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Relevant bibliographies by topics / Differential equations, Nonlinear Fluid dynamics

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Academic literature on the topic 'Differential equations, Nonlinear Fluid dynamics'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Differential equations, Nonlinear Fluid dynamics"

1

Ramshaw, John D. "Nonlinear ordinary differential equations in fluid dynamics." American Journal of Physics 79, no. 12 (2011): 1255–60. http://dx.doi.org/10.1119/1.3636635.

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Oke, Abayomi S., Winifred N. Mutuku, Mark Kimathi, and Isaac L. Animasaun. "Insight into the dynamics of non-Newtonian Casson fluid over a rotating non-uniform surface subject to Coriolis force." Nonlinear Engineering 9, no. 1 (2020): 398–411. http://dx.doi.org/10.1515/nleng-2020-0025.

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AbstractCasson fluid model is the most accurate mathematical expression for investigating the dynamics of fluids with non-zero plastic dynamic viscosity like that of blood. Despite huge number of published articles on the transport phenomenon, there is no report on the increasing effects of the Coriolis force. This report presents the significance of increasing not only the Coriolis force and reducing plastic dynamic viscosity, but also the Prandtl number and buoyancy forces on the motion of non-Newtonian Casson fluid over the rotating non-uniform surface. The relevant body forces are derived and incorporated into the Navier-Stokes equations to obtain appropriate equations for the flow of Newtonian Casson fluid under the action of Coriolis force. The governing equations are non-dimensionalized using Blasius similarity variables to reduce the nonlinear partial differential equations to nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations is solved using the Runge-Kutta-Gills method with the Shooting technique, and the results depicted graphically. An increase in Coriolis force and non-Newtonian parameter decreases the velocity profile in the x-direction, causes a dual effect on the shear stress, increases the temperature profiles, and increases the velocity profile in the z-direction.

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Holmes, Philip. "Nonlinear Dynamics, Chaos, and Mechanics." Applied Mechanics Reviews 43, no. 5S (1990): S23—S39. http://dx.doi.org/10.1115/1.3120814.

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Nonlinear Dynamics or “Chaos Theory” is an ill-defined but energetic and rapidly developing subject which cuts across the boundaries of traditional disciplines. In this review, I describe a small part of it: some of the analytical approaches to nonlinear differential equations which have been developed in the last ten to fifteen years. I illustrate them with applications in solid and fluid mechanics.

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El-Nabulsi, Rami Ahmad. "Modified plasma–fluid equations from nonstandard Lagrangians with applications to nuclear fusion." Canadian Journal of Physics 93, no. 1 (2015): 55–67. http://dx.doi.org/10.1139/cjp-2014-0233.

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Nonstandard Lagrangian dynamics have gained great interest recently, in particular within the theory of nonlinear differential equations and dissipative dynamical systems. In this paper, we address their implications in plasma–fluid dynamics. The mathematical settings are constructed starting from the modified Vlasov–Boltzmann transport equation, which is derived from modified Euler–Lagrange equations of motion. Far from giving a self-consistent nonstandard Lagrangian theory of plasma–fluid dynamics, in this paper we have just introduced the basic settings and discussed some illustrative examples that such a modified theory should have in plasma–fluid theory and nuclear fusion.

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Doering, Charles R., Evelyn M. Lunasin, and Anna Mazzucato. "Introduction to Special Issue: Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics." Physica D: Nonlinear Phenomena 376-377 (August 2018): 1–4. http://dx.doi.org/10.1016/j.physd.2018.06.001.

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Polyanin, Andrei D., and Alexei I. Zhurov. "Parametrically defined nonlinear differential equations and their solutions: Applications in fluid dynamics." Applied Mathematics Letters 55 (May 2016): 72–80. http://dx.doi.org/10.1016/j.aml.2015.12.002.

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Shiralashetti, S. C., M. H. Kantli, and A. B. Deshi. "Haar wavelet based numerical solution of nonlinear differential equations arising in fluid dynamics." International Journal of Computational Materials Science and Engineering 05, no. 02 (2016): 1650010. http://dx.doi.org/10.1142/s204768411650010x.

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In this paper, we obtained the Haar wavelet-based numerical solution of the nonlinear differential equations arising in fluid dynamics, i.e., electrohydrodynamic flow, elastohydrodynamic lubrication and nonlinear boundary value problems. Error analysis is observed, it shows that the Haar wavelet-based results give better accuracy than the existing methods, which is justified through illustrative examples.

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Chang, Tai Ping. "Stochastic Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes." Applied Mechanics and Materials 284-287 (January 2013): 362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.362.

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This paper investigates the stochastic dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton’s principle. The Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to the position to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin’s method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed. It is concluded that the mean value and standard deviation of the amplitude of the displacement increase nonlinearly with the increase of the frequencies.

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Becker, E., W. J. Hiller, and T. A. Kowalewski. "Nonlinear dynamics of viscous droplets." Journal of Fluid Mechanics 258 (January 10, 1994): 191–216. http://dx.doi.org/10.1017/s0022112094003290.

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Nonlinear viscous droplet oscillations are analysed by solving the Navier-Stokes equation for an incompressible fluid. The method is based on mode expansions with modified solutions of the corresponding linear problem. A system of ordinary differential equations, including all nonlinear and viscous terms, is obtained by an extended application of the variational principle of Gauss to the underlying hydrodynamic equations. Results presented are in a very good agreement with experimental data up to oscillation amplitudes of 80% of the unperturbed droplet radius. Large-amplitude oscillations are also in a good agreement with the predictions of Lundgren & Mansour (boundary integral method) and Basaran (Galerkin-finite element method). The results show that viscosity has a large effect on mode coupling phenomena and that, in contradiction to the linear approach, the resonant mode interactions remain for asymptotically diminishing amplitudes of the fundamental mode.

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Liu, Jin-Peng, Herman Øie Kolden, Hari K. Krovi, Nuno F. Loureiro, Konstantina Trivisa, and Andrew M. Childs. "Efficient quantum algorithm for dissipative nonlinear differential equations." Proceedings of the National Academy of Sciences 118, no. 35 (2021): e2026805118. http://dx.doi.org/10.1073/pnas.2026805118.

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Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum mechanics has limited analogous progress for the nonlinear case. Despite this obstacle, we develop a quantum algorithm for dissipative quadratic n-dimensional ordinary differential equations. Assuming R<1, where R is a parameter characterizing the ratio of the nonlinearity and forcing to the linear dissipation, this algorithm has complexity T2q poly(log⁡T,log⁡n,log⁡1/ϵ)/ϵ, where T is the evolution time, ϵ is the allowed error, and q measures decay of the solution. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in T. While exponential decay precludes efficiency, driven equations can avoid this issue despite the presence of dissipation. Our algorithm uses the method of Carleman linearization, for which we give a convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for R≥2. Finally, we discuss potential applications, showing that the R<1 condition can be satisfied in realistic epidemiological models and giving numerical evidence that the method may describe a model of fluid dynamics even for larger values of R.

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Dissertations / Theses on the topic "Differential equations, Nonlinear Fluid dynamics"

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Kim, Tae Eun. "Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532.

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Handel, Andreas. "Limits of Localized Control in Extended Nonlinear Systems." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5025.

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We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under which circumstances a given number of controllers can successfully stabilize a given system.

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Paddick, Matthew. "Stabilité de couches limites et d'ondes solitaires en mécanique des fluides." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S049/document.

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La présente thèse traite de deux questions de stabilité en mécanique des fluides. Les deux premiers résultats de la thèse sont consacrés au problème de la limite non-visqueuse pour les équations de Navier-Stokes. Il s'agit de déterminer si une famille de solutions de Navier-Stokes dans un demi-espace avec une condition de Navier au bord converge vers une solution du modèle non visqueux, l'équation d'Euler, lorsque les paramètres de viscosité tendent vers zéro. Dans un premier temps, on considère le modèle incompressible 2D. Nous obtenons la convergence dans L2 des solutions faibles de Navier-Stokes vers une solution forte d'Euler, et une instabilité dans L∞ en temps très court pour certaines données initiales qui sont des solutions stationnaires de l'équation d'Euler. Ces résultats ne sont pas contradictoires, et on construit un exemple de donnée initiale permettant de voir se réaliser les deux phénomènes simultanément dans le cadre périodique. Dans un second temps, on s'intéresse au modèle compressible isentropique (température constante) en 3D. On démontre l'existence de solutions dans des espaces de Sobolev conormaux sur un temps qui ne dépend pas de la viscosité lorsque celle-ci devient très petite, et on obtient la convergence forte de ces solutions vers une solution de l'équation d'Euler sur ce temps uniforme par des arguments de compacité. Le troisième résultat de cette thèse traite d'un problème de stabilité d'ondes solitaires. Précisément, on considère un fluide isentropique et non visqueux avec capillarité interne, régi par le modèle d'Euler-Korteweg, et on montre l'instabilité transverse non-linéaire de solitons, c'est-à-dire que des perturbations 2D initialement petites d'une solution sous forme d'onde progressive 1D peuvent s'éloigner de manière importante de celle-ci<br>This thesis deals with a couple of stability problems in fluid mechanics. In the first two parts, we work on the inviscid limit problem for Navier-Stokes equations. We look to show whether or not a sequence of solutions to Navier-Stokes in a half-space with a Navier slip condition on the boundary converges towards a solution of the inviscid model, the Euler equation, when the viscosity parameters vanish. First, we consider the 2D incompressible model. We obtain convergence in L2 of weak solutions of Navier-Stokes towards a strong solution of Euler, as well as the instability in L∞ in a very short time of some initial data chosen as stationary solutions to the Euler equation. These results are not contradictory, and we construct initial data that allows both phenomena to occur simultaneously in the periodic setting. Second, we look at the 3D isentropic (constant temperature) compressible equations. We show that solutions exist in conormal Sobolev spaces for a time that does not depend on the viscosity when this is small, and we get strong convergence towards a solution of the Euler equation on this uniform time of existence by compactness arguments. In the third part of the thesis, we work on a solitary wave stability problem. To be precise, we consider an isentropic, compressible, inviscid fluid with internal capillarity, governed by the Euler-Korteweg equations, and we show the transverse nonlinear instability of solitons, that is that initially small 2D perturbations of a 1D travelling wave solution can end up far from it

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Kasnakoglu, Cosku. "Reduced order modeling, nonlinear analysis and control methods for flow control problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1195629380.

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Sweet, Erik. "ANALYTICAL AND NUMERICAL SOLUTIONS OF DIFFERENTIALEQUATIONS ARISING IN FLUID FLOW AND HEAT TRANSFER PROBLEMS." Doctoral diss., University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2585.

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The solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the thesis) are provided. In the chapters that follow, we apply HAM to a variety of problems to highlight its use and versatility in solving a range of nonlinear problems arising in fluid flow. In chapter 2, a viscous fluid flow problem is considered to illustrate the application of HAM. In chapter 3, we explore the solution of a non-Newtonian fluid flow and provide a proof for the existence of solutions. In addition, chapter 3 sheds light on the versatility and the ease of the application of the Homotopy Analysis Method, and its capability in handling non-linearity (of rational powers). In chapter 4, we apply HAM to the case in which the fluid is flowing along stretching surfaces by taking into the effects of "slip" and suction or injection at the surface. In chapter 5 we apply HAM to a Magneto-hydrodynamic fluid (MHD) flow in two dimensions. Here we allow for the fluid to flow between two plates which are allowed to move together or apart. Also, by considering the effects of suction or injection at the surface, we investigate the effects of changes in the fluid density on the velocity field. Furthermore, the effect of the magnetic field is considered. Chapter 6 deals with MHD fluid flow over a sphere. This problem gave us the first opportunity to apply HAM to a coupled system of nonlinear differential equations. In chapter 7, we study the fluid flow between two infinite stretching disks. Here we solve a fourth order nonlinear ordinary differential equation. In chapter 8, we apply HAM to a nonlinear system of coupled partial differential equations known as the Drinfeld Sokolov equations and bring out the effects of the physical parameters on the traveling wave solutions. Finally, in chapter 9, we present prospects for future work.<br>Ph.D.<br>Department of Mathematics<br>Sciences<br>Mathematics PhD

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Philipowski, Robert. "Stochastic interacting particle systems and nonlinear partial differential equations from fluid mechanics." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=986005622.

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Manna, Utpal. "Harmonic and stochastic analysis aspects of the fluid dynamics equations." Laramie, Wyo. : University of Wyoming, 2007. http://proquest.umi.com/pqdweb?did=1414120661&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.

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Lam, Chun-kit, and 林晉傑. "The dynamics of wave propagation in an inhomogeneous medium: the complex Ginzburg-Landau model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40887881.

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Lam, Chun-kit. "The dynamics of wave propagation in an inhomogeneous medium the complex Ginzburg-Landau model /." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40887881.

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Books on the topic "Differential equations, Nonlinear Fluid dynamics"

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The energy method, stability, and nonlinear convection. 2nd ed. Springer, 2004.

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The energy method, stability, and nonlinear convection. Springer-Verlag, 1992.

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M, Hedberg Claes, ed. Theory of nonlinear acoustics in fluids. Kluwer Academic Publishers, 2002.

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Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1990.

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Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1990.

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AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on the Connection between Infinite and Finite Dimensional Dynamical Systems (1987 University of Colorado). The connection between infinite dimensional and finite dimensional dynamical systems: Proceedings of the AMS-IMS-SIAM joint summer research conference held July 19-25, 1987, with support from the National Science Foundation and the Air Force Office of Scientific Research. Edited by Nicolaenko Basil 1943-, Foiaş Ciprian, Temam Roger, American Mathematical Society, Institute of Mathematical Statistics, and Society for Industrial and Applied Mathematics. American Mathematical Society, 1989.

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Joachim, Peinke, Talamelli Alessandro, Castillo Luciano, Hölling Michael, and SpringerLink (Online service), eds. Progress in Turbulence and Wind Energy IV: Proceedings of the iTi Conference in Turbulence 2010. Springer Berlin Heidelberg, 2012.

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S, Johnson R., ed. Solitons: An introduction. Cambridge University Press, 1989.

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1962-, Wang Shouhong, ed. Bifurcation theory and applications. World Scientific, 2005.

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Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman, and B. Prinari. Nonlinear wave equations: Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. American Mathematical Society, 2015.

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Book chapters on the topic "Differential equations, Nonlinear Fluid dynamics"

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Caffarelli, Luis A., and Alexis Vasseur. "The De Giorgi Method for Nonlocal Fluid Dynamics." In Nonlinear Partial Differential Equations. Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0191-1_1.

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Frehse, Jens, and Josef Málek. "Problems Due to the No-Slip Boundary in Incompressible Fluid Dynamics." In Geometric Analysis and Nonlinear Partial Differential Equations. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55627-2_29.

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Stone, H. A. "Partial Differential Equations in Thin Film Flows in Fluid Dynamics and Rivulets." In Nonlinear PDE’s in Condensed Matter and Reactive Flows. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0307-0_12.

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Puu, Tönu. "Differential Equations." In Nonlinear Economic Dynamics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60775-2_2.

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Shivamoggi, Bhimsen K. "Nonlinear Differential Equations." In Fluid Mechanics and Its Applications. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-2442-5_2.

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Shivamoggi, Bhimsen K. "Nonlinear Ordinary Differential Equations." In Fluid Mechanics and Its Applications. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-7094-2_1.

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Sell, George R., and Yuncheng You. "Nonlinear Partial Differential Equations." In Dynamics of Evolutionary Equations. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-5037-9_5.

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Anderson, J. D. "Discretization of Partial Differential Equations." In Computational Fluid Dynamics. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-11350-9_5.

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Anderson, J. D. "Discretization of Partial Differential Equations." In Computational Fluid Dynamics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85056-4_5.

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Durran, Dale R. "Ordinary Differential Equations." In Numerical Methods for Fluid Dynamics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6412-0_2.

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Conference papers on the topic "Differential equations, Nonlinear Fluid dynamics"

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Peng, Liqian, and Kamran Mohseni. "Nonlinear Dimensionality Reduction for Parameterized Partial Differential Equation." In 43rd AIAA Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2967.

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Veroy, Karen, Christophe Prud'homme, Dimitrios Rovas, and Anthony Patera. "A Posteriori Error Bounds for Reduced-Basis Approximation of Parametrized Noncoercive and Nonlinear Elliptic Partial Differential Equations." In 16th AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-3847.

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Rand, Richard H., Erika T. Wirkus, and J. Robert Cooke. "Nonlinear Dynamics of the Bombardier Beetle." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8011.

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Abstract This work investigates the dynamics by which the bombardier beetle releases a pulsed jet of fluid as a defense mechanism. A mathematical model is proposed which takes the form of a pair of piece wise continuous differential equations with dependent variables as fluid pressure and quantity of reactant. The model is shown to exhibit an effective equilibrium point (EEP). Conditions for the existence, classification and stability of an EEP are derived and these are applied to the model of the bombardier beetle.

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Ghayesh, Mergen H., and Michael P. Pai¨doussis. "Dynamics of a Fluid-Conveying Cantilevered Pipe With Intermediate Spring Support." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30084.

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The aim of this study is to investigate the three-dimensional (3-D) nonlinear dynamics of a fluid-conveying cantilevered pipe, additionally supported by an array of four springs attached at a point along its length. In the theoretical analysis, the 3-D equations are discretized via Galerkin’s technique, yielding a set of coupled nonlinear differential equations. These equations are solved numerically using a finite difference technique along with the Newton-Raphson method. The dynamic behaviour of the system is presented in the form of bifurcation diagrams, along with phase-plane plots, time-histories, PSD plots, and Poincare´ maps for two different spring locations and inter-spring configurations. Interesting dynamical phenomena, such as planar or circular flutter, divergence, quasiperiodic and chaotic motions, have been observed with increasing flow velocity. Experiments were conducted for the cases studied theoretically, and good qualitative and quantitative agreement was observed.

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Semler, C., and M. P. Païdoussis. "Parametric Resonances of a Cantilevered Pipe Conveying Fluid: A Nonlinear Analysis." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0272.

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Abstract This paper deals with the nonlinear dynamics and the stability of cantilevered pipes conveying fluid, where the fluid has a harmonic component of flow velocity, assumed to be small, superposed on a constant mean value. The mean flow velocity is near the critical value for which the pipe becomes unstable by flutter through a Hopf bifurcation. The partial differential equation is transformed into a set of ordinary differential equations (ODEs) using the Galerkin method. The equations of motion contain nonlinear inertial terms, and hence cannot be put into standard form for numerical integration. Various approaches are adopted to tackle the problem: (a) a perturbation method via which the nonlinear inertial terms are removed by finding an equivalent term using the linear equation; the system is then put into first-order form and integrated using a Runge-Kutta scheme; (b) a finite difference method based on Houbolt’s scheme, which leads to a set of nonlinear algebraic equations that is solved with a Newton-Raphson approach; (c) the stability boundaries are obtained using an incremental harmonic balance method as proposed by S.L. Lau. Using the three methods, the dynamics of the pipe conveying fluid is investigated in detail. For example, the effects of (i) the forcing frequency, (ii) the perturbation amplitude, and (iii) the flow velocity are considered. Particular attention is paid to the effects of the nonlinear terms. These results are compared with experiments undertaken in our laboratory, utilizing elastomer pipes conveying water. The pulsating component of the flow is generated by a plunger pump, and the motions are monitored by a noncontacting optical follower system. It is shown, both numerically and experimentally, that periodic and quasiperiodic oscillations can exist, depending on the parameters.

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Kheiri, M., M. P. Pai¨doussis, and M. Amabili. "On the Feasibility of Using Linear Fluid Dynamics in an Overall Nonlinear Model for the Dynamics of Cantilevered Cylinders in Axial Flow." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30082.

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A curiosity-driven study is presented here which introduces and tests an analytical model to be employed for describing the dynamics of cantilevered cylinders in axial flow. This model is called “hybrid” because it encompasses linear fluid dynamics and nonlinear structural dynamics. Also, both the linear and fully nonlinear models are recalled here. For all these models Galerkin’s method is used to discretize the nondimensional equation of motion. For the hybrid and nonlinear models a numerical method based on Houbolt’s Finite Difference Method (FDM) is used to solve the discretized equations, as well as AUTO, which is a software used to solve continuation and bifurcation problems for differential equations. The capability of the hybrid model to predict the dynamical behaviour of cantilevered cylinders in axial flow is assessed by examining three different sets of parameters. Here, the main focus is put on the onset of instabilities and the amplitude of the predicted motion. According to the results given in the form of bifurcation diagrams and several tabulated numerical values, the hybrid model is proved to be unacceptable although it can predict the onset of first instability, and even the onset of post-divergence instability in some cases.

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Yao, Ming-Hui, Wei Zhang, and Dong-Xing Cao. "Multi-Pulse Chaotic Dynamics of the Cantilevered Pipe Conveying Pulsating Fluid." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87699.

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The multi-pulse orbits and chaotic dynamics of the cantilevered pipe conveying pulsating fluid with harmonic external force are studied in detail. The nonlinear geometric deformation of the pipe and the Kelvin constitutive relation of the pipe material are considered. The nonlinear governing equations of motion for the cantilevered pipe conveying pulsating fluid are determined by using Hamilton principle. The four-dimensional averaged equation under the case of principle parameter resonance, 1/2 subharmonic resonance and 1:2 internal resonance and primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the cantilevered pipe. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the cantilevered pipe conveying pulsating fluid. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the cantilevered pipe are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the pulsating fluid conveying cantilevered pipe.

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Alioli, Mattia, Marco Morandini, and Pierangelo Masarati. "Coupled Multibody-Fluid Dynamics Simulation of Flapping Wings." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12198.

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This paper deals with the coupled structural and fluid-dynamics analysis of flexible flapping wings using multibody dynamics. A general-purpose multidisciplinary multibody solver is coupled with a computational fluid dynamics code by means of a general-purpose, meshless boundary interfacing approach based on Moving Least Squares with Radial Basis Functions. The general-purpose, free software multibody solver MBDyn is used. A nonlinear 4-node shell element has been used for the structural model. The fluid dynamics code is based on a stabilized finite element approximation of the unsteady Navier-Stokes equations. The method (often referred to in the literature as G2 method) has been implemented within the programming environment provided by the free software project FEniCS, a collection of libraries specifically designed for the automated and efficient solution of differential equations. FEniCS provides extensive scripting capabilities, with a domain-specific language for the specification of variational formulations of Partial Differential Equations that is embedded within the programming language Python. This approach makes it possible to easily and quickly build complex simulation codes that are, at the same time, extremely efficient and easily adapted to run in parallel. The coupling of the multibody and Navier-Stokes codes is strictly enforced at each time step. The fluid dynamics discretization is automatically refined to keep the error on the overall lift and drag coefficients below a user-defined tolerance. The method is first tested by computing the drag force of a non-oscillating NACA 0012 airfoil traveling in air. Subsequently, the drag and lift forces on a rigid and flexible oscillating NACA 0012 wing are compared with experimental data. Encouraging results obtained from the modeling and analysis of the dynamics and aeroelasticity of flexible oscillating wing models confirm the ability of the structural and fluid dynamics models to capture the physics of the problem.

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Yamashita, Kiyotaka, Masatsugu Yoshizawa, Jun Agata, and Arata Motoki. "Nonlinear Dynamics of a Pipe Conveying Pulsatile Flow: Effect of an Asymmetric Spring Supported End." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48600.

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Flow-induced vibration of a fluid conveying pipe with a spring supported end is examined theoretically and experimentally under the condition that the fluid velocity has a small pulsatile component. The parametric resonance of the lateral pipe vibration is occurred due to the pulsating flow. In this paper, the four first-order ordinary differential equations, which govern the amplitudes and phases of the nonplanar pipe vibration, are derived from the nonlinear nonself-adjoint integro partial differential equations by the method of the Liapnov-Schmidt reduction. The effect of the asymmetric spring support on the nonlinear stability of the lateral pipe vibration is discussed with the obtained equations of amplitudes and phases. Furthermore, the experiments were conducted with the silicon rubber pipe conveying water. The lateral deflections of the pipe were measured by the image processing system, which was based on the images from two CCD cameras. The typical features of the parametric resonance were confirmed qualitatively.

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Assadi, Armand D., and James H. Oliver. "Real-Time Particle Simulation for Virtual Environments." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dfm-4422.

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Abstract A real-time interactive environment for particle simulation is presented with specific attention given to fluid flow from a fountain system. The complex Navier-Stokes equations from fluid dynamics theory give way to simple dynamic equations of motion for systems of independent particles from particle theory. Due to the ease of integration of the dynamic linear first order differential equations, compared to the nonlinear second order partial differential equations of Navier-Stokes, a real-time rate was achieved for a visually aesthetic model of fluid flow. The primary contribution is that interactive changes made by the user are perceived to occur simultaneously in the environment. There is no need to resolve a predetermined set of equations when making the changes.

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Reports on the topic "Differential equations, Nonlinear Fluid dynamics"

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Knightly, George H. An Analytical Study of Some Problems in Partial Differential Equations With Applications to Fluid Dynamics and Wave Propagation. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada260351.

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