检索结果-内蒙古大学图书馆

Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems?

CHAOS SOLITONS & FRACTALS 2022年 161卷

作者： Timsina, Archana Neupane James, J. D. Mireles Florida Atlantic Univ Dept Math Sci Boca Raton FL 33431 USA

We develop a multiple shooting parameterization method for studying stable/unstable manifolds attached to periodic orbits of systems whose dynamics is determined by an implicit rule. We represent the local invariant manifold using high order polynomials and show that the method leads to efficient numerical calculations. We implement the method for several example systems in dimension two and three. The resulting manifolds provide useful information about the orbit structure of the implicit system even in the case that the implicit relation is neither invertible nor single-valued.

关键词： Implicitly defined dynamical systems Computational methods Invariant manifolds Periodic orbits parameterization method

来源：评论

学校读者我要写书评

暂无评论

Study of the ejection/collision orbits in the spatial RTBP using the McGehee regularization

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2022年 111卷 1页

作者： Olle, M. Rodriguez, O. Soler, J. Univ Politecn Cataluna Dept Matemat Av Diagonal 647 Barcelona 08028 Spain Univ Politecn Cataluna IMTech Pau Gargallo 14 Barcelona 08028 Spain CRM Campus Bellaterra Edifici C Bellaterra 08193 Spain Univ Politecn Cataluna Dept Engn Civil & Ambiental Campus NordEdifici C2 Barcelona 08034 Spain

In this paper we analyse the McGehee regularization of the collision in the spatial Restricted three-body problem (3D RTBP). As a particular application, we study the ejection (collision) orbits. The parameterization method is applied up to high order to obtain suitable initial conditions of ejection (collision) orbits. Moreover, assuming ejection orbits, different methods are discussed to detect which of them are also collision orbits. Finally we explore the so called ejection-collision (EC) orbits, that is, orbits where the particle ejects from one primary, reaches a maximum in the distance with respect to the same primary, and ends at collision with that primary. Some results concerning the existence of spatial EC orbits are described. (C) 2022 The Author(s). Published by Elsevier B.V.

关键词： McGehee's regularization parameterization method Ejection-collision orbits

来源：评论

学校读者我要写书评

暂无评论

Optimal Design of Three-Dimensional Circular-to-Rectangular Transition Nozzle Based on Data Dimensionality Reduction

引用

ENERGIES 2022年第24期15卷 9316页

作者： Yang, Haoqi Yang, Qingzhen Mu, Zhongqiang Du, Xubo Chen, Lingling Northwestern Polytech Univ Sch Power & Energy Xian 710129 Peoples R China CARDC Sci & Technol Scramjet Lab Mianyang 621000 Peoples R China

The parametric representation and aerodynamic shape optimization of a three-dimensional circular-to-rectangular transition nozzle designed and built using control lines distributed along the circumferential direction were investigated in this study. A surrogate model based on class/shape transformation, principal component analysis and radial basis neural network was proposed with fewer design parameters for parametric representation and performance parameter prediction of the three-dimensional circular-to-rectangular transition nozzle. The surrogate model was combined with Non-dominated Sorting Genetic Algorithm-II to optimize the aerodynamic shape of the nozzle. The results showed that the surrogate model effectively achieved the parametric representation and aerodynamic shape optimization of the three-dimensional circular-to-rectangular transition nozzle. The geometric dimensions and performance parameters of the parametric reconstructed model were comparable to that of the initial model, implying that they can meet the needs of optimal design. The axial thrust coefficient and lift of the optimized nozzle were increased by approximately 0.742% and 15.707%, respectively.

关键词： asymmetric expansion nozzle parameterization method principal component analysis aerodynamic shape optimization surrogate model

来源：评论

学校读者我要写书评

暂无评论

Aerodynamic Optimization of Winglet-Cavity Tip in an Axial High Pressure Turbine Stage

引用

INTERNATIONAL JOURNAL OF TURBO & JET-ENGINES 2020年第4期37卷 399-411页

作者： Zhou, Zhihua Chen, Shaowen Wang, Songtao Harbin Inst Technol Sch Energy Sci & Engn 92 West Da Zhi St Harbin 150001 Heilongjiang Peoples R China

A new geometry parametric method of winglet-cavity tip has been introduced in the optimization procedure based on three-dimensional steady CFD numerical calculation and analysis. Firstly, the reliability of numerical method and grid independency are studied. Then an aerodynamic optimization is performed in an unshrouded axial high pressure turbine with winglet-cavity tip. The optimum winglet-cavity tip has higher turbine stage efficiency and smaller tip leakage mass flow rate than the cavity tip and flat tip. Compared with the results of cavity tip, the effects of the optimum winglet-cavity tip indicate that the stage efficiency is improved effectively by 0.41% with less reduction of tip leakage mass flow rate. The variation of turbine stage efficiency with tip gap states that the optimum winglet-cavity tip obtains the smallest efficiency change rate Delta eta/(Delta tau/H). For the optimum winglet-cavity tip, the endwall flow and blade tip leakage flow pattern are used to analysis the physical mechanical of losses. In addition, the effects of pressure-side winglet and suction-side winglet are analyzed respectively by the deformation of the optimum winglet-cavity tip. The numerical results show that the pressure-side winglet reduces the tip leakage flow effectively, and the suction-side winglet shows a great improvement on the turbine stage efficiency.

关键词： aerodynamic optimization winglet-cavity tip parameterization method aerodynamic performance high pressure turbine

来源：评论

学校读者我要写书评

暂无评论

Global dynamics in nonconservative nonlinear Schrodinger equations

引用

ADVANCES IN MATHEMATICS 2022年 398卷 108234-108234页

作者： Jaquette, Jonathan Lessard, Jean-Philippe Takayasu, Akitoshi Boston Univ Dept Math & Stat Boston MA 02215 USA McGill Univ Dept Math & Stat Montreal PQ H3A 0B9 Canada Univ Tsukuba Fac Engn Informat & Syst Tsukuba Ibaraki 3058573 Japan

In this paper, we study the global dynamics of a class of nonlinear Schrodinger equations using perturbative and nonperturbative methods. We prove the semi-global existence of solutions for initial conditions close to constant. That is, solutions will exist for all positive time or all negative time. The existence of an open set of initial data which limits to zero in both forward and backward time is also demonstrated. This result in turn forces the non-existence of any real-analytic conserved quantities. For the quadratic case, we prove the existence of two (infinite) families of nontrivial unstable equilibria and prove the existence of heteroclinic orbits limiting to the nontrivial equilibria in backward time and to zero in forward time. By a time reversal argument, we also obtain heteroclinic orbits limiting to the nontrivial equilibria in forward time and to zero in backward time. The proofs for the quadratic equation are computer-assisted and rely on three separate ingredients: an enclosure of a local unstable manifold at the equilibria, a rigorous integration of the flow (starting from the unstable manifold) and a proof that the solution enters a validated stable set (hence showing convergence to zero).(c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Nonlinear Schrodinger equations Nonconservative equation Semi-global existence parameterization method Stable and unstable sets Homoclinic and heteroclinic orbits

来源：评论

学校读者我要写书评

暂无评论

Resonant tori, transport barriers, and chaos in a vector field with a Neimark?Sacker bifurcation ?

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2020年 85卷 105226-105226页

作者： Fleurantin, Emmanuel James, J. D. Mireles Florida Atlantic Univ Dept Math 777 Glades Rd Boca Raton FL 33431 USA

We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark–Sacker bifurcation giving rise to an attracting invariant torus. Our main goals are to (A) follow the torus via parameter continuation from its appearance to its disappearance, studying its dynamics between these events, and to (B) study the embeddings of the stable/unstable manifolds of the hyperbolic equilibrium solutions over this parameter range, focusing on their role as transport barriers and their participation in global bifurcations. Taken together the results highlight the main features of the global dynamics of the system.

关键词： Invariant tori Neimark–Sacker bifurcation parameterization method

来源：评论

学校读者我要写书评

暂无评论

A new method to compute periodic orbits in general symplectic maps

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2021年 99卷 105838-105838页

作者： Calleja, R. del-Castillo-Negrete, D. Martinez-del-Rio, D. Olvera, A. Univ Nacl Autonoma Mexico IIMAS Mexico City 04510 DF Mexico Oak Ridge Natl Lab Oak Ridge TN 37831 USA Univ Warwick Math Inst Coventry W Midlands England

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton-Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. The method is also applied to verify the renormalization prediction of the residues' convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Periodic orbits Symplectic maps parameterization method Reversible maps

来源：评论

学校读者我要写书评

暂无评论

High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2021年 97卷 105691-105691页

作者： Kumar, Bhanu Anderson, Rodney L. de la Llave, Rafael Georgia Inst Technol Sch Math 686 Cherry St Atlanta GA 30332 USA CALTECH Jet Prop Lab 4800 Oak Grove Dr Pasadena CA 91109 USA

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approximations of the manifolds. Since such approximations are not accurate except very close to the base invari-ant object, this requires large amounts of numerical integration to globalize the manifolds and locate intersections. In this paper, we study hyperbolic resonant periodic orbits in the planar circular restricted 3-body problem, and transfer trajectories between them, by: 1) determining where to search for resonant periodic orbits;2) developing and implementing a parameterization method for accurate computation of their invariant manifolds as Tay-lor series;and 3) developing a procedure to compute intersections of the computed sta-ble and unstable manifolds. We develop and implement algorithms that accomplish these three goals, and demonstrate their application to the problem of transferring between res-onances in the Jupiter-Europa system. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Manifolds parameterization method Resonance Three-body problem Melnikov

来源：评论

学校读者我要写书评

暂无评论

Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: Formalism, implementation and rigorous validation

引用

INDAGATIONES MATHEMATICAE-NEW SERIES 2019年第1期30卷 39-80页

作者： Reinhardt, Christian James, J. D. Mireles Vrije Univ Amsterdam Dept Math Amsterdam Netherlands Florida Atlantic Univ Dept Math Sci Boca Raton FL 33431 USA

We study polynomial expansions of local unstable manifolds attached to equilibrium solutions of parabolic partial differential equations. Due to the smoothing properties of parabolic equations, these manifolds are finite dimensional. Our approach is based on an infinitesimal invariance equation and recovers the dynamics on the manifold in addition to its embedding. The invariance equation is solved, to any desired order in space and time, using a Newton scheme on the space of formal Fourier-Taylor series. Under mild non-resonance conditions we show that the formal series converge in some small enough neighborhood of the equilibrium. An a-posteriori computer assisted argument is given which, when successful, provides mathematically rigorous convergence proofs in explicit and much larger neighborhoods. We give example computations and applications. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

关键词： Parabolic partial differential equations parameterization method Unstable manifold Computer-assisted proof Connecting orbit

来源：评论

学校读者我要写书评

暂无评论

High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem 70

High-order resonant orbit manifold expansions for mission de...

引用

70th International Astronautical Congress, IAC 2019

作者： Kumar, Bhanu Anderson, Rodney L. de la Llave, Rafael School of Mathematics Georgia Institute of Technology 686 Cherry St AtlantaGA30332 United States Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Dr PasadenaCA91109 United States

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approximations of the manifolds. Since such approximations are not accurate except very close to the base invariant object, this requires large amounts of numerical integration to globalize the manifolds and locate intersections. In this paper, we study hyperbolic resonant periodic orbits in the planar circular restricted 3-body problem, and transfer trajectories between them, by: 1) determining where to search for resonant periodic orbits;2) developing and implementing a parameterization method for accurate computation of their invariant manifolds as Taylor series;and 3) developing a procedure to compute intersections of the computed stable and unstable manifolds. We develop and implement algorithms that accomplish these three goals, and demonstrate their application to the problem of transferring between resonances in the Jupiter-Europa system. Copyright © 2019 by the International Astronautical Federation (IAF). All rights reserved.

关键词： Manifolds Melnikov parameterization method Resonance Three-Body Problem

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：