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

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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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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2

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

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3

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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4

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 examp

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5

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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6

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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7

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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8

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 equa

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9

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

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10

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

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11

Farajpour, Ali, Hamed Farokhi, and Mergen H. Ghayesh. "A nonlinear viscoelastic model for NSGT nanotubes conveying fluid incorporating slip boundary conditions." Journal of Vibration and Control 25, no. 12 (2019): 1883–94. http://dx.doi.org/10.1177/1077546319839882.

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A nonlinear viscoelastic model is developed for the dynamics of nanotubes conveying fluid. The influences of strain gradients and stress nonlocality are incorporated via a nonlocal strain gradient theory (NSGT). Since at nanoscales, the assumptions of no-slip boundary conditions are not valid, the Beskok–Karniadakis theory is used to overcome this problem. The coupled nonlinear differential equations are derived via performing an energy/work balance. The derived equations along the transverse and axial axes are simultaneously solved to obtain the nonlinear frequency response. For this purpose,

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12

Chang, Tai Ping. "Small Scale Effect on Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes with Uncertainty." Applied Mechanics and Materials 479-480 (December 2013): 121–25. http://dx.doi.org/10.4028/www.scientific.net/amm.479-480.121.

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This paper investigates the statistical 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. Besides, the small scale effects of the nonlinear vibration of the DWCNTs are studied by using the theory of nonlocal elasticity. 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 to actually describe the random ma

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13

Zhou, Sha, Tian-Jun Yu, Xiao-Dong Yang, and Wei Zhang. "Global Dynamics of Pipes Conveying Pulsating Fluid in the Supercritical Regime." International Journal of Applied Mechanics 09, no. 02 (2017): 1750029. http://dx.doi.org/10.1142/s1758825117500296.

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Global dynamics of supercritical pipes conveying pulsating fluid considering superharmonic resonance of the second mode with 1:2 internal resonance are investigated. The governing partial differential equations in the supercritical regime are obtained based on the nontrivial equilibrium configuration of the pipes conveying fluid and then transformed into a discretized nonlinear gyroscopic system via assumed modes and Galerkin’s method. The method of multiple scales and canonical transformation are applied to reduce the equations of motion to the near-integrable Hamiltonian standard form. The e

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14

Hou, Yu, and Guo Hua Zeng. "Research on Nonlinear Dynamic Characteristics of Fluid-Conveying Pipes System." Advanced Materials Research 228-229 (April 2011): 574–79. http://dx.doi.org/10.4028/www.scientific.net/amr.228-229.574.

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Lateral vibration equations of fluid-conveying pipes system are high order partial differential equations, and the analytic solution is difficult to obtain, so in this paper the numerical solution is obtained by the finite element method. Firstly, the finite element equations of lateral vibration of fluid-conveying pipes were set up, and four kinds of boundary constraints were proposed. The modal analysis of vibration system was carried out by using mode decomposition method, and the system responses were solved by using Newmark method. The impact of pipe span, flow rate, fluid pressure, flow

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15

VANNESTE, JACQUES. "Nonlinear dynamics over rough topography: homogeneous and stratified quasi-geostrophic theory." Journal of Fluid Mechanics 474 (January 10, 2003): 299–318. http://dx.doi.org/10.1017/s0022112002002707.

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The weakly nonlinear dynamics of quasi-geostrophic flows over a one-dimensional, periodic or random, small-scale topography is investigated using an asymptotic approach. Averaged (or homogenized) evolution equations which account for the flow–topography interaction are derived for both homogeneous and continuously stratified quasi-geostrophic fluids. The scaling assumptions are detailed in each case; for stratified fluids, they imply that the direct influence of the topography is confined within a thin bottom boundary layer, so that it is through a new bottom boundary condition that the topogr

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16

Eitzinger, B., and G. Ederer. "The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation." Beiträge zur Tabakforschung International/Contributions to Tobacco Research 19, no. 4 (2001): 177–88. http://dx.doi.org/10.2478/cttr-2013-0706.

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AbstractThis study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic,

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17

Lu, Dianchen, Aly R. Seadawy, and M. Arshad. "Solitary wave and elliptic function solutions of sinh-Gordon equation and its applications." Modern Physics Letters B 33, no. 35 (2019): 1950436. http://dx.doi.org/10.1142/s0217984919504360.

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The [Formula: see text]-Gordon model is an important model in special nonlinear partial differential equations (PDEs) which is arising in solid-state physics, mathematical physics, fluid dynamics, fluid flow, differential geometry, quantum theory, etc. The exact solutions in the type of solitary wave and elliptic functions solutions are created of [Formula: see text]-Gordon model by employing modified direct algebraic scheme. Moments of a few solutions are also depicted graphically. These solutions helps the physicians and mathematicians to understand the physical phenomena of this model. This

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18

YAKUBOVICH, E. I., and D. A. ZENKOVICH. "Matrix approach to Lagrangian fluid dynamics." Journal of Fluid Mechanics 443 (September 25, 2001): 167–96. http://dx.doi.org/10.1017/s0022112001005195.

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A new approach to ideal-fluid hydrodynamics based on the notion of continuous deformation of infinitesimal material elements is proposed. The matrix approach adheres to the Lagrangian (material) view of fluid motion, but instead of Lagrangian particle trajectories, it treats the Jacobi matrix of their derivatives with respect to Lagrangian variables as the fundamental quantity completely describing fluid motion.A closed set of governing matrix equations equivalent to conventional Lagrangian equations is formulated in terms of this Jacobi matrix. The equation of motion is transformed into a non

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19

Fahrenthold, E. P., and M. Venkataraman. "System Dynamics Modeling of Porous Media." Journal of Dynamic Systems, Measurement, and Control 119, no. 2 (1997): 251–59. http://dx.doi.org/10.1115/1.2801241.

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A wide range of engineering problems involve porous media modeling. General porous media models are highly nonlinear, geometrically complex, and must account for energy transfer between fluid and solid constituents normally modeled in distinct Lagrangian and Eulerian reference frames. Combining finite element discretization techniques with bond graph methods greatly simplifies the model formulation process, as compared to alternative schemes based on weighted residual solutions of the governing partial differential equations. The result generalizes existing numerical models of porous media and

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20

Papaefthymiou, E. S., D. T. Papageorgiou, and G. A. Pavliotis. "Nonlinear interfacial dynamics in stratified multilayer channel flows." Journal of Fluid Mechanics 734 (October 8, 2013): 114–43. http://dx.doi.org/10.1017/jfm.2013.443.

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AbstractThe dynamics of viscous immiscible pressure-driven multilayer flows in channels are investigated using a combination of modelling, analysis and numerical computations. More specifically, the particular system of three stratified layers with two internal fluid–fluid interfaces is considered in detail in order to identify the nonlinear mechanisms involved due to multiple fluid surface interactions. The approach adopted is analytical/asymptotic and is valid for interfacial waves that are long compared with the channel height or individual undisturbed liquid layer thicknesses. This leads t

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21

M. Fares, Mohammad, Usama M. Abdelsalam, and Faiza M. Allehiany. "Travelling Wave Solutions for Fisher’s Equation Using the Extended Homogeneous Balance Method." Sultan Qaboos University Journal for Science [SQUJS] 26, no. 1 (2021): 22–30. http://dx.doi.org/10.53539/squjs.vol26iss1pp22-30.

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In this work, the extended homogeneous balance method is used to derive exact solutions of nonlinear evolution equations. With the aid of symbolic computation, many new exact travelling wave solutions have been obtained for Fisher’s equation and Burgers-Fisher equation. Fisher’s equation has been widely used in studying the population for various systems, especially in biology, while Burgers-Fisher equation has many physical applications such as in gas dynamics and fluid mechanics. The method used can be applied to obtain multiple travelling wave solutions for nonlinear partial differential eq

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22

Nguyen, Nhan, and Mark Ardema. "Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application." Journal of Dynamic Systems, Measurement, and Control 128, no. 4 (2006): 946–59. http://dx.doi.org/10.1115/1.2362814.

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This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The parti

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23

THESS, A., D. SPIRN, and B. JÜTTNER. "A two-dimensional model for slow convection at infinite Marangoni number." Journal of Fluid Mechanics 331 (January 25, 1997): 283–312. http://dx.doi.org/10.1017/s0022112096003989.

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The free surface of a viscous fluid is a source of convective flow (Marangoni convection) if its surface tension is distributed non-uniformly. Such non-uniformity arises from the dependence of the surface tension on a scalar quantity, either surfactant concentration or temperature. The surface-tension-induced velocity redistributes the scalar forming a closed-loop interaction. It is shown that under the assumptions of (i) small Reynolds number and (ii) vanishing diffusivity this nonlinear process is described by a single self-consistent two-dimensional evolution equation for the scalar field a

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24

Zaib, A., Umair Khan, Ilyas Khan, El-Sayed M. Sherif, Kottakkaran Sooppy Nisar, and Asiful H. Seikh. "Impact of Nonlinear Thermal Radiation on the Time-Dependent Flow of Non-Newtonian Nanoliquid over a Permeable Shrinking Surface." Symmetry 12, no. 2 (2020): 195. http://dx.doi.org/10.3390/sym12020195.

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Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear t

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25

Ahmad, Farooq, A. Othman Almatroud, Sajjad Hussain, Shan E. Farooq, and Roman Ullah. "Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain." Mathematics 8, no. 5 (2020): 854. http://dx.doi.org/10.3390/math8050854.

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A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numeri

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26

Ma, Wen-Xiu, Mohamed R. Ali, and R. Sadat. "Analytical Solutions for Nonlinear Dispersive Physical Model." Complexity 2020 (August 28, 2020): 1–8. http://dx.doi.org/10.1155/2020/3714832.

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Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Ap

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27

Perelomova, Anna. "Acoustic heating produced in resonators filled by a newtonian fluid." Canadian Journal of Physics 90, no. 7 (2012): 693–99. http://dx.doi.org/10.1139/p2012-071.

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Acoustic heating in resonators is studied. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. This equation is instantaneous and includes nonlinear acoustic terms that form a source of acoustic heating, it is valid for weakly nonlinear flows with weak attenuation. In general, dynamics of sound in a resonator is described by coupling nonlinea

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28

Papageorgiou, Demetrios T., and Saleh Tanveer. "Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (2021): 20210307. http://dx.doi.org/10.1098/rspa.2021.0307.

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This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The on

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29

Nadeem, S., Z. Ahmed, and S. Saleem. "The Effect of Variable Viscosities on Micropolar Flow of Two Nanofluids." Zeitschrift für Naturforschung A 71, no. 12 (2016): 1121–29. http://dx.doi.org/10.1515/zna-2015-0491.

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AbstractA study of nanofluids is carried out that reveals the effect of rotational inertia and other physical parameters on the heat transfer and fluid flow. Temperature-dependent dynamic viscosity makes the microrotation viscosity parameter and the micro inertia density variant as well. The governing nonlinear partial differential equations are converted into a set of nonlinear ordinary differential equations by introducing suitable similarity transformations. These reduced nonlinear differential equations are then solved numerically by Keller-box method. The obtained numerical and graphical

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30

Enciso-Salas, Luis, Gustavo Pérez-Zuñiga, and Javier Sotomayor-Moriano. "Fault Diagnosis via Neural Ordinary Differential Equations." Applied Sciences 11, no. 9 (2021): 3776. http://dx.doi.org/10.3390/app11093776.

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Implementation of model-based fault diagnosis systems can be a difficult task due to the complex dynamics of most systems, an appealing alternative to avoiding modeling is to use machine learning-based techniques for which the implementation is more affordable nowadays. However, the latter approach often requires extensive data processing. In this paper, a hybrid approach using recent developments in neural ordinary differential equations is proposed. This approach enables us to combine a natural deep learning technique with an estimated model of the system, making the training simpler and mor

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31

Webb, G. M., R. H. Burrows, X. Ao, and G. P. Zank. "Ion acoustic traveling waves." Journal of Plasma Physics 80, no. 2 (2014): 147–71. http://dx.doi.org/10.1017/s0022377813001013.

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AbstractModels for traveling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron–proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the traveling waves can be reduced to a single first-order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamilton

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32

Perelomova, Anna. "Acoustic Heating Produced in the Thermoviscous Flow of a Shear-Thinning Fluid." Archives of Acoustics 36, no. 3 (2011): 629–42. http://dx.doi.org/10.2478/v10168-011-0044-6.

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AbstractThis study is devoted to the instantaneous acoustic heating of a shear-thinning fluid. Apparent viscosity of a shear-thinning fluid depends on the shear rate. That feature distinguishes it from a viscous Newtonian fluid. The special linear combination of conservation equations in the differential form makes it possible to derive dynamic equations governing both the sound and non-wave entropy mode induced in the field of sound. These equations are valid in a weakly nonlinear flow of a shear-thinning fluid over an unbounded volume. They both are instantaneous, and do not require a period

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33

Polly, James B., and J. M. McDonough. "Application of the Poor Man's Navier-Stokes Equations to Real-Time Control of Fluid Flow." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/746752.

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Control of fluid flow is an important, underutilized process possessing potential benefits ranging from avoidance of separation and stall on aircraft wings to reduction of friction in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier-Stokes (N.-S.) equations, whose solutions describe such flows, consist of a system of time-dependent, multidimensional, nonlinear partial differential equations (PDEs) which cannot be solved in real time using current computing hardware. The poor man's Navier-Stokes (PMNS) equations comprise a discrete dynamical system that is algebra

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34

Alam, Md Sarwar, Md Abdul Hakim Khan, and Oluwole Daniel Makinde. "Magneto-Nanofluid Dynamics in Convergent-Divergent Channel and its Inherent Irreversibility." Defect and Diffusion Forum 377 (September 2017): 95–110. http://dx.doi.org/10.4028/www.scientific.net/ddf.377.95.

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The effects of Cu-nanoparticles on the entropy generation of steady magnetohydrodynamic incompressible flow with viscous dissipation and Joule heating through convergent-divergent channel are analysed in this paper. The basic nonlinear partial differential equations are transformed into a system of coupled ordinary differential equations using suitable transformations which are then solved using power series with Hermite- Padé approximation technique. The velocity profiles, temperature distributions, entropy generation rates, Bejan number as well as the rate of heat transfer at the wall are pr

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35

Dimitrova, Zlatinka I. "Numerical Investigation Of Nonlinear Waves Connected To Blood Flow In An Elastic Tube With Variable Radius." Journal of Theoretical and Applied Mechanics 45, no. 4 (2015): 79–92. http://dx.doi.org/10.1515/jtam-2015-0025.

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Abstract We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the fluid-structure interaction in large human arteries and especially to nonlinear effects. The long-wave approximation is applied to solve model equations. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of three first order differential equations. The low probability of a solitary wave arising is shown. Periodic wave solutions of the mo

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36

BÉG, O. ANWAR, M. M. RASHIDI, T. A. BÉG, and M. ASADI. "HOMOTOPY ANALYSIS OF TRANSIENT MAGNETO-BIO-FLUID DYNAMICS OF MICROPOLAR SQUEEZE FILM IN A POROUS MEDIUM: A MODEL FOR MAGNETO-BIO-RHEOLOGICAL LUBRICATION." Journal of Mechanics in Medicine and Biology 12, no. 03 (2012): 1250051. http://dx.doi.org/10.1142/s0219519411004642.

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The transient squeezing flow of a magneto-micropolar biofluid in a noncompressible porous medium intercalated between two parallel plates in the presence of a uniform strength transverse magnetic field is investigated. The partial differential equations describing the two-dimensional flow regime are transformed into nondimensional, nonlinear coupled ordinary differential equations for linear and angular momentum (micro-inertia). These equations are solved using the robust Homotopy Analysis Method (HAM) and also numerical shooting quadrature. Excellent correlation is achieved. The influence of

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37

Ly, Nguyen, Zvi Rusak, and Shixiao Wang. "Swirling flow states of compressible single-phase supercritical fluids in a rotating finite-length straight circular pipe." Journal of Fluid Mechanics 849 (June 21, 2018): 576–614. http://dx.doi.org/10.1017/jfm.2018.394.

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Steady states of inviscid, compressible and axisymmetric swirling flows of a single-phase, inert, thermodynamically supercritical fluid in a rotating, finite-length, straight, long circular pipe are studied. The fluid thermodynamic behaviour is modelled by the van der Waals equation of state. A nonlinear partial differential equation for the solution of the flow streamfunction is derived from the fluid equations of motion in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. This equation reflects the complicated, nonlinear thermo-physical interactions

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38

Pellicano, F., M. Amabili, and A. F. Vakakis. "Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 2: Perturbation Analysis." Journal of Vibration and Acoustics 122, no. 4 (2000): 355–64. http://dx.doi.org/10.1115/1.1288591.

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The nonlinear ordinary differential equations describing the dynamics of a fluid filled circular cylindrical shell, obtained in Part 1 of the present study, is studied by using a second order perturbation approach and direct simulations. Strong modal interactions are found when the structure is excited with small resonant loads. Modal interactions arise in the whole range of vibration amplitude, showing that the internal resonance condition makes the system non-linearizable even for extremely small amplitudes of oscillation. Stationary and nonstationary oscillations are observed and the comple

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39

Shiralashetti, S. C., L. M. Angadi, A. B. Deshi, and M. H. Kantli. "Haar wavelet method for the numerical solution of Klein–Gordan equations." Asian-European Journal of Mathematics 09, no. 01 (2016): 1650012. http://dx.doi.org/10.1142/s1793557116500121.

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Wavelets have become a powerful tool for having applications in almost all the areas of engineering and science such as numerical simulation of partial differential equations. In this paper, we present the Haar wavelet method (HWM) to solve the linear and nonlinear Klein–Gordon equations which occur in several applied physics fields such as, quantum field theory, fluid dynamics, etc. The fundamental idea of HWM is to convert the Klein–Gordon equations into a group of algebraic equations, which involve a finite number of variables. The examples are given to demonstrate the numerical results obt

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Rashid, Umair, Azhar Iqbal, Haiyi Liang, Waris Khan, and Muhammad Waqar Ashraf. "Dynamics of water conveying zinc oxide through divergent-convergent channels with the effect of nanoparticles shape when Joule dissipation are significant." PLOS ONE 16, no. 1 (2021): e0245208. http://dx.doi.org/10.1371/journal.pone.0245208.

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Aim of study The shape effects of nanoparticles are very significant in fluid flow and heat transfer. In this paper, we discuss the effects of nanoparticles shape in nanofluid flow between divergent-convergent channels theoretically. In this present study, various shapes of nanoparticles, namely sphere, column and lamina in zinc oxide-water nanofluid are used. The effect of the magnetic field and joule dissipation are also considered. Research methodology The system of nonlinear partial differential equations (PDEs) is converted into ordinary differential equations (ODES). The analytical solut

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Rizvi, Syed Tahir Raza, Ijaz Ali, Kashif Ali, and Ghulam Mustafa. "Conserved densities and fluxes for nonlinear Schrödinger equations using scaling invariance approach." Modern Physics Letters B 34, no. 26 (2020): 2050275. http://dx.doi.org/10.1142/s0217984920502759.

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We have adopted a direct method for the computation of polynomial conservation laws (CLs) of three nonlinear Schrödinger equations (NLSEs). The equations under consideration are firstly converted to evolution forms. Instead of using advanced differential-geometric tools, our method utilizes tools from linear algebra and variational calculus. This method can be implemented on NLSEs which occur in quantum physics, plasma physics, and fluid dynamics. In case of NLSEs with parameters, our method evaluates conditions on the parameters involved in order to find a sequence of conserved densities. The

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Khan, Razi, M. Zaydan, Abderrahim Wakif, et al. "A Note on the Similar and Non-Similar Solutions of Powell-Eyring Fluid Flow Model and Heat Transfer over a Horizontal Stretchable Surface." Defect and Diffusion Forum 401 (May 2020): 25–35. http://dx.doi.org/10.4028/www.scientific.net/ddf.401.25.

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Deliberation on the dynamics of non-Newtonian fluids, most especially Powell-Eyring fluid flow can be described as an open question. In this investigation, the flow and heat transfer characteristics are examined numerically by means of similarity analysis for a Powell-Eyring fluid moving over an isothermal stretched surface along the horizontal direction, whose velocity varies nonlinearly as a function of and follows a specified power-law degree formula. In order to solve the problem under consideration, the resulting system of coupled nonlinear partial differential equations with their corres

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Rahmati-Alaei, Ahmad, Majid Sharavi, and Masoud Samadian Zakaria. "Development of a coupled numerical model for the interaction between transient fluid slosh and tank wagon vibration." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 3 (2018): 568–82. http://dx.doi.org/10.1177/1464419318809616.

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In this paper, a coupled model is developed to evaluate the effect of transient fluid slosh on the railway tank wagon dynamic vice versa. This model has computational complexity in solving the Navier–Stokes equations and nonlinear differential equations of tank wagon vibration with nonlinear wheel–rail contact. The coupled model can be used as an effective and robust tool compared to simplified models for assessing the stability of tank wagon. The transient fluid slosh model is analysed using the computational fluid dynamic method combined with the volume of fluid technique. The tank wagon dyn

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Velmisov, Petr A., Yuliya A. Tamarova, and Yuliya V. Pokladova. "Investigation of the dynamic stability of bending-torsional deformations of the pipeline." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 1 (2021): 72–81. http://dx.doi.org/10.15507/2079-6900.23.202101.72-81.

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Nonlinear mathematical models are proposed that describe the dynamics of a pipeline with a fluid flowing in it: a) the model of bending-torsional vibrations with two degrees of freedom; b) the model describing flexural-torsional vibrations taking into account the nonlinearity of the bending moment and centrifugal force; c) the model that takes into account joint longitudinal, bending (transverse) and torsional vibrations. All proposed models are described by nonlinear partial differential equations for unknown strain functions. To describe the dynamics of a pipeline, the nonlinear theory of a

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MAHMOUD, GAMAL M., and TASSOS BOUNTIS. "THE DYNAMICS OF SYSTEMS OF COMPLEX NONLINEAR OSCILLATORS: A REVIEW." International Journal of Bifurcation and Chaos 14, no. 11 (2004): 3821–46. http://dx.doi.org/10.1142/s0218127404011624.

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Dynamical systems in the real domain are currently one of the most popular areas of scientific study. A wealth of new phenomena of bifurcations and chaos has been discovered concerning the dynamics of nonlinear systems in real phase space. There is, however, a wide variety of physical problems, which, from a mathematical point of view, can be more conveniently studied using complex variables. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. In this survey, we shall focus on such classes of autonomous, parametrically excited and modulated

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Abu Arqub, Omar. "Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 4 (2018): 828–56. http://dx.doi.org/10.1108/hff-07-2016-0278.

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Purpose The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit. Design/methodology/approach The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. This representation is given in the W(Ω) and H(Ω) inner product spaces, while the computation of

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MICHIELS, WIM, and SILVIU-IULIAN NICULESCU. "STABILITY ANALYSIS OF A FLUID FLOW MODEL FOR TCP LIKE BEHAVIOR." International Journal of Bifurcation and Chaos 15, no. 07 (2005): 2277–82. http://dx.doi.org/10.1142/s021812740501323x.

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This note focuses on the stability analysis of some classes of nonlinear time-delay models, encountered as fluid models for TCP/AQM network. By combining analytical and numerical tools, the attractors of these models, as well as the local and global behaviors of the solutions are studied. Among others, the presence of a chaotic attractor is shown, which supports the proposition that TCP itself as a deterministic process can cause or contribute to chaotic behavior in a network. The main goals of the paper are firstly to provide qualitative and quantitative information on the dynamics of the mod

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Keskinen, R. P. "Transient Hydroelastic Vibration of Piping With Local Nonlinearities." Journal of Pressure Vessel Technology 107, no. 4 (1985): 350–55. http://dx.doi.org/10.1115/1.3264463.

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A mode superposition algorithm is presented to solve fluid and structural dynamics problems in piping systems with a local cross-sectional material nonlinearity, such as cavitation of fluid or circumferential cracking of the pipe material. Two families of eigenmodes are used to decompose the total response into so-called compatibility-controlling and resistance-controlling responses which satisfy the governing partial differential equations. The responses are simultaneously solved in time by means of convolution integral techniques. Either response is always predicting for the other an additio

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Summers, Danny, Hiroshi Matsumoto, and Takafumi Ohnishi. "Spectral Analysis of the Flow of a Neutralized Electron Beam." International Journal of Bifurcation and Chaos 07, no. 05 (1997): 1075–101. http://dx.doi.org/10.1142/s0218127497000893.

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The flow of a neutralized electron beam in the classical Pierce beam–plasma system is examined. The system comprises two grounded electrodes containing a stationary background population of neutralizing ions, and electrons are steadily injected with speed V0 from the left-hand electrode at which the charge density is maintained constant. According to cold fluid theory, the system is governed by a single dimensionless parameter α = Lωp/V0, where L is the separation of the electrodes and ωp the plasma frequency. We cast the governing partial differential equations of the cold fluid model in gene

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DZWINEL, WITOLD, and DAVID A. YUEN. "MIXING DRIVEN BY RAYLEIGH–TAYLOR INSTABILITY IN THE MESOSCALE MODELED WITH DISSIPATIVE PARTICLE DYNAMICS." International Journal of Modern Physics C 12, no. 01 (2001): 91–118. http://dx.doi.org/10.1142/s0129183101001560.

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In the mesoscale, mixing dynamics involving immiscible fluids is truly an outstanding problem in many fields, ranging from biology to geology, because of the multiscale nature which causes severe difficulties for conventional methods using partial differential equations. The existing macroscopic models incorporating the two microstructural mechanisms of breakup and coalescence do not have the necessary physical ingredients for feedback dynamics. We demonstrate here that the approach of dissipative particle dynamics (DPD) does include the feedback mechanism and thus can yield much deeper insigh

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