This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to ...Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to investigate the broader model,namely the asymmetric piecewise linear system.The traditional averaging method is frequently used for studying nonlinear systems,particularly symmetric piecewise linear systems,with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions.However,asymmetric systems inherently exhibit nonharmonic,asymmetric responses,rendering the traditional averaging method inapplicable.To overcome this limitation,this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs.Unlike the traditional method,which assumes a purely harmonic response,the improved averaging method redefines the system response as a superposition of a direct current(DC)term and a first harmonic component.Herein,the DC term can be regarded as the offset induced by model asymmetry.Furthermore,the DC term is treated as a slow variable function of time,with its time derivative assumed to be zero when calculating the steady-state solution,akin to the amplitude and phase in the traditional averaging method.Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method.Leveraging these improved results,the study also examines the parameter effect,stability,and bifurcation phenomena within the amplitude-frequency responses.展开更多
Piecewise linear blade twist is studied as a method for reducing the rotor vibratory loads.A rotor model based on an elastic beam concept is used to predict the loads.A four-bladed rotor with a shape similar to the UH...Piecewise linear blade twist is studied as a method for reducing the rotor vibratory loads.A rotor model based on an elastic beam concept is used to predict the loads.A four-bladed rotor with a shape similar to the UH-60 rotor is used as a baseline for comparisons.The blade is divided into three segments,which are inner,middle and outer segments respectively.Effect of the twist at different segments on the loads is discussed.The twists at all the segments can reduce the 4/rev(revolution)vertical hub force at low speeds.The 4/rev force can be reduced by 99.5%with a-24°/R(R is the blade radius)twist at the middle segment at 80 km/h.The twist at the inner segment is not helpful for reducing the 4/rev rolling and pitching moments,while the twists at other segments can control both the moments at most speeds.A parameter sweep is conducted to minimize these loads.To reduce the 4/rev force,all the segments need to be twisted at low speeds,while untwisted blades perform better at high speeds.For controlling the 4/rev moments,the outer segment should be highly twisted at low speeds,while high twists at the middle segment are essential at medium to high speeds.展开更多
This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and ...This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.展开更多
To prevent sub-harmonic oscillation and improve the stability and load capacity of the system,a piecewise linear slope compensation circuit is designed. Compared with the traditional design, this circuit provides a co...To prevent sub-harmonic oscillation and improve the stability and load capacity of the system,a piecewise linear slope compensation circuit is designed. Compared with the traditional design, this circuit provides a compensation signal whose slope varies from different duty cycles at - 40-85℃ ,and reduces the negative effect of slope compensation on the system＇s load capacity and transient response. A current mode PWM Boost DC-DC converter employing this slope compensation circuit is implemented in a UMC 0.6μm-BCD process. The results indicate that the circuit works well and effectively,and the load capacity is increased by 20%. The chip area of the piecewise linear slope compensation circuit is 0.01mm^2 ,which consumes only 8μA quiescent current,and the efficiency ranges up to 93%.展开更多
A bandgap voltage reference is presented with a piecewise linear compensating circuit in order to reduce the temperature coefficient.The basic principle is to divide the whole operating temperature range into some su...A bandgap voltage reference is presented with a piecewise linear compensating circuit in order to reduce the temperature coefficient.The basic principle is to divide the whole operating temperature range into some sub ranges.At different temperature sub ranges the bandgap reference can be compensated by different linear functions.Since the temperature sub range is much narrower than the whole range,the compensation error can be reduced significantly.Theoretically,the precision can be improved unlimitedly if the sub ranges are narrow enough.In the given example,with only three temperature sub ranges,the temperature coefficient of a conventional bandgap reference drops from 1 5×10 -5 /℃ to 2×10 -6 /℃ over the -40℃ to 120℃ temperature range.展开更多
The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bo...The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.展开更多
This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable wit...This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.展开更多
A novel 2D analytical model for the doping profile of the bulk silicon RESURF LDMOS drift region is proposed. According to the proposed model, to obtain good performance, the doping profile in the total drift region o...A novel 2D analytical model for the doping profile of the bulk silicon RESURF LDMOS drift region is proposed. According to the proposed model, to obtain good performance, the doping profile in the total drift region of a RESURF LDMOS with a field plate should be piecewise linearly graded. The breakdown voltage of the proposed RESURF LDMOS with a piecewise linearly graded doping drift region is improved by 58. 8%, and the specific on-resistance is reduced by 87. 4% compared with conventional LDMOS. These results are verified by the two-dimensional process simulator Tsuprem-4 and the device simulator Medici.展开更多
Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is t...Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.展开更多
This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the tradi...This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.展开更多
This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncerta...This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are...Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.展开更多
The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficie...The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficiency advantages. A PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time is presented, enabled the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations the reflection and transmission coefficients through a magnetized plasma layer. The results show that the PLRC-FDTD method has significantly improved the accuracy over the original RC method.展开更多
Horizon control,maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient,is a key technique in longwall mining automation.To identify the coal seam gradient,a geological model o...Horizon control,maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient,is a key technique in longwall mining automation.To identify the coal seam gradient,a geological model of the coal seam was constructed using in-seam seismic surveying technology.By synthesizing the control resolution of the range arm and the geometric characteristics of the coal seam,a gradient identification method based on piecewise linear representation(PLR)is proposed.To achieve the maximum exploitation rate within the shearer's capacity,the control resolution of the range arm is selected as the threshold parameter of PLR.The control resolution significantly influenced the number of line segments and the fitting error.With the decrease of the control resolution from 0.01 to 0.02 m,the number of line segments decreased from 65 to 15,which was beneficial to horizon control.However,the average fitting error increased from 0.055 to 0.14 m,which would induce a decrease in the exploitation rate.To avoid significant deviation between the cutting range and the coal seam,the control resolution of the range arm must be lower than 0.02 m.In a field test,the automated horizon control of the longwall face was realized by coal seam gradient identification.展开更多
The paper presents an improved plane layout for stabilizing piles based on a proposed piecewise function expression for the irregular driving force. Based on the specific morphological characteristics of a highway lan...The paper presents an improved plane layout for stabilizing piles based on a proposed piecewise function expression for the irregular driving force. Based on the specific morphological characteristics of a highway landslide, the piecewise function is used to calculate the irregular driving force by dividing the landslide into several sub-areas.Furthermore, the reasonable layout range and pile spacing can be obtained based on the piecewise function expression of the irregular driving force and on relevant research results of the plane layout for stabilizing piles. Therefore, an improved plane layout of stabilizing piles is presented in consideration of a piecewise function expression of the irregular driving force. A highway landslide located in eastern Guizhou Province, China, is analyzed as a case study using the proposed method. The results demonstrate that the theory presented in this paper provides improved economic benefits and can reduce the requirednumber of stabilizing piles by 28.6% compared with the conventional plane layout scheme.展开更多
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
基金Project supported by the National Natural Science Foundation of China(Nos.12272242 and U1934201)。
文摘Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to investigate the broader model,namely the asymmetric piecewise linear system.The traditional averaging method is frequently used for studying nonlinear systems,particularly symmetric piecewise linear systems,with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions.However,asymmetric systems inherently exhibit nonharmonic,asymmetric responses,rendering the traditional averaging method inapplicable.To overcome this limitation,this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs.Unlike the traditional method,which assumes a purely harmonic response,the improved averaging method redefines the system response as a superposition of a direct current(DC)term and a first harmonic component.Herein,the DC term can be regarded as the offset induced by model asymmetry.Furthermore,the DC term is treated as a slow variable function of time,with its time derivative assumed to be zero when calculating the steady-state solution,akin to the amplitude and phase in the traditional averaging method.Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method.Leveraging these improved results,the study also examines the parameter effect,stability,and bifurcation phenomena within the amplitude-frequency responses.
基金This work was supported by the Active Control Rotor Technology Project(No.FKFB20231108055)the National Natural Science Foundation of China(No.11972181)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX21_0228).
文摘Piecewise linear blade twist is studied as a method for reducing the rotor vibratory loads.A rotor model based on an elastic beam concept is used to predict the loads.A four-bladed rotor with a shape similar to the UH-60 rotor is used as a baseline for comparisons.The blade is divided into three segments,which are inner,middle and outer segments respectively.Effect of the twist at different segments on the loads is discussed.The twists at all the segments can reduce the 4/rev(revolution)vertical hub force at low speeds.The 4/rev force can be reduced by 99.5%with a-24°/R(R is the blade radius)twist at the middle segment at 80 km/h.The twist at the inner segment is not helpful for reducing the 4/rev rolling and pitching moments,while the twists at other segments can control both the moments at most speeds.A parameter sweep is conducted to minimize these loads.To reduce the 4/rev force,all the segments need to be twisted at low speeds,while untwisted blades perform better at high speeds.For controlling the 4/rev moments,the outer segment should be highly twisted at low speeds,while high twists at the middle segment are essential at medium to high speeds.
文摘This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.
文摘To prevent sub-harmonic oscillation and improve the stability and load capacity of the system,a piecewise linear slope compensation circuit is designed. Compared with the traditional design, this circuit provides a compensation signal whose slope varies from different duty cycles at - 40-85℃ ,and reduces the negative effect of slope compensation on the system＇s load capacity and transient response. A current mode PWM Boost DC-DC converter employing this slope compensation circuit is implemented in a UMC 0.6μm-BCD process. The results indicate that the circuit works well and effectively,and the load capacity is increased by 20%. The chip area of the piecewise linear slope compensation circuit is 0.01mm^2 ,which consumes only 8μA quiescent current,and the efficiency ranges up to 93%.
文摘A bandgap voltage reference is presented with a piecewise linear compensating circuit in order to reduce the temperature coefficient.The basic principle is to divide the whole operating temperature range into some sub ranges.At different temperature sub ranges the bandgap reference can be compensated by different linear functions.Since the temperature sub range is much narrower than the whole range,the compensation error can be reduced significantly.Theoretically,the precision can be improved unlimitedly if the sub ranges are narrow enough.In the given example,with only three temperature sub ranges,the temperature coefficient of a conventional bandgap reference drops from 1 5×10 -5 /℃ to 2×10 -6 /℃ over the -40℃ to 120℃ temperature range.
基金supported by the National Science Fund of China for Distinguished Young Scholars(No.60725311)
文摘The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.
基金Supported by the State Key Program of National Natural Science of China （60534010）, National Basic Research Program of China （973 Program）（2009CB320604）, National Natural Science Foundation of China （60674021）, the Funds for Creative Research Groups of China （60521003）, the 111 Project（B08015）, and the Funds of Ph.D. Program of Ministry of Eduction, China （20060145019）.
文摘This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.
文摘A novel 2D analytical model for the doping profile of the bulk silicon RESURF LDMOS drift region is proposed. According to the proposed model, to obtain good performance, the doping profile in the total drift region of a RESURF LDMOS with a field plate should be piecewise linearly graded. The breakdown voltage of the proposed RESURF LDMOS with a piecewise linearly graded doping drift region is improved by 58. 8%, and the specific on-resistance is reduced by 87. 4% compared with conventional LDMOS. These results are verified by the two-dimensional process simulator Tsuprem-4 and the device simulator Medici.
文摘Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.
文摘This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61004038)
文摘This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
基金Project supported by the National Natural Science Foundation of China (Grant No 10275053)
文摘Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.
基金The project was supported by the National Natural Science Foundation of China (60471002) and the Jiangxi ProvincialNatural Science Foundation (0412014)
文摘The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficiency advantages. A PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time is presented, enabled the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations the reflection and transmission coefficients through a magnetized plasma layer. The results show that the PLRC-FDTD method has significantly improved the accuracy over the original RC method.
基金supported in part by the Funds of the National Natural Science Foundation of China(Nos.51874279 and U1610251)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘Horizon control,maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient,is a key technique in longwall mining automation.To identify the coal seam gradient,a geological model of the coal seam was constructed using in-seam seismic surveying technology.By synthesizing the control resolution of the range arm and the geometric characteristics of the coal seam,a gradient identification method based on piecewise linear representation(PLR)is proposed.To achieve the maximum exploitation rate within the shearer's capacity,the control resolution of the range arm is selected as the threshold parameter of PLR.The control resolution significantly influenced the number of line segments and the fitting error.With the decrease of the control resolution from 0.01 to 0.02 m,the number of line segments decreased from 65 to 15,which was beneficial to horizon control.However,the average fitting error increased from 0.055 to 0.14 m,which would induce a decrease in the exploitation rate.To avoid significant deviation between the cutting range and the coal seam,the control resolution of the range arm must be lower than 0.02 m.In a field test,the automated horizon control of the longwall face was realized by coal seam gradient identification.
基金supported by the National Key R&D Program of China (2017YFC1501304)the National Natural Science Fund of China (No. 41472261)+1 种基金 the Key Technical Project of Shenzhen Science Technology Project (No. JSGG20160331154546471) the Open Fund of State Key Laboratory of Geohazard Prevention and Geoenviroment Protection (Grant No. SKLGP2017K017)
文摘The paper presents an improved plane layout for stabilizing piles based on a proposed piecewise function expression for the irregular driving force. Based on the specific morphological characteristics of a highway landslide, the piecewise function is used to calculate the irregular driving force by dividing the landslide into several sub-areas.Furthermore, the reasonable layout range and pile spacing can be obtained based on the piecewise function expression of the irregular driving force and on relevant research results of the plane layout for stabilizing piles. Therefore, an improved plane layout of stabilizing piles is presented in consideration of a piecewise function expression of the irregular driving force. A highway landslide located in eastern Guizhou Province, China, is analyzed as a case study using the proposed method. The results demonstrate that the theory presented in this paper provides improved economic benefits and can reduce the requirednumber of stabilizing piles by 28.6% compared with the conventional plane layout scheme.
