Готові списки джерел за темами / Transversal set of vector fields

Добірка наукової літератури з теми "Transversal set of vector fields"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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Статті в журналах з теми "Transversal set of vector fields"

ANDRADE, Plácido. "The set of vector fields with transverse foliations." Journal of the Mathematical Society of Japan 45, no. 1 (January 1993): 21–35. http://dx.doi.org/10.2969/jmsj/04510021.

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Ройтенберг, Владимир Шлеймович. "Planar vector fields with central symmetry: roughness and first degree of non-roughness." Вестник Адыгейского государственного университета, серия «Естественно-математические и технические науки», no. 2(281) (September 28, 2021): 27–40. http://dx.doi.org/10.53598/2410-3225-2021-2-281-27-40.

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Рассматривается пространство гладких векторных полей, заданных в замкнутой области D на плоскости, инвариантных относительно центральной симметрии и трансверсальных границе D. Описано множество векторных полей, грубых относительно этого пространства; показано, что оно открыто и всюду плотно. Во множестве всех негрубых векторных полей выделено открытое всюду плотное подмножество, состоящее из векторных полей первой степени негрубости. We consider the space of smooth vector fields defined in a closed domain D on the plane, invariant under the central symmetry and transversal to the boundary D. The set of vector fields that are rough with respect to this space is described; it is shown that it is open and everywhere dense. In the set of all non-rough vector fields, an open everywhere dense subset consisting of vector fields of the first degree of non-roughness is distinguished.

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DEGIOVANNI, L., and G. MAGNANO. "TRI–HAMILTONIAN VECTOR FIELDS, SPECTRAL CURVES AND SEPARATION COORDINATES." Reviews in Mathematical Physics 14, no. 10 (October 2002): 1115–63. http://dx.doi.org/10.1142/s0129055x0200151x.

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We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P0,P1,P2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P1-λP0) and (P2-μP0); (ii) a suitable set of vector fields, preserving P0 but transversal to its symplectic leaves. The framework is applied to Lax equations with spectral parameter, for which not only it establishes a theoretical link between the separation techniques of Sklyanin and of Magri, but also provides a more efficient "inverse" procedure to obtain separation variables, not involving the extraction of roots.

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Goodman, Sue. "Vector fields with transverse foliations, II." Ergodic Theory and Dynamical Systems 6, no. 2 (June 1986): 193–203. http://dx.doi.org/10.1017/s0143385700003400.

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AbstractWhen does a non-singular flow on a 3-manifold have a 2-dimensional foliation everywhere transverse to it? A complete answer is given for a large class of flows, those with 1-dimensional hyperbolic chain recurrent set. We find a simple necessary and sufficient condition on the linking of periodic orbits of the flow.

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Vavryčuk, Václav. "Calculation of the slowness vector from the ray vector in anisotropic media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2067 (January 10, 2006): 883–96. http://dx.doi.org/10.1098/rspa.2005.1605.

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The wave quantities needed in constructing wave fields propagating in anisotropic elastic media are usually calculated as a function of the slowness vector, or of its direction called the wave normal. In some applications, however, it is desirable to calculate the wave quantities as a function of the ray direction. In this paper, a method of calculating the slowness vector for a specified ray direction is proposed. The method is applicable to general anisotropy of arbitrary strength with arbitrary complex wave surface. The slowness vector is determined by numerically solving a system of multivariate polynomial equations of the sixth order. By solving the equations, we obtain a complete set of slowness vectors corresponding to all wave types and to all branches of the wave surface including the slowness vectors along the acoustic axes. The wave surface can be folded to any degree. The system of equations is further specified for rays shot in the symmetry plane of an orthorhombic medium and for a transversely isotropic medium. The system is decoupled into two polynomial equations of the fourth order for the P –SV waves, and into equations for the SH wave, which yield an explicit closed-form solution. The presented approach is particularly advantageous in constructing ray fields, ray-theoretical Green functions, wavefronts and wave fields in strong anisotropy.

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Ramachandra, L. S., and D. Roy. "A New Method for Nonlinear Two-Point Boundary Value Problems in Solid Mechanics." Journal of Applied Mechanics 68, no. 5 (May 17, 2001): 776–86. http://dx.doi.org/10.1115/1.1387444.

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A local and conditional linearization of vector fields, referred to as locally transversal linearization (LTL), is developed for accurately solving nonlinear and/or nonintegrable boundary value problems governed by ordinary differential equations. The locally linearized vector field is such that solution manifolds of the linearized equation transversally intersect those of the nonlinear BVP at a set of chosen points along the axis of the only independent variable. Within the framework of the LTL method, a BVP is treated as a constrained dynamical system, which in turn is posed as an initial value problem. (IVP) In the process, the LTL method replaces the discretized solution of a given system of nonlinear ODEs by that of a system of coupled nonlinear algebraic equations in terms of certain unknown solution parameters at these chosen points. A higher order version of the LTL method, with improved path sensitivity, is also considered wherein the dimension of the linearized equation needs to be increased. Finally, the procedure is used to determine post-buckling equilibrium paths of a geometrically nonlinear column with and without imperfections. Moreover, deflections of a tip-loaded nonlinear cantilever beam are also obtained. Comparisons with exact solutions, whenever available, and other approximate solutions demonstrate the remarkable accuracy of the proposed LTL method.

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Li, Yuanjin, Tao Chen, and Defu Liu. "Path Planning for Laser Cladding Robot on Artificial Joint Surface Based on Topology Reconstruction." Algorithms 13, no. 4 (April 15, 2020): 93. http://dx.doi.org/10.3390/a13040093.

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Artificial joint surface coating is a hot issue in the interdisciplinary fields of manufacturing, materials and biomedicine. Due to the complex surface characteristics of artificial joints, there are some problems with efficiency and precision in automatic cladding path planning for coating fabrication. In this study, a path planning method for a laser cladding robot for artificial joints surface was proposed. The key of this method was the topological reconstruction of the artificial joint surface. On the basis of the topological relation, a set of parallel planes were used to intersect the CAD model to generate a set of continuous, directed and equidistant surface transversals on the artificial joint surface. The arch height error method was used to extract robot interpolation points from surface transversal lines according to machining accuracy requirements. The coordinates and normal vectors of interpolation points were used to calculate the position and pose of the robot tool center point (TCP). To ensure that the laser beam was always perpendicular to the artificial joint surface, a novel laser cladding set-up with a robot was designed, of which the joint part clamped by a six-axis robot moved while the laser head was fixed on the workbench. The proposed methodology was validated with the planned path on the surface of an artificial acetabular cup using simulation and experimentation via an industrial NACHI robot. The results indicated that the path planning method based on topological reconstruction was feasible and more efficient than the traditional robot teaching method.

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Shi, Peng, Luping Du, Congcong Li, Anatoly V. Zayats, and Xiaocong Yuan. "Transverse spin dynamics in structured electromagnetic guided waves." Proceedings of the National Academy of Sciences 118, no. 6 (February 1, 2021): e2018816118. http://dx.doi.org/10.1073/pnas.2018816118.

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Spin–momentum locking, a manifestation of topological properties that governs the behavior of surface states, was studied intensively in condensed-matter physics and optics, resulting in the discovery of topological insulators and related effects and their photonic counterparts. In addition to spin, optical waves may have complex structure of vector fields associated with orbital angular momentum or nonuniform intensity variations. Here, we derive a set of spin–momentum equations which describes the relationship between the spin and orbital properties of arbitrary complex electromagnetic guided modes. The predicted photonic spin dynamics is experimentally verified with four kinds of nondiffracting surface structured waves. In contrast to the one-dimensional uniform spin of a guided plane wave, a two-dimensional chiral spin swirl is observed for structured guided modes. The proposed framework opens up opportunities for designing the spin structure and topological properties of electromagnetic waves with practical importance in spin optics, topological photonics, metrology and quantum technologies and may be used to extend the spin-dynamics concepts to fluid, acoustic, and gravitational waves.

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Lee, Manseob, and Seunghee Lee. "Robust chain transitive vector fields." Asian-European Journal of Mathematics 08, no. 02 (June 2015): 1550026. http://dx.doi.org/10.1142/s1793557115500266.

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Let M be a closed n(≥2)-dimensional smooth Riemannian manifold and let X be a vector field on M. In this paper, we show that the robust chain transitive set is hyperbolic if and only if there are a C1-neighborhood [Formula: see text] of X and a compact neighborhood U of the chain transitive set such that for any [Formula: see text], the index of the continuation on ΛY(U) = ⋂t∈ℝYt(U) of every critical point does not change.

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Ciaglia, F. M., F. Di Cosmo, A. Ibort, M. Laudato, and G. Marmo. "Dynamical Vector Fields on the Manifold of Quantum States." Open Systems & Information Dynamics 24, no. 03 (September 2017): 1740003. http://dx.doi.org/10.1142/s1230161217400030.

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In this paper we shall consider the stratified manifold of quantum states and the vector fields which act on it. In particular, we show that the infinitesimal generator of the GKLS evolution is composed of a generator of unitary transformations plus a gradient vector field along with a Kraus vector field transversal to the strata defined by the involutive distribution generated by the former ones.

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Більше джерел

Дисертації з теми "Transversal set of vector fields"

Моравецька, Катерина Вiталiївна. "Мiри на банахових многовидах з рiвномiрною структурою". Doctoral thesis, Київ, 2018. https://ela.kpi.ua/handle/123456789/26061.

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Дисертацiя присвячена диференцiйовним мiрам на банахових многовидах з рiвномiрною структурою. Запропоновано метод побудови асоцiйованих мiр на поверхнях скiнченної корозмiрностi, вкладених у банахiв многовид з рiвномiрною структурою. Введено поняття асоцiйованої диференцiальної форми поверхнi та строго трансверсального до поверхнi набору векторних полiв. Доведено теорему “про узгодженiсть”, згiдно з якою поверхнева мiра задається однозначно асоцiйованою диференцiальною формою поверхнi. Показано транзитивнiсть запропонованої конструкцiї. На прикладi мiри Лебега в скiнченновимiрному просторi Rn та мiри об’єму на рiмановому многовидi з рiвномiрною структурою обґрунтовано її адекватнiсть. Отримано узагальнення низки результатiв з теорiї диференцiйовних мiр на лiнiйних просторах на випадок банахових многовидiв з рiвномiрною структурою. Доведено критерiй слабкої диференцiйовностi мiри уздовж обмеженого векторного поля, що узагальнює вiдомий результат В. I. Богачова.

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Книги з теми "Transversal set of vector fields"

Wave Front Set Of Solutions To Sums Of Squares Of Vector Fields. American Mathematical Society, 2013.

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Boules, Adel N. Fundamentals of Mathematical Analysis. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198868781.001.0001.

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Fundamentals of Mathematical Analysis is a beginning graduate textbook on real and functional analysis, with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Instructors can choose material from this part as their students’ background warrants. Chapter 4 is the spine of the book and is essential for an effective reading of the rest of the book. It is an extensive study of metric spaces, including the core topics of completeness, compactness, and function spaces, with a good number of applications. The remaining chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. The entire book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology, real analysis, or functional analysis. The book is designed as an accessible classical introduction to the subject, aims to achieve excellent breadth and depth, and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.

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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.

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Частини книг з теми "Transversal set of vector fields"

Adilkhanov, A. N., A. V. Pavlov, and I. A. Taimanov. "Discrete Analog of the Jacobi Set for Vector Fields." In Computational Topology in Image Context, 1–11. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-10828-1_1.

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Luo, Albert C. J. "Transversal Singularity and Bouncing Flows." In Singularity and Dynamics on Discontinuous Vector Fields, 113–46. Elsevier, 2006. http://dx.doi.org/10.1016/s1574-6917(06)03005-4.

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Perrin, G., C. Soize, D. Duhamel, and C. Funfschilling. "Statistical inverse problems for non-Gaussian vector valued random fields with a set of experimental realizations." In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures, 2811–16. CRC Press, 2014. http://dx.doi.org/10.1201/b16387-407.

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Constant, Jean. "Digital Approaches to Visualization of Geometric Problems in Wooden Sangaku Tablets." In Biologically-Inspired Computing for the Arts, 240–53. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-0942-6.ch013.

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This chapter describes the digitalization process of 19th century scientific representations from the Japanese culture – a set of mathematical problems etched on wooden boards. The object of the demonstration is to apply computing techniques to the creation of artistic statements based on geometrical problems, highlight the dynamics of interaction between art and science, and examine how much both fields enrich the larger discourse and appreciation of Art. The following text describes the steps adopted in a visualization project. First, the data collection included selecting specific geometry problems from various Sangaku wooden tablets and converting them into digital information as a single black and white outline to define shapes, volumes, and textures. The vectorization of the underlying shapes transferred the exact mathematical information onto the virtual canvas. In the next step, the vector outlines were converted into bitmaps. Each individual plate was assigned a specific color scheme to enhance object size, positioning, and dynamic of the composition. At the last stage, vector-based sketches, colorizations, and the monochrome sketches were blended together to complete full color visualization. Finally, the step-by-step development of the creative process was recorded as a QuickTime movie, including an original soundtrack. Discussion refers to the dissemination of the project in art galleries and online, its potential instructional use, and it examines the audience responses.

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Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. "Empirical Potential-Energy Surfaces Fitting Using Feed forward Neural Networks." In Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.003.0012.

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When the system of interest becomes too complex to permit the use of ab initio methods to obtain the system potential-energy surfaces (PES), empirical potential surfaces are frequently employed to represent the force fields present in the system under investigation. In most cases, the functional forms present in these potentials are selected on the basis of chemical and physical intuitions. The parameters of the surface are frequently adjusted to fit a very small set of experimental data that comprise bond energies, equilibrium bond distances and angles, fundamental vibrational frequencies, and perhaps measured barrier heights to reactions of interest. Such potentials generally yield only qualitative or semiquantitative descriptions of the system dynamics. Several research groups have significantly improved the accuracy of the values of the experimental properties computed using empirical potential surfaces by fitting the chosen functional form for the potential to the force fields obtained from trajectories using ab initio Car-Parrinello molecular dynamics simulations. The fitting to the force fields is usually done using a least-squares fitting approach. This method has been employed by Izvekov et al. to obtain effective non-polarizable three-site force fields for liquid water. Carré et al. have employed such a procedure to obtain a new pair potential for silica. In their investigation, the vector of potential parameters was fitted using an iterative Levenberg-Marquardt algorithm. Tangney and Scandolo have also developed an interatomic force field for liquid SiO2 in which the parameters were fitted to the forces, stresses, and energies obtained from ab initio calculations. Ercolessi and Adams have used a quasi-Newtonian procedure to fit an empirical potential for aluminum to data obtained from first-principals computations. Empirical potentials can be improved by making the parameters parameterized functions of the coordinates defining the instantaneous positions of the atoms of the system. This approach has been successfully employed by numerous investigators The difficulty with this procedure is that the number of parameters that must be adjusted increases rapidly. Appropriate fitting of these parameters requires a much more extensive database. Finally, the actual fitting process can often be tedious, difficult, and time-consuming.

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Brooks, Christopher. "A Genetic Algorithm to Design Optimal Patch Configurations Using Raster Data Structures." In Spatial Evolutionary Modeling. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780195135688.003.0013.

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The design of optimal patch configurations is a generic problem relevant to many spatial planning exercises. Spatial pattern affects processes in the natural and manufacture of environment and should be incorporated as a criterion in planning. Currently, while geographic inormation systems (GISs) are adequate for data storage, analysis, and visualization they do not provide sophisticated spatial decision-making functions. With the help of GISs, pattern can be incorporated into spatial decision-making explicitly, using ad hoc procedures, or implicitly, through visualization of alternative plans. Other computer technologies like remote sensing and decision support systems facilitate decision-making by supplying timely data and techniques for solving multi-criteria evaluation problems. There are now a number of artificial intelligence techniques that can be coupled with GIS to address a variety of hard spatial problems. Genetic algorithms are particularly attractive for optimization problems because they are efficient and effective in complex search spaces. Landscape ecologists use the twin concepts of patch and matrix to describe the spatial structure of the environment (McGarigal & Marks, 1994). The matrix is the dominant landscape element and patches are distributed within it. Patches can be crisp objects with well-defined boundaries, such as administrative areas, or inferred objects with fuzzy boundaries, such as vegetation or habitat patches in natural environments. In the former case, patches can be adequately represented by polygons in a vector GIS. In the second case patches are inferred from a continuous spatial distribution of attribute values. The raster data model is the most common representation of continuous fields within a GIS and is preferred to vector models in environmental applications because it is a better representation of the continuous variation characteristic of natural phenomena. There is a need for decision support tools that use raster GISs when spatial criteria relate to natural phenomena. Patch design involves many complexities: in a raster GIS it is also a complex problem in spatial geometry. This chapter describes a genetic algorithm for designing patch configurations in raster GISs. The genetic algorithm is coupled with GIS and multicriteria evaluation functions to build an autonomous system that explicitly includes pattern as a criterion in the design of patch networks. Conceptually, the problem is to extract from an infinite set of possible spatial patterns a single pattern that is optimal by some criterion.

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Chen, Sheng, and Kenji Suzuki. "Computerized Detection of Lung Nodules on Chest Radiographs." In Machine Learning in Computer-Aided Diagnosis, 122–44. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-0059-1.ch006.

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Most lung nodules missed by radiologists as well as Computer-Aided Diagnostic (CADe) schemes overlap ribs or clavicles in Chest Radiographs (CXRs). This chapter introduces an image-processing technique for suppressing the contrast of ribs and clavicles in CXRs by means of anatomically specific Multiple Massive-Training Artificial Neural Networks (MTANNs). For bone suppression, an MTANN is trained by use of input CXRs and the corresponding “teaching” images. The authors employed bone images obtained by the use of a dual-energy subtraction technique as the teaching images. For the effective suppression of ribs, having various spatial frequencies, the authors developed a multi-resolution MTANN consisting of multi-resolution decomposition/composition techniques and three MTANNs for three different-resolution images. After training with input CXRs and the corresponding dual-energy bone images, the multi-resolution MTANN was able to provide “bone-image-like” images which were similar to the teaching bone images. By subtracting the “bone-image-like” images from the corresponding CXRs, the authors were able to produce “soft-tissue-image-like” images in which ribs and clavicles were substantially suppressed. A single set of multi-resolution MTANNs cannot suppress all bone structures in a CXR, because the orientation, width, contrast, and density of bones differ from location to location, and the capability of a single set of multi-resolution MTANNs is limited. To address this issue, the authors developed anatomically specific multiple MTANNs which consist of eight sets of multi-resolution MTANNs that were designed to process different segments in the lung fields in a CXR. Each set of anatomically specific MTANNs was trained with only the samples in the corresponding segment in the CXR. In order to make the contrast and density between the segments consistent, the authors applied a histogram matching technique to input images. To improve the performance of their CADe scheme, the authors incorporated their MTANN bone suppression into their CADe scheme for nodules in CXRs. In their CADe scheme, 64 morphologic and gray-level-based features were extracted from each nodule candidate in both the original and the “soft-tissue-image-like images,” and a nonlinear support vector classifier was employed for the classification of the candidates. The authors used a validation test database consisting of 118 CXRs with pulmonary nodules and a publicly available database containing 126 nodules. When their technique was applied to non-training CXRs, bones in the CXRs were suppressed substantially, while the visibility of nodules and lung vessels was maintained. With the use of “soft-tissue-image-like images,” the performance of the authors’ CADe scheme was improved from a sensitivity of 76% to 84% with 5 false positives per image. Thus, the authors’ image-processing technique for bone suppression by means of anatomically specific multiple MTANNs is useful for radiologists as well as for CAD schemes in the detection of lung nodules on CXRs.

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Тези доповідей конференцій з теми "Transversal set of vector fields"

Sakhnovskyj, M. Y., B. M. Tymochko, and Miroslav T. Strinadko. "Transversal and longitudinal field components and their role in formation of coherent vector fields." In SPIE Proceedings, edited by Oleg V. Angelsky. SPIE, 2004. http://dx.doi.org/10.1117/12.558817.

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Narmanov, Abdigappar Yakubovich. "On the geometry of the reachability set of vector fields." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Moscow: Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc23016.

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Chunhapongpipat, Krisorn, Ratinan Boonklurb, Sirod Sirisup, and Rajalida Lipikorn. "Initial contour independent level set image segmentation method using synergetic vector flow fields." In 2012 6th International Conference on Signal Processing and Communication Systems (ICSPCS 2012). IEEE, 2012. http://dx.doi.org/10.1109/icspcs.2012.6507987.

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Liu, Yachong, Ankang Hu, Fenglei Han, and Yu Lu. "Numerical Method Research on Nonlinear Roll System of Large Container Ship." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41493.

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When dealing with the ship-roll problem, the roll motion is mainly regarded as a single degree-of-freedom dynamical system, and the nonlinear properties are reflected in the nonlinear damping term and restoring moment term. Previous studies have shown that transverse chaotic phenomenon means the damage of ship-roll stability which will lead to ship capsizing, and for ultra large container ships, the wind area above water surface can not be neglected, which turns the ship-roll system into asymmetric dynamical system. The concept of safe basin is usually used to express the boundedness of motion. It is defined as the set of bounded solution to dynamical system, and the erosion phenomenon of safe basin is normally explained as the global instability. This concept was firstly brought out by Thompson [1] when he studied the problem of ship capsizing and then was applied to different fields of engineering. Based on this background, the following three tasks are completed in this paper. a) For the calculation of chaos threshold, two numerical methods, namely, Pade approximation and Gauss-Legendre integration are adopted, analyzed and compared. b) One 9200TEU container ship is selected and the chaos threshold is calculated by virtue of Gauss-Legendre method. As numerical verification, the gradually erosion phenomenon of ship’s safe basin is observed and phase trajectories of points located in broken domain are traced; c) When encountered with crosswind (When winds are not parallel to or directly against the line of travel, the wind is said to have a crosswind component; that is, the force can be separated into two vector components, a crosswind component and a headwind or tailwind component.), the symmetry of ship-roll system begin to break. In the last part of this paper, the effect of crosswind on safe basin, asymmetry, and stability are studied.

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GARCÍA, I. A., and D. S. SHAFER. "LIMIT SETS OF PLANAR VECTOR FIELDS AND THE VANISHING SET OF INVERSE INTEGRATING FACTORS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0051.

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ÖZDEĞER, ABDÜLKADIR. "A FUNCTION OF DIRECTION IN A WEYL SUBSPACE ASSOCIATED WITH A SET OF ORTHOGONAL VECTOR FIELDS." In Proceedings of the 6th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704191_0017.

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Arena, Andrea, Giovanni Formica, Walter Lacarbonara, and Harry Dankowicz. "Nonlinear Finite Element-Based Path Following of Periodic Solutions." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48673.

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A computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) u˙ = f(u,s,t;c) where u(s,t) is the vector collecting all state variables including the velocities/time rates, s is a space coordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f. This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and coworkers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f. A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures.

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Hummel, Tobias, Frederik Berger, Michael Hertweck, Bruno Schuermans, and Thomas Sattelmayer. "High-Frequency Thermoacoustic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors: Part Two — Modeling and Analysis." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57500.

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This paper deals with high-frequency thermoacoustic instabilities in swirl-stabilized gas turbine combustors. Driving mechanisms associated with periodic flame displacement and flame shape deformations are theoretically discussed, and corresponding flame transfer functions are derived from first principles. These linear feedback models are then evaluated by means of a lab-scale swirl-stabilized combustor in combination with part one of this joint publication. For this purpose, the models are used to thermoacoustically characterize a complete set of operation points of a this combustor facility. Specifically, growth rates of the first transversal modes are computed, and compared against experimentally obtained pressure amplitudes as an indicator for thermoacoustic stability. The characterization is based on a hybrid analysis approach relying on a frequency domain formulation of acoustic conservation equations, in which non-uniform temperature fields and distributed thermoacoustic source terms / flame transfer functions can be straightforwardly considered. The relative contribution of flame displacement and deformation driving mechanisms — i.e. their significance with respect to the total driving — is identified. Furthermore, promoting/ inhibiting conditions for the occurrence of high frequency, transversal acoustic instabilities within swirl-stabilized gas turbine combustors are revealed.

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Lowe, Robert L., Joseph G. Beckett, Christopher G. Cooley, Zongwu Bai, and Paul E. Kladitis. "Soft Piezoelectric Composites: Synthesis, Electro-Elastic Property Characterization, and Non-Linear Constitutive Modeling." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-71197.

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Abstract Soft piezoelectric composites (SPCs) show great promise as next-generation energy harvesting materials, with the potential to outperform piezoelectric polymers with limited elastic stretchability (e.g., PVDF) and traditional brittle piezoelectric ceramics (e.g., PZT). Presently, however, SPCs remain an emerging class of materials, with relatively few comprehensive investigations holistically exploring their synthesis, electro-mechanical property characterization, large-strain constitutive modeling, and non-linear mechanics and dynamics. In this paper, we take first steps toward addressing this compelling research opportunity. A three-component SPC is synthesized, consisting of an ultra-stretchable Ecoflex silicone rubber matrix, micron-sized PMN-PT piezoelectric particles, and CNTs that serve as inter-particle conductive “bridges.” Mechanical, electrical, and coupled electro-mechanical properties are quantified. A thermodynamically consistent, fully non-linear, finite-strain constitutive model is presented, based on a gentle adaptation of an existing transversely isotropic non-linear electro-elastic constitutive framework. Use of the particle orientation vector as an independent variable leads to two-way coupling between mechanics and electricity not present in the isotropic counterpart of this constitutive model. A prototype free energy function with the electric field as the independent variable is proposed that captures the essential physics. This free energy leads to a compact set of non-linear, finite-strain constitutive equations whose mathematical forms have direct analogue to the linear, small-strain theory of piezoelectricity.

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Lee, Chae J., Bernard D. Reger, Matthew C. Tresch, J. Edward Colgate, and Ferdinando A. Mussa-Ivaldi. "Emulation of Biological Motor Primitives in an Artificial System: The Generation of Static Force Fields." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0122.

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Abstract We have used observations of posture and movements in biological limbs to derive a controller for an artificial mechanism. The controller architecture emulates some of the known relations between spinal cord circuitry and the musculoskeletal system of vertebrates and, specifically, of the rat. This work relates to recent experiments suggesting that the neural circuitry of the spinal cord may be partitioned into a small set of functional modules. Activation of these modules, each connected to a set of limb muscles, resulted in force fields that have been measured at the endpoint of a limb. These force fields map each position of the foot into a corresponding static force vector. The force fields have been found to converge toward equilibrium positions located inside the leg’s workspace. The experimental observation that vector fields induced by multiple stimulations add vectorially, suggested that convergent force fields form a system of building blocks (or “primitives”) for the generation of stable postures and movements. To emulate this biological mechanism in the control of an artificial two-joint limb, we established relationships among three hierarchical levels — spinal modules, muscles, and actuators — by deriving the mappings among the respective output fields. These mappings are used in combination with an inverse model of the actuators to calculate the actuator commands that generate a desired force field. We tested the ability of this control system to reproduce the force fields generated by the leg muscles of the rat and a set of force fields with significant geometrical features. Our results show that we can successfully and reliably transfer to our artificial system the features of muscle force fields. In addition, we exploited the same principle of vector summation observed in the biological system to combine these muscle fields into a variety of force field patterns, including the gradients of Gaussian potentials and locally parallel fields. We consider this a first step in the generation of a biomorphic motor control system. This work is supported by ONR grant N00014-95-1-0571 and NIH grant MH48185.

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