there is also a reference sample with the same thickness.Based on the tribology test,the number of grooves of samples with the keeled structures is higher than that of samples with smooth surfaces,which indicates that the keeled structure dramatically enhances the wear resistance of snake scales,especially during the wear in the vertical direction.The experiment on surface morphology greatly compromised the result of the tribology test.In addition,the bottom portion of the keeled snake scales can be protected by the keeled structure.Besides,the overlapped distribution can protect the central region of snake scales and provide double-layer protection of the snake body.Overall,the keeled structure and the overlapped distribution play a significant part in the improvement of wear resistance of the snake skin.These findings can enhance the knowledge of the reptiles-mimic surface structure and facilitate the application of military uniforms under high-wear conditions.
基金supported by the National Natural Science Foundation of China(Nos.52035009,52105475).
文摘With the rapid development in advanced industries,such as microelectronics and optics sectors,the functional feature size of devises/components has been decreasing from micro to nanometric,and even ACS for higher performance,smaller volume and lower energy consumption.By this time,a great many quantum structures are proposed,with not only an extreme scale of several or even single atom,but also a nearly ideal lattice structure with no material defect.It is almost no doubt that such structures play critical role in the next generation products,which shows an urgent demand for the ACSM.Laser machining is one of the most important approaches widely used in engineering and scientific research.It is high-efficient and applicable for most kinds of materials.Moreover,the processing scale covers a huge range from millimeters to nanometers,and has already touched the atomic level.Laser–material interaction mechanism,as the foundation of laser machining,determines the machining accuracy and surface quality.It becomes much more sophisticated and dominant with a decrease in processing scale,which is systematically reviewed in this article.In general,the mechanisms of laser-induced material removal are classified into ablation,CE and atomic desorption,with a decrease in the scale from above microns to angstroms.The effects of processing parameters on both fundamental material response and machined surface quality are discussed,as well as theoretical methods to simulate and understand the underlying mechanisms.Examples at nanometric to atomic scale are provided,which demonstrate the capability of laser machining in achieving the ultimate precision and becoming a promising approach to ACSM.
基金supported partly by the National Key R&D Program of China(2018YFA0702200)the Science and Technology Project of State Grid Shandong Electric Power Company(520604190002)。
文摘With the development of carbon electricity,achieving a low-carbon economy has become a prevailing and inevitable trend.Improving low-carbon expansion generation planning is critical for carbon emission mitigation and a lowcarbon economy.In this paper,a two-layer low-carbon expansion generation planning approach considering the uncertainty of renewable energy at multiple time scales is proposed.First,renewable energy sequences considering the uncertainty in multiple time scales are generated based on the Copula function and the probability distribution of renewable energy.Second,a two-layer generation planning model considering carbon trading and carbon capture technology is established.Specifically,the upper layer model optimizes the investment decision considering the uncertainty at a monthly scale,and the lower layer one optimizes the scheduling considering the peak shaving at an hourly scale and the flexibility at a 15-minute scale.Finally,the results of different influence factors on low-carbon generation expansion planning are compared in a provincial power grid,which demonstrate the effectiveness of the proposed model.
基金in major projects of Henan Province University Science and Technology Innovation Talent Support Program of China (No. 15HASTIT050)Funding Scheme for Henan Province the Young Key Teachers (No. 2013GGJS-049) of ChinaScience and Technology Department of Henan Province of China (No. 142102210050)
文摘There are millimeter, micron and nanometer scales of pores and fractures in coal to describe different scales of coal pores and fissures communicating path and to quantitatively characterize their permeability. Such information provides an important basis for studying coalbed methane output mechanism. The pores and fissures in a large number of coal samples were observed and counted by scanning electron microscopy and optical microscopy. The probability distribution models of pore-fissure network were then established. Different scales of pore-fissures 2D network models were reconstructed by Monte Carlo method. The 2D seepage models were obtained through assignment zero method and using Matlab software. The effect of permeability on different scale pore-fractures network was obtained by two-dimensional seepage equation. Predicted permeability is compared with the measured ones. The results showed that the dominant order of different scale pore-fractures connected path from high to low is millimeter-sized fractures, seepage pores and micron-size fractures. The contribution of coal reservoir permeability from large to small is millimeter-size fractures, micron-size fractures and seepage pores. Different parameters in different scale pore-fractures are of different influence permeability.Reconstruction of different scale pore-fractures network can clearly display the connectivity of porefractures, which can provide a basis for selecting migration path and studying gas flow pattern.
文摘Evaluation of the quality of small-bowel cleansing is required to assess the reliability of findings in capsule endoscopy(CE). Moreover, consensus regarding the need of intestinal preparation for CE remains to be achieved. The presence of multiple grading scales for smallbowel preparation in CE, which are time-consuming and complicated, adds difficulty to the comparison of different small-bowel cleansing regimens and their application in clinical practice. Nowadays, a validated scale universally accepted for grading small-bowel cleansing is lacking. In fact, there are numerous grading systems with very different technical characteristics, namely, the parameters and the portion of the CE video that are analyzed, the objectivity of the analysis, the lesser or greater dependency on the operator, and the validation of the score. The authors performed a review which aims to systematize and summarize currently available smallbowel grading scales in CE.
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.
基金Supported by the NNSF of China(11071222)Supported by the NSF of Hunan Province(12JJ6006)Supported by Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)
文摘This paper is concerned with the oscillatory behavior of a class of third-order nonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)the Natural Science Foundation of Jiangsu Province of China(Grant BK20191454).
文摘We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s principle.Secondly,the definitions of Mei symmetry on time scales are given and its criterions are deduced.Finally,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are obtained.Results are illustrated with two examples.
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)
文摘The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.
基金supported in part by the National Key R&D Program of China (No.2017YFE0109000)the project of China Datang Corporation Ltd
文摘With the increasing proportion of wind power integration, the volatility of wind power brings huge challenges to the safe and stable operation of the electric power system. At present, the indexes commonly used to evaluate the volatility of wind power only consider its overall characteristics, such as the standard deviation of wind power, the average of power variables, etc., while ignoring the detailed volatility of wind power, that is, the features of the frequency distribution of power variables. However, how to accurately describe the detailed volatility of wind power is the key foundation to reduce its adverse influences. To address this, a quantitative method for evaluating the detailed volatility of wind power at multiple temporal-spatial scales is proposed. First, the volatility indexes which can evaluate the detailed fluctuation characteristics of wind power are presented, including the upper confidence limit, lower confidence limit and confidence interval of power variables under the certain confidence level. Then, the actual wind power data from a location in northern China is used to illustrate the application of the proposed indexes at multiple temporal(year–season–month–day) and spatial scales(wind turbine–wind turbines–wind farm–wind farms) using the calculation time windows of 10 min, 30 min, 1 h, and 4 h. Finally, the relationships between wind power forecasting accuracy and its corresponding detailed volatility are analyzed to further verify the effectiveness of the proposed indexes. The results show that the proposed volatility indexes can effectively characterize the detailed fluctuations of wind power at multiple temporal-spatial scales. It is anticipated that the results of this study will serve as an important reference for the reserve capacity planning and optimization dispatch in the electric power system which with a high proportion of renewable energy.
基金Project supported by the Scientific Research Foundation of the National Natural Science Foundation of China–Outstanding Youth Foundation(Grant No.51622906)the National Natural Science Foundation of China(Grant No.51479173)+3 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.201304030577)the Scientific Research Funds of Northwest A&F University,China(Grant No.2013BSJJ095)the Science Fund for Excellent Young Scholars from Northwest A&F University(Grant No.Z109021515)the Shaanxi Provincial Nova Program,China(Grant No.2016KJXX-55)
文摘A fast-slow coupled model of the hydro-turbine governing system(HTGS)is established by introducing frequency disturbance in this paper.Based on the proposed model,the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams,time waveforms and phase portraits.We find that stability and operational characteristics of the HTGS change with the value of system parameter k_d.Furthermore,the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out.Meanwhile,we obtain that the relative deviation of the mechanical torque mt rises with the increase of a.These methods and results of the study,combined with the performance of two time scales and the fast-slow coupled engineering model,provide some theoretical bases for investigating interesting physical phenomena of the engineering system.
文摘In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.
文摘This paper, divided into three parts (Part II-A, Part II-B and Part II-C), contains the detailed factorizational theory of asymptotic expansions of type (?)?, , , where the asymptotic scale?, , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of . It follows two pre-viously published papers: the first, labelled as Part I, contains the complete (elementary but non-trivial) theory for;the second is a survey highlighting only the main results without proofs. All the material appearing in §2 of the survey is here reproduced in an expanded form, as it contains all the preliminary formulas necessary to understand and prove the results. The remaining part of the survey—especially the heuristical considerations and consequent conjectures in §3—may serve as a good introduction to the complete theory.
基金supported by the National Natural Science Foundation of China(Grants11632008 and 11872189)
文摘A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.
文摘The aims of this study were to prepare natural hydroxyapatite from fish scales(FsHAp)for potential use as a filler in polymer.The FsHAp was prepared from Tilapia fish scales using thermal method.The FsHAp was milled for 48 h and dried by spray method.The morphology was characterized using field emission scanning electron microscope(FESEM)which showed irregular shape of FsHAp particles with particle size around 7μm.The analysis of FsHAp was carried out using Fourier transform infrared spectroscopy(FTIR)and X-ray diffraction(XRD)to confirm chemical structure of FsHAp.
基金Supported by the the NNSF of China（60404022 60604004） Supported by the Special Projects in Mathematics Funded by Natural Science Foundation of Hebei Province（07M005）
文摘In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are obtained for the oscillation of the dynamic equations.The main result is illustrated by an example.
文摘In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori bound of exact solution are not needed for the choice rule. Numerical tests show that the proposed method is effective and stable.
文摘-In this paper, the factors for SSTA development in finite sea area of low latitudes are discussed with simpler linearized equations, According to the coupling conditions at the interface of atmosphere and ocean, we studied the horizontal scale relations of air-sea coupled system satisfying the dynamical and thermodynamical requirements, From the fluctuation viewpoint, the relation of horizontal scales and wave numbers are presented for a linear atmosphere-ocean coupled system with the same time scales. At last part of the paper, the state of fluctuations is examined for different sea scales under certain given atmospheric scale with a simpler two-layer coupled model, and some significant results obtained.
文摘Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger,the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.
