This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two...This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,showing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(i)the explicit symmetrization of the system,which can be achieved by adding terms that contain linear combinations of the curl involution,similar to the Godunov-Powell terms in the MHD equations;(ii)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illustrate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.展开更多
This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto t...This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.展开更多
The aim of this study is to develop processing maps based on two models and compare them with conventional processing maps.The hyperbolic sinus constitutive equation and artificial neural network(ANN)approaches were u...The aim of this study is to develop processing maps based on two models and compare them with conventional processing maps.The hyperbolic sinus constitutive equation and artificial neural network(ANN)approaches were used in this investigation to predict flow stress and to develop processing maps in various conditions.The hot compression tests of InX-750 superalloy were carried out above the gamma prime phase temperature and within the temperature range of 1000-1150℃and strain rate of 0.001-1.000 s^(-1).The processing maps were conducted based upon dynamic material model(DMM)for data by experimental,constitutive equation and ANN approaches.The processing maps drawn by either of the prediction methods show that the method developed by ANN data does not significantly differ from the experimental processing map.The ANN approach is thus a suitable way to predict the flow stress as well as hot working processing map of engineering metals and materials.展开更多
In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamicall...In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.展开更多
In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is introduced.To define the fractional g...In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is introduced.To define the fractional generalized hyperbolic process,the non-fractional variant is derived by subordinating time-changed Brownian motion to the generalized inverse Gaussian process,and thereafter,the fractional generalized hyperbolic process is obtained using the Volterra kernel.Based on the ARMA–GARCH model with standard normal innovations,the parameters are estimated for the high-frequency returns of six U.S.stocks.Subsequently,the residuals extracted from the estimated ARMA–GARCH parameters are fitted to the fractional and non-fractional generalized hyperbolic processes.The results show that the fractional generalized hyperbolic process performs better in describing the behavior of the residual process of high-frequency returns than the non-fractional processes considered in this study.展开更多
Because of good quality of compressive resistance, the hyperbolic arch dam is being increasingly applied to engineering projects. In order to satisfy the needs of compressive resistance under the conditions of high wa...Because of good quality of compressive resistance, the hyperbolic arch dam is being increasingly applied to engineering projects. In order to satisfy the needs of compressive resistance under the conditions of high water pressure, a stress analysis is required for the dam. During the stress analysis process however, due to the complexity of the three-dimensional modeling, it is very hard to form a model. Therefore, the stress analysis process is a barrier for the arch dam. In this article, based on the research of the new line-type arch dam, a mathematical model in different degree of convexity conditions of the dam is established; using the C ＋ ＋ language program, a computer three-dimensional model simulation is realized on AutoCAD. The accurate three-dimensional model is providing a finite element optimization design of the involute hyperbolic arch dam for the next step.展开更多
A standard part of the calculus curriculum is learning exponential growth models. This paper, designed to serve as a teaching aid, extends the standard modeling by showing that simple exponential models, relying on tw...A standard part of the calculus curriculum is learning exponential growth models. This paper, designed to serve as a teaching aid, extends the standard modeling by showing that simple exponential models, relying on two points to fit parameters do not do a good job in modeling population data of the distant past. Moreover, they provide a constant doubling time. Therefore, the student is introduced to hyperbolic modeling, and it is demonstrated that with only two population data points, an amazing amount of information can be obtained, such as reasonably accurate doubling times that are a function of t, as well as accurate estimates of such entertaining topics as the total number of people that have ever lived on earth.展开更多
In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation p...In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.展开更多
Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Men...Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.展开更多
In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.
In complex media, especially for seismic prospecting in deep layers in East China and in the mountainous area in West China, due to the complex geological condition, the common-mid-point （CMP） gather of deep reflect...In complex media, especially for seismic prospecting in deep layers in East China and in the mountainous area in West China, due to the complex geological condition, the common-mid-point （CMP） gather of deep reflection event is neither hyperbolic, nor any simple function. If traditional normal move-out （NMO） and stack imaging technology are still used, it is difficult to get a clear stack image. Based on previous techniques on non-hyperbolic stack, it is thought in this paper that no matter how complex the geological condition is, in order to get an optimized stack image, the stack should be non time move-out stack, and any stacking method limited to some kind of curve will be restricted to application conditions. In order to overcome the above-mentioned limit, a new method called optimized non-hyperbolic stack imaging based on interpretation model is presented in this paper. Based on CMP/CRP （Common-Reflection-Point） gather after NMO or pre-stack migration, this method uses the interpretation model of reflectors as constraint, and takes comparability as a distinguishing criterion, and finally forms a residual move-out correction for the gather of constrained model. Numerical simulation indicates that this method could overcome the non hyperbolic problem and get fine stack image.展开更多
A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed...A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model＇ s performance on prediction of wave heights around breaking point for the wave motions in surf zone.展开更多
New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations fo...New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is gready saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.展开更多
In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-di...In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.展开更多
Taking the hyperbolic glass curtain wall project of the Wuhan Jinyinhu Commercial Plaza as an example,the characteristics of different curved glass forming technologies were analyzed in this paper.Combined with the ac...Taking the hyperbolic glass curtain wall project of the Wuhan Jinyinhu Commercial Plaza as an example,the characteristics of different curved glass forming technologies were analyzed in this paper.Combined with the actual engineering situation,the curved steel process is selected to produce the hyperbolic glass curtain wall,and the application of BIM technology in the quality control of hyperbolic glass curtain wall in the production process was analyzed,and the effects of heating condition,bending time,cooling condition,and bending tempering error in the manufacturing accuracy of the curved glass curtain wall were studied,in hope that this project can provide practical reference for similar curtain wall design construction in the future.展开更多
In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invari...In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invariant points. Moreover, we can see that M?bius transformation is hyperbolic isometries that form a group action PSL (2, R) on the upper half plane model.展开更多
In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic S...In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.展开更多
基金Initiative 2018–2027 attributed to DICAM of the University of Trento(grant L.232/2016)the PRIN 2022 project High-order structure-preserving semi-implicit schemes for hyperbolic equations and by the European Union-Next GenerationEU(PNRR,Spoke 7 CN HPC).
文摘This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,showing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(i)the explicit symmetrization of the system,which can be achieved by adding terms that contain linear combinations of the curl involution,similar to the Godunov-Powell terms in the MHD equations;(ii)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illustrate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60325311,60534010,60572070 and 60521003)the Program for Cheung Kong Scholars and Innovative Research Team in University (Grant No IRT0421)
文摘This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.
基金the support by the Faculty of Engineering,Hakim Sabzevari University,Sabzevar,Iran。
文摘The aim of this study is to develop processing maps based on two models and compare them with conventional processing maps.The hyperbolic sinus constitutive equation and artificial neural network(ANN)approaches were used in this investigation to predict flow stress and to develop processing maps in various conditions.The hot compression tests of InX-750 superalloy were carried out above the gamma prime phase temperature and within the temperature range of 1000-1150℃and strain rate of 0.001-1.000 s^(-1).The processing maps were conducted based upon dynamic material model(DMM)for data by experimental,constitutive equation and ANN approaches.The processing maps drawn by either of the prediction methods show that the method developed by ANN data does not significantly differ from the experimental processing map.The ANN approach is thus a suitable way to predict the flow stress as well as hot working processing map of engineering metals and materials.
文摘In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.
文摘In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is introduced.To define the fractional generalized hyperbolic process,the non-fractional variant is derived by subordinating time-changed Brownian motion to the generalized inverse Gaussian process,and thereafter,the fractional generalized hyperbolic process is obtained using the Volterra kernel.Based on the ARMA–GARCH model with standard normal innovations,the parameters are estimated for the high-frequency returns of six U.S.stocks.Subsequently,the residuals extracted from the estimated ARMA–GARCH parameters are fitted to the fractional and non-fractional generalized hyperbolic processes.The results show that the fractional generalized hyperbolic process performs better in describing the behavior of the residual process of high-frequency returns than the non-fractional processes considered in this study.
基金Supported by Postgraduate Education Innovation Fund of Chongqing Jiaotong University
文摘Because of good quality of compressive resistance, the hyperbolic arch dam is being increasingly applied to engineering projects. In order to satisfy the needs of compressive resistance under the conditions of high water pressure, a stress analysis is required for the dam. During the stress analysis process however, due to the complexity of the three-dimensional modeling, it is very hard to form a model. Therefore, the stress analysis process is a barrier for the arch dam. In this article, based on the research of the new line-type arch dam, a mathematical model in different degree of convexity conditions of the dam is established; using the C ＋ ＋ language program, a computer three-dimensional model simulation is realized on AutoCAD. The accurate three-dimensional model is providing a finite element optimization design of the involute hyperbolic arch dam for the next step.
文摘A standard part of the calculus curriculum is learning exponential growth models. This paper, designed to serve as a teaching aid, extends the standard modeling by showing that simple exponential models, relying on two points to fit parameters do not do a good job in modeling population data of the distant past. Moreover, they provide a constant doubling time. Therefore, the student is introduced to hyperbolic modeling, and it is demonstrated that with only two population data points, an amazing amount of information can be obtained, such as reasonably accurate doubling times that are a function of t, as well as accurate estimates of such entertaining topics as the total number of people that have ever lived on earth.
文摘In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.
文摘Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.
文摘In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.
文摘In complex media, especially for seismic prospecting in deep layers in East China and in the mountainous area in West China, due to the complex geological condition, the common-mid-point （CMP） gather of deep reflection event is neither hyperbolic, nor any simple function. If traditional normal move-out （NMO） and stack imaging technology are still used, it is difficult to get a clear stack image. Based on previous techniques on non-hyperbolic stack, it is thought in this paper that no matter how complex the geological condition is, in order to get an optimized stack image, the stack should be non time move-out stack, and any stacking method limited to some kind of curve will be restricted to application conditions. In order to overcome the above-mentioned limit, a new method called optimized non-hyperbolic stack imaging based on interpretation model is presented in this paper. Based on CMP/CRP （Common-Reflection-Point） gather after NMO or pre-stack migration, this method uses the interpretation model of reflectors as constraint, and takes comparability as a distinguishing criterion, and finally forms a residual move-out correction for the gather of constrained model. Numerical simulation indicates that this method could overcome the non hyperbolic problem and get fine stack image.
基金the National Natural Science Foundation of China (Grant Nos .50479053 and10672034)the Programfor Changjiang Scholars and Innovative Research Teamin Universitythe foundation for doctoral degree education of the Education Ministry of China
文摘A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model＇ s performance on prediction of wave heights around breaking point for the wave motions in surf zone.
基金supported by the National Natural Science Foundation of China(Grant Nos.50479053and10672034)the Program for Changjiang Scholars and Innovative Research Teamin University,and thefoundationfordoctoral degree education of the Education Ministry of China
文摘New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is gready saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.
基金Supported by the National Natural Science Foundation of China(11131005)the Fundamental Research Funds for the Central Universities(2014201020202)
文摘In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.
基金Supported by National Basic Research Program of China （973 Program） （2009CB320601）, National Natural Science Foundation of China （60774048, 60821063）, the Program for Cheung Kong Scholars, and the Research Fund for the Doctoral Program of China Higher Education （20070145015）
文摘这份报纸学习样品数据的问题为有变化时间的延期的不明确的连续时间的模糊大规模系统的可靠 H 夸张控制。第一，模糊夸张模型( FHM )被用来为某些复杂大规模系统建立模型，然后根据 Lyapunov 指导方法和大规模系统的分散的控制理论，线性 matrixine 质量( LMI )基于条件 arederived toguarantee H 性能不仅当所有控制部件正在操作很好时，而且面对一些可能的致动器失败。而且，致动器的精确失败参数没被要求，并且要求仅仅是失败参数的更低、上面的界限。条件依赖于时间延期的上面的界限，并且不依赖于变化时间的延期的衍生物。因此，获得的结果是不太保守的。最后，二个例子被提供说明设计过程和它的有效性。
基金The Hubei Provincial Building Technology Project in 2021 (Project Number: 43)。
文摘Taking the hyperbolic glass curtain wall project of the Wuhan Jinyinhu Commercial Plaza as an example,the characteristics of different curved glass forming technologies were analyzed in this paper.Combined with the actual engineering situation,the curved steel process is selected to produce the hyperbolic glass curtain wall,and the application of BIM technology in the quality control of hyperbolic glass curtain wall in the production process was analyzed,and the effects of heating condition,bending time,cooling condition,and bending tempering error in the manufacturing accuracy of the curved glass curtain wall were studied,in hope that this project can provide practical reference for similar curtain wall design construction in the future.
文摘In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invariant points. Moreover, we can see that M?bius transformation is hyperbolic isometries that form a group action PSL (2, R) on the upper half plane model.
文摘In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.
