scholarly journals Exact Solutions Superimposed with Nonlinear Plane Waves

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
B. S. Desale ◽  
Vivek Sharma
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Large Scale ◽  
Plane Waves ◽  
Boussinesq Equations ◽  
Integral Curves ◽  
Nonlinear Plane ◽  
Scale Motion

The flow of fluid in atmosphere and ocean is governed by rotating stratified Boussinesq equations. Through the literature, we found that many researchers are trying to find the solutions of rotating stratified Boussinesq equations. In this paper, we have obtained special exact solutions and nonlinear plane waves. Finally, we provide exact solutions to rotating stratified Boussinesq equations with large scale motion superimposed with the nonlinear plane waves. In support of our investigations, we provided two examples: one described the special exact solution and in second example, we have determined the special exact solution superimposed with nonlinear plane wave. Also, we depicted some integral curves that represent the flow of an incompressible fluid particle on the planex1+x2=L(constant)as the particular case.

An Exact Solution for Pistonlike Leak-Off of Compressible Fluids

1984 ◽  
Vol 106 (4) ◽  
pp. 539-542 ◽  
Author(s):  
R. H. Dean ◽  
S. H. Advani
Keyword(s):  
Exact Solution ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Parameter Sensitivity ◽  
Compressible Fluids ◽  
Reservoir Fluid ◽  
Special Cases ◽  
Fluid Leak

Exact solutions associated with the problem of a compressible or an incompressible fluid displacing a compressible reservoir fluid are derived. Simplified forms for the fluid leak-off coefficients, available in the literature, are deduced as special cases. Nondimensionalized expressions suitable for parameter sensitivity calculations and assumption validation are also presented.

NONLINEAR PLANE WAVES IN A LONG-WAVELENGTH CONVECTION MODEL

2001 ◽  
Vol 11 (11) ◽  
pp. 2867-2874
Author(s):  
A. M. MANCHO ◽  
L. VÁZQUEZ ◽  
H. HERRERO ◽  
S. HOYAS
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Plane Wave ◽  
Prandtl Number ◽  
Plane Waves ◽  
Long Wavelength ◽  
Wave Solutions ◽  
Convection Model ◽  
Nonlinear Plane

The partial differential equation (PDE) associated with the long-wavelength regime that describes convection between rigid and poorly conducting boundaries in an infinite Prandtl number fluid is studied in this document. This PDE is reduced to a set of ordinary differential equations (ODE) by looking for the exact nonlinear plane wave solutions. Solving this ODE several kinds of oscillatory attractors are obtained. These attractors are compared to oscillations observed in experiments on fluids and some features are also recovered.

scholarly journals Exact Solution of 3D Navier–Stokes Equations

2020 ◽  
pp. 306-313
Author(s):  
Alexander V. Koptev
Keyword(s):  
Exact Solution ◽  
Fluid Flow ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
First Integral ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Particular Solutions

Procedure for constructing exact solutions of 3D Navier–Stokes equations for an incompressible fluid flow is proposed. It is based on the relations representing the previously obtained first integral of the Navier–Stokes equations. A primary generator of particular solutions is proposed. It is used to obtain new classes of exact solutions

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Interaction of Very Large Scale Motion of Coherent Structures with Sediment Particle Exposure

Water ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 248
Author(s):  
Sencer Yücesan ◽  
Daniel Wildt ◽  
Philipp Gmeiner ◽  
Johannes Schobesberger ◽  
Christoph Hauer ◽  
...  
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Numerical Study ◽  
Local Maximum ◽  
Wave Number ◽  
Exposure Level ◽  
Sediment Particle ◽  
High Wave Number ◽  
Large Scale Motion ◽  
Scale Motion

A systematic variation of the exposure level of a spherical particle in an array of multiple spheres in a high Reynolds number turbulent open-channel flow regime was investigated while using the Large Eddy Simulation method. Our numerical study analysed hydrodynamic conditions of a sediment particle based on three different channel configurations, from full exposure to zero exposure level. Premultiplied spectrum analysis revealed that the effect of very-large-scale motion of coherent structures on the lift force on a fully exposed particle resulted in a bi-modal distribution with a weak low wave number and a local maximum of a high wave number. Lower exposure levels were found to exhibit a uni-modal distribution.

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaozhou Liu ◽  
Jian Ma ◽  
Haibin Wang ◽  
Sha Gao ◽  
Yifeng Li ◽  
...  
Keyword(s):  
Plane Wave ◽  
Field Distribution ◽  
Scattered Field ◽  
Phased Array ◽  
Simulation Analysis ◽  
Plane Waves ◽  
Theoretical Solution ◽  
Steel Matrix ◽  
Field Distributions ◽  
Scattered Fields

AbstractThe scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

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