The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application,...The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.展开更多
This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these ...This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.展开更多
In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in thec...In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in theconventional methods, and significantly save computing time as well.展开更多
The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with t...The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved.展开更多
In this paper,we consider symbolic(hybrid trigonometric)parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials,with the restricti...In this paper,we consider symbolic(hybrid trigonometric)parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials,with the restriction that variables in each block of functions are different.We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension.In addition,we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one,and vice versa.We illustrate by some examples the applicability of having these different types of parametrizations,namely,hybrid trigonometric and unirational.展开更多
This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant.As a consequence,we get a new pro...This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant.As a consequence,we get a new proof of the degree formula relating the degree of the surface,the degree of the parametrization,the base point multiplicity and the degree of the rational map induced by the parametrization.In addition,we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related.As an application of these results,we explore how the degree of a surface reparametrization is affected by the presence of base points.展开更多
The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which...The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.展开更多
In isogeometric analysis(IGA),parametrization is an important and difficultissue that greatly influences the numerical accuracy and efficiency of the numericalsolution.One of the problems facing the parametrization in...In isogeometric analysis(IGA),parametrization is an important and difficultissue that greatly influences the numerical accuracy and efficiency of the numericalsolution.One of the problems facing the parametrization in IGA is the existence ofthe singular points in the parametrization domain.To avoid producing singular points,boundary-mapping parametrization is given by mapping the computational domainto a polygon domain which may not be a square domain and mapping each segmentof the boundary in computational domain to a corresponding boundary edge of thepolygon.Two numerical examples in finite element analysis are presented to show thenovel parametrization is efficient.展开更多
We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equa...We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equations belongs to this class, and if it does, we reparametrize it such that the new parametric equations are proper.展开更多
We consider a class of planar self-affine tiles T = M-1 a∈D(T + a) generated by an expanding integral matrix M and a collinear digit set D as follows:M =(0-B 1-A),D = {(00),...,(|B|0-1)}.We give a parametrization S1 ...We consider a class of planar self-affine tiles T = M-1 a∈D(T + a) generated by an expanding integral matrix M and a collinear digit set D as follows:M =(0-B 1-A),D = {(00),...,(|B|0-1)}.We give a parametrization S1 →T of the boundary of T with the following standard properties.It is H¨older continuous and associated with a sequence of simple closed polygonal approximations whose vertices lie on T and have algebraic preimages.We derive a new proof that T is homeomorphic to a disk if and only if 2|A| |B + 2|.展开更多
In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for su...In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.展开更多
We develop an empirical formula to parameterize the 3-dimension （3D） distribution of electromagnetic showers in the Alpha Magnetic Spectrometer Ⅱ electromagnetic calorimeter（ECAL）. The formula was verified by ECA...We develop an empirical formula to parameterize the 3-dimension （3D） distribution of electromagnetic showers in the Alpha Magnetic Spectrometer Ⅱ electromagnetic calorimeter（ECAL）. The formula was verified by ECAL test beam data in 2002 and found to perform well. The distribution of electron showers in the ECAL are well described by the formula, which has parameters that allow one to determine the 3D shape of electromagnetic showers in the ECAL. We use this formula to correct for lateral energy leakage and dead channels in the ECAL; good results are obtained.展开更多
In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orth...In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.展开更多
The Casas-Ibarra parametrization is a description of the Dirac neutrino mass matrix MD in terms of the neutrino mixing matrix V , an orthogonal matrix O and the diagonal mass matrices of light and heavy Majorana neutr...The Casas-Ibarra parametrization is a description of the Dirac neutrino mass matrix MD in terms of the neutrino mixing matrix V , an orthogonal matrix O and the diagonal mass matrices of light and heavy Majorana neutrinos in the type-I seesaw mechanism. Because MDMD is apparently independent of V but dependent on O in this parametrization, a number of authors have claimed that unflavored leptogenesis has nothing to do with CP violation at low energies. Here we question this logic by clarifying the physical meaning of O. We establish a clear relationship between O and the observable quantities, and find that O does depend on V . We show that both unflavored leptogenesis and flavored leptogenesis have no direct connection with low-energy CP violation.展开更多
In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decen...In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decentralized control systems is developed. What is more, the parametrization of all normal decentralized properly stabilizing controllers is characterized and interpreted on the basis of the decentralized Bezout identity presented here. In fact, the work done in this paper is an extension of which was derived for normal decentralized control systems in the references by Date (1991) and Date and Chow (1994).展开更多
The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new me...The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new method using one-loop scalar integrals with propagators of higher power.More explicitly,with the improved version of the method,we can cancel the dimension shift and terms with unwanted power shifting.Thus,the obtained integrating-by-parts relations are significantly simpler and can be solved easily.Using this method,we present explicit examples of a bubble,triangle,box,and pentagon with one doubled propagator.With these results,we complete our previous computations in[3]with the missing tadpole coefficients and show the potential of Chen’s method for efficient reduction in higher loop integrals.展开更多
We conduct an investigation to explore late-time cosmic acceleration through various dark energy parametrizations(Wettrich,Efstathiou,and Ma-Zhang)within the Horava-Lifshitz gravity framework.As an alternative to gene...We conduct an investigation to explore late-time cosmic acceleration through various dark energy parametrizations(Wettrich,Efstathiou,and Ma-Zhang)within the Horava-Lifshitz gravity framework.As an alternative to general relativity,this theory introduces anisotropic scaling at ultraviolet scales.Our primary objective is to constrain the key cosmic parameters and baryon acoustic oscillation(BAO)scale,specifically the sound horizon(rd),by utilizing 24 uncorrelated measurements of BAOs derived from recent galaxy surveys spanning a redshift range from z=0.106 to z=2.33.Additionally,we integrate the most recent Hubble constant measurement by Riess in 2022(denoted as R22)as an extra prior.For the parametrizations of Wettrich,Efstathiou,and Ma-Zhang,our analysis of BAO data yields sound horizon results of r_(d)=148.1560±2.7688 Mpc,r_(d)=148.6168±10.2469 Mpc,and r_(d)=147.9737±10.6096 Mpc,respectively.Incorporating the R22 prior into the BAO dataset results in r_(d)=139.5806±3.8522 Mpc,r_(d)=139.728025±2.7858 Mpc,and r_(d)=139.6001±2.7441 Mpc.These outcomes highlight a distinct inconsistency between early and late observational measurements,analogous to the H_(0) tension.A notable observation is that,when we do not include the R22 prior,the outcomes for rd tend to be in agreement with Planck and SDSS results.Following this,we conducted a cosmography test and comparative study of each parametrization within the Lambda Cold Dark Matter paradigm.Our diagnostic analyses demonstrate that all models fit seamlessly within the phantom region.All dark energy parametrizations predict an equation of state parameter close ω=-1,indicating a behavior similar to that of a cosmological constant.The statistical analysis indicates that neither of the two models can be ruled out based on the latest observational measurements.展开更多
This study explores the nonlinear resonance of a rotating solar sail membrane exposed to time-varying solar thermal and solar radiation pressure.The sail membrane is modeled using a cantilever membrane,applying the vo...This study explores the nonlinear resonance of a rotating solar sail membrane exposed to time-varying solar thermal and solar radiation pressure.The sail membrane is modeled using a cantilever membrane,applying the von Kármán theory for membrane large deflection.The membrane’s nonlinear equation is derived by employing the Lagrange equation while accounting for excitations from solar thermal and radiation pressure.The equation is solved via the Rayleigh-Ritz method.The bifurcation diagram of membrane motion is applied to reveal membrane resonance responses under different solar sail rotating frequencies.The displacement time history,phase portrait,Poincarémap,frequency spectrum,and the largest Lyapunov exponent are used to study nonlinear vibrations that occur near resonance regions.The results indicate that time-varying thermal loading excites membrane motions with multiple natural frequencies by the parametric resonance mechanics,leading to the onset of membrane chaotic motion.The membrane’s primary resonance is stimulated in harmonic oscillation by the time-varying radiation pressure.The divergence instability caused by thermal excitation is also illustrated by comparing the membrane’s vibration amplitude with and without thermal excitation.The membrane’s nonlinear vibration characteristics vary significantly with solar illumination angles,the membrane’s thermal expansion coefficients,and structural damping.展开更多
Unmanned aircraft are highly vulnerable to crosswind-induced turbulence during complex maneuvers such as turning,which can significantly compromise control and reduce autopilot effectiveness.This paper presents a nove...Unmanned aircraft are highly vulnerable to crosswind-induced turbulence during complex maneuvers such as turning,which can significantly compromise control and reduce autopilot effectiveness.This paper presents a novel control strategy to improve the controllability of unmanned aircraft in challenging wind conditions.First,the equations of motion for the aircraft are reformulated as a system of stochastic differential equations,which are subsequently transformed into a deterministic form.By modeling turbulence as a Gaussian random process and incorporating it directly into the control system,the proposed method proactively compensates for the adverse effects of turbulence.The transformation is achieved using semi-invariant techniques.Second,the control problem is formulated as an optimization task,aiming to minimize the deviation between the actual and desired turn characteristics,specifically the angular velocity.Finally,a new numerical method with proven global convergence is employed to compute the optimal autopilot parameters.Simulation results using a medium-range unmanned aircraft model under continuous turbulent gusts demonstrate that the proposed method significantly outperforms existing approaches,ensuring both stability and precision in turbulent wind conditions.展开更多
Automation and intelligence have become the primary trends in the design of investment casting processes.However,the design of gating and riser systems still lacks precise quantitative evaluation criteria.Numerical si...Automation and intelligence have become the primary trends in the design of investment casting processes.However,the design of gating and riser systems still lacks precise quantitative evaluation criteria.Numerical simulation plays a significant role in quantitatively evaluating current processes and making targeted improvements,but its limitations lie in the inability to dynamically reflect the formation outcomes of castings under varying process conditions,making real-time adjustments to gating and riser designs challenging.In this study,an automated design model for gating and riser systems based on integrated parametric 3D modeling-simulation framework is proposed,which enhances the flexibility and usability of evaluating the casting process by simulation.Firstly,geometric feature extraction technology is employed to obtain the geometric information of the target casting.Based on this information,an automated design framework for gating and riser systems is established,incorporating multiple structural parameters for real-time process control.Subsequently,the simulation results for various structural parameters are analyzed,and the influence of these parameters on casting formation is thoroughly investigated.Finally,the optimal design scheme is generated and validated through experimental verification.Simulation analysis and experimental results show that using a larger gate neck(24 mm in side length) and external risers promotes a more uniform temperature distribution and a more stable flow state,effectively eliminating shrinkage cavities and enhancing process yield by 15%.展开更多
基金Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)
文摘The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.
文摘This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.
基金Supported by National Natural Science Foundation of China under Grant No.10374093the National Program for Basic Research of MOST of Chinathe Knowledge Innovation Project of Chinese Academy of Sciences
文摘In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in theconventional methods, and significantly save computing time as well.
文摘The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved.
基金the CRUE-CSIC agreement with Springer Nature.the project ID2019-105621GB-I00 of Ministerio de Ciencia e Innovación.+1 种基金the GrantPID2020-113192GB-100(Math-ematical Visualization:Foundations,Algorithms and Applications)from the Spanish MICINN.A.Lastra is member of the Research Group ASYNACS(Ref.CT-CE2019/683).
文摘In this paper,we consider symbolic(hybrid trigonometric)parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials,with the restriction that variables in each block of functions are different.We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension.In addition,we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one,and vice versa.We illustrate by some examples the applicability of having these different types of parametrizations,namely,hybrid trigonometric and unirational.
基金partially supported by FEDER/Ministerio de Ciencia,Innovación y Universidades-Agencia Estatal de Investigación/MTM2017-88796-P(Symbolic Computation:new challenges in Algebra and Geometry together with its applications)。
文摘This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant.As a consequence,we get a new proof of the degree formula relating the degree of the surface,the degree of the parametrization,the base point multiplicity and the degree of the rational map induced by the parametrization.In addition,we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related.As an application of these results,we explore how the degree of a surface reparametrization is affected by the presence of base points.
基金supported by Beijing Nova Program under Grant No.Z121104002512065The author PerezDíaz S is a member of the Research Group ASYNACS(Ref.CCEE2011/R34)
文摘The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.
基金973 Program 2011CB302400the National Natural Sci-ence Foundation of China(Nos.11371341 and 11426236)the 111 Project(No.b07033).
文摘In isogeometric analysis(IGA),parametrization is an important and difficultissue that greatly influences the numerical accuracy and efficiency of the numericalsolution.One of the problems facing the parametrization in IGA is the existence ofthe singular points in the parametrization domain.To avoid producing singular points,boundary-mapping parametrization is given by mapping the computational domainto a polygon domain which may not be a square domain and mapping each segmentof the boundary in computational domain to a corresponding boundary edge of thepolygon.Two numerical examples in finite element analysis are presented to show thenovel parametrization is efficient.
基金This paper is partially supported by National Key Research Program of People's Republic of China under Grant No. 2004CB318000.
文摘We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equations belongs to this class, and if it does, we reparametrize it such that the new parametric equations are proper.
基金supported by Japanese Ministry of Education,Culture,Sports,Science and Technology,Grantin Aid for Fundamental Research (Grant No.21540010)the Japanese Society for the Promotion of Science (Grant No.08F08714)
文摘We consider a class of planar self-affine tiles T = M-1 a∈D(T + a) generated by an expanding integral matrix M and a collinear digit set D as follows:M =(0-B 1-A),D = {(00),...,(|B|0-1)}.We give a parametrization S1 →T of the boundary of T with the following standard properties.It is H¨older continuous and associated with a sequence of simple closed polygonal approximations whose vertices lie on T and have algebraic preimages.We derive a new proof that T is homeomorphic to a disk if and only if 2|A| |B + 2|.
基金This research is supported by the National Key Basic Research Project of China under Grant No. 2011CB302400 and the National Natural Science Foundation of China under Grant No. 10901163.
文摘In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.
基金Supported by NSFS(10099630),International S&T Collaboration Key Program,Ministry of Science and Technology of China
文摘We develop an empirical formula to parameterize the 3-dimension （3D） distribution of electromagnetic showers in the Alpha Magnetic Spectrometer Ⅱ electromagnetic calorimeter（ECAL）. The formula was verified by ECAL test beam data in 2002 and found to perform well. The distribution of electron showers in the ECAL are well described by the formula, which has parameters that allow one to determine the 3D shape of electromagnetic showers in the ECAL. We use this formula to correct for lateral energy leakage and dead channels in the ECAL; good results are obtained.
文摘In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.
基金Supported by National Natural Science Foundation of China (10425522, 10875131)
文摘The Casas-Ibarra parametrization is a description of the Dirac neutrino mass matrix MD in terms of the neutrino mixing matrix V , an orthogonal matrix O and the diagonal mass matrices of light and heavy Majorana neutrinos in the type-I seesaw mechanism. Because MDMD is apparently independent of V but dependent on O in this parametrization, a number of authors have claimed that unflavored leptogenesis has nothing to do with CP violation at low energies. Here we question this logic by clarifying the physical meaning of O. We establish a clear relationship between O and the observable quantities, and find that O does depend on V . We show that both unflavored leptogenesis and flavored leptogenesis have no direct connection with low-energy CP violation.
基金This work was supported by National Natural Science Foundation of China!( 69874 0 2 7) Hong Kong Research Grant Council! 71
文摘In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decentralized control systems is developed. What is more, the parametrization of all normal decentralized properly stabilizing controllers is characterized and interpreted on the basis of the decentralized Bezout identity presented here. In fact, the work done in this paper is an extension of which was derived for normal decentralized control systems in the references by Date (1991) and Date and Chow (1994).
基金Supported by the National Natural Science Foundation of China(11935013)。
文摘The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new method using one-loop scalar integrals with propagators of higher power.More explicitly,with the improved version of the method,we can cancel the dimension shift and terms with unwanted power shifting.Thus,the obtained integrating-by-parts relations are significantly simpler and can be solved easily.Using this method,we present explicit examples of a bubble,triangle,box,and pentagon with one doubled propagator.With these results,we complete our previous computations in[3]with the missing tadpole coefficients and show the potential of Chen’s method for efficient reduction in higher loop integrals.
文摘We conduct an investigation to explore late-time cosmic acceleration through various dark energy parametrizations(Wettrich,Efstathiou,and Ma-Zhang)within the Horava-Lifshitz gravity framework.As an alternative to general relativity,this theory introduces anisotropic scaling at ultraviolet scales.Our primary objective is to constrain the key cosmic parameters and baryon acoustic oscillation(BAO)scale,specifically the sound horizon(rd),by utilizing 24 uncorrelated measurements of BAOs derived from recent galaxy surveys spanning a redshift range from z=0.106 to z=2.33.Additionally,we integrate the most recent Hubble constant measurement by Riess in 2022(denoted as R22)as an extra prior.For the parametrizations of Wettrich,Efstathiou,and Ma-Zhang,our analysis of BAO data yields sound horizon results of r_(d)=148.1560±2.7688 Mpc,r_(d)=148.6168±10.2469 Mpc,and r_(d)=147.9737±10.6096 Mpc,respectively.Incorporating the R22 prior into the BAO dataset results in r_(d)=139.5806±3.8522 Mpc,r_(d)=139.728025±2.7858 Mpc,and r_(d)=139.6001±2.7441 Mpc.These outcomes highlight a distinct inconsistency between early and late observational measurements,analogous to the H_(0) tension.A notable observation is that,when we do not include the R22 prior,the outcomes for rd tend to be in agreement with Planck and SDSS results.Following this,we conducted a cosmography test and comparative study of each parametrization within the Lambda Cold Dark Matter paradigm.Our diagnostic analyses demonstrate that all models fit seamlessly within the phantom region.All dark energy parametrizations predict an equation of state parameter close ω=-1,indicating a behavior similar to that of a cosmological constant.The statistical analysis indicates that neither of the two models can be ruled out based on the latest observational measurements.
基金supported by the Science Fund of NPU-Duke China Seeds Program(Grant No.119003067)the CAST-BISEE Fund(Grant No.MC010175)+1 种基金the Project of National Natural Science Foundation of China(Grant No.12372233)the“111”project of China(Grant No.B17037).
文摘This study explores the nonlinear resonance of a rotating solar sail membrane exposed to time-varying solar thermal and solar radiation pressure.The sail membrane is modeled using a cantilever membrane,applying the von Kármán theory for membrane large deflection.The membrane’s nonlinear equation is derived by employing the Lagrange equation while accounting for excitations from solar thermal and radiation pressure.The equation is solved via the Rayleigh-Ritz method.The bifurcation diagram of membrane motion is applied to reveal membrane resonance responses under different solar sail rotating frequencies.The displacement time history,phase portrait,Poincarémap,frequency spectrum,and the largest Lyapunov exponent are used to study nonlinear vibrations that occur near resonance regions.The results indicate that time-varying thermal loading excites membrane motions with multiple natural frequencies by the parametric resonance mechanics,leading to the onset of membrane chaotic motion.The membrane’s primary resonance is stimulated in harmonic oscillation by the time-varying radiation pressure.The divergence instability caused by thermal excitation is also illustrated by comparing the membrane’s vibration amplitude with and without thermal excitation.The membrane’s nonlinear vibration characteristics vary significantly with solar illumination angles,the membrane’s thermal expansion coefficients,and structural damping.
基金co-supported by the Fund of Robot Technology Used for Special Environment Key Laboratory of Sichuan Province(No.22kftk01)the Key Research and Development Program of Heilongjiang,China(No.2024ZXJ07B05)the National Natural Science Foundation of China(No.92471103)。
文摘Unmanned aircraft are highly vulnerable to crosswind-induced turbulence during complex maneuvers such as turning,which can significantly compromise control and reduce autopilot effectiveness.This paper presents a novel control strategy to improve the controllability of unmanned aircraft in challenging wind conditions.First,the equations of motion for the aircraft are reformulated as a system of stochastic differential equations,which are subsequently transformed into a deterministic form.By modeling turbulence as a Gaussian random process and incorporating it directly into the control system,the proposed method proactively compensates for the adverse effects of turbulence.The transformation is achieved using semi-invariant techniques.Second,the control problem is formulated as an optimization task,aiming to minimize the deviation between the actual and desired turn characteristics,specifically the angular velocity.Finally,a new numerical method with proven global convergence is employed to compute the optimal autopilot parameters.Simulation results using a medium-range unmanned aircraft model under continuous turbulent gusts demonstrate that the proposed method significantly outperforms existing approaches,ensuring both stability and precision in turbulent wind conditions.
基金financially supported by the National Key Research and Development Program of China (2022YFB3706802)。
文摘Automation and intelligence have become the primary trends in the design of investment casting processes.However,the design of gating and riser systems still lacks precise quantitative evaluation criteria.Numerical simulation plays a significant role in quantitatively evaluating current processes and making targeted improvements,but its limitations lie in the inability to dynamically reflect the formation outcomes of castings under varying process conditions,making real-time adjustments to gating and riser designs challenging.In this study,an automated design model for gating and riser systems based on integrated parametric 3D modeling-simulation framework is proposed,which enhances the flexibility and usability of evaluating the casting process by simulation.Firstly,geometric feature extraction technology is employed to obtain the geometric information of the target casting.Based on this information,an automated design framework for gating and riser systems is established,incorporating multiple structural parameters for real-time process control.Subsequently,the simulation results for various structural parameters are analyzed,and the influence of these parameters on casting formation is thoroughly investigated.Finally,the optimal design scheme is generated and validated through experimental verification.Simulation analysis and experimental results show that using a larger gate neck(24 mm in side length) and external risers promotes a more uniform temperature distribution and a more stable flow state,effectively eliminating shrinkage cavities and enhancing process yield by 15%.
