scholarly journals Electromagnetic Waves in Annular Regions

2020 ◽  
Vol 10 (5) ◽  
pp. 1780
Author(s):  
Daniele Funaro
Keyword(s):  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Periodic Wave ◽  
Vortex Rings ◽  
Periodic Wave Solutions ◽  
Special Cases ◽  
Time Periodic Solutions ◽  
The Waves ◽  
Analytical Expressions ◽  
Time Periodic

In suitable bounded regions immersed in vacuum, time periodic wave solutions solving a full set of electrodynamics equations can be explicitly computed. Analytical expressions are available in special cases, whereas numerical simulations are necessary in more complex situations. The attention here is given to selected three-dimensional geometries, which are topologically equivalent to a toroid, where the behavior of the waves is similar to that of fluid-dynamics vortex rings. The results show that the shape of the sections of these rings depends on the behavior of the eigenvalues of a certain elliptic differential operator. Time-periodic solutions are obtained when at least two of such eigenvalues attain the same value. The solutions obtained are discussed in view of possible applications in electromagnetic whispering galleries or plasma physics.

scholarly journals New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Faruk Dusunceli
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Ordinary Differential Equation ◽  
Wave Transformation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Parameter Values ◽  
Singular Soliton

The Konopelchenko-Dubrovsky (KD) system is presented by the application of the improved Bernoulli subequation function method (IBSEFM). First, The KD system being Nonlinear partial differential equations system is transformed into nonlinear ordinary differential equation by using a wave transformation. Last, the resulting equation is successfully explored for new explicit exact solutions including singular soliton, kink, and periodic wave solutions. All the obtained solutions in this study satisfy the Konopelchenko-Dubrovsky model. Under suitable choice of the parameter values, interesting two- and three-dimensional graphs of all the obtained solutions are plotted.

On the Onset of Breakup in Inviscid and Viscous Jets

1979 ◽  
Vol 46 (2) ◽  
pp. 291-297 ◽  
Author(s):  
D. A. Caulk ◽  
P. M. Naghdi
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Periodic Wave ◽  
One Dimensional ◽  
Periodic Wave Solutions ◽  
Viscous Jets ◽  
Elliptical Jet ◽  
Basic Equations ◽  
The One ◽  
Small Disturbances

This paper is concerned with the instability of inviscid and viscous jets utilizing the basic equations of the one-dimensional direct theory of a fluid jet based on the concept of a Cosserat (or a directed) curve. First, a system of differential equations is derived for small motions superposed on uniform flow of an inviscid straight circular jet which can twist along its axis. Periodic wave solutions are then obtained for this system of linear equations; and, with reference to a description of growth in the unstable mode, the resulting dispersion relation is found to agree extremely well with the classical (three-dimensional) results of Rayleigh. Next, constitutive equations are obtained for a viscous elliptical jet and these are used to discuss both the symmetric and the antisymmetric small disturbances in the shape of the free surface of a circular jet. Through a comparison with available three-dimensional numerical results, the solution obtained is shown to be an improvement over an existing approximate solution of the problem.

RIEMANN THETA FUNCTIONS SOLUTIONS WITH RATIONAL CHARACTERISTICS FOR (2+1)-DIMENSIONAL SINH-GORDON EQUATION

2010 ◽  
Vol 24 (06) ◽  
pp. 575-584
Author(s):  
YANG FENG ◽  
HONG-QING ZHANG
Keyword(s):  
Gordon Equation ◽  
Theta Functions ◽  
Periodic Wave ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Wave Numbers ◽  
Riemann Theta Functions ◽  
The Waves ◽  
Hirota Bilinear

In this letter, we use the Riemann theta functions with rational characteristics and the Hirota bilinear method to construct quasi-periodic wave solutions for (2+1)-dimensional sinh-Gordon equation. This method not only conveniently obtains quasi-periodic solutions of nonlinear equations, but also directly gets the explicit expressions of frequencies, wave numbers, phase and amplitudes for the waves.

Tertiary and quaternary solutions for plane Couette flow

1997 ◽  
Vol 344 ◽  
pp. 137-153 ◽  
Author(s):  
R. M. CLEVER ◽  
F. H. BUSSE
Keyword(s):  
Periodic Solutions ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Plane Couette Flow ◽  
Longitudinal Vortices ◽  
Wave Solutions ◽  
Time Periodic Solutions ◽  
Steady Solutions ◽  
Time Periodic

The plane Couette system does not exhibit any secondary solutions bifurcating from the primary solution of constant shear. Since the work of Nagata (1990) it has been well known that three-dimensional steady solutions exist. Here the manifold of those steady solutions is explored in the parameter space of the problem and their instabilities are investigated. These instabilities usually lead to time-periodic solutions whose properties do not differ much from those of the steady solutions except that the amplitude varies in time. In some cases travelling wave solutions which are asymmetric with respect to the midplane of the layer are found as quaternary states of flow. Similarities with longitudinal vortices recently observed in experiments are discussed.

scholarly journals ROTATING ELECTROMAGNETIC WAVES IN TOROID-SHAPED REGIONS

2010 ◽  
Vol 21 (01) ◽  
pp. 11-32 ◽  
Author(s):  
CLAUDIA CHINOSI ◽  
LUCIA DELLA CROCE ◽  
DANIELE FUNARO
Keyword(s):  
Fluid Dynamics ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Angular Speed ◽  
Vortex Rings ◽  
Bounded Region ◽  
Three Dimensional Space

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three-dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.

scholarly journals Oblique wave groups in deep water

1984 ◽  
Vol 146 ◽  
pp. 1-20 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Deep Water ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Periodic Wave ◽  
Two Dimensions ◽  
Wave Groups ◽  
Oblique Wave ◽  
Parallel Lines ◽  
The Waves

Oblique wave groups consist of waves whose straight parallel lines of constant phase are oblique to the straight parallel lines of constant group phase. Numerical solutions for periodic oblique wave groups with envelopes of permanent shape are calculated from the equations for irrotational three-dimensional deep-water motion with nonlinear upper free-surface conditions. Two distinct families of periodic wave groups are found, one in which the waves in each group are in phase with those in all other groups, and the other in which there is a phase difference of π between the waves in consecutive groups. It is shown that some analytical solutions for oblique wave groups calculated from the nonlinear Schrödinger equation are in error because they ignore the resonant forcing of certain harmonics in two dimensions. Particular attention is given to oblique wave groups whose group-to-wave angle is in the neighbourhood of the critical angle tan−1√½, corresponding to waves on the boundary wedge of the Kelvin ship-wave pattern.

scholarly journals Weak Solutions and Their Kinetic Energy Regarding Time-Periodic Navier–Stokes Equations in Three Dimensional Whole-Space

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1528
Author(s):  
Mads Kyed
Keyword(s):  
Kinetic Energy ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Periodic Forcing ◽  
Navier Stokes Equations ◽  
Whole Space ◽  
Time Periodic Solutions ◽  
Time Periodic

The existence of weak time-periodic solutions to Navier–Stokes equations in three dimensional whole-space with time-periodic forcing terms are established. The solutions are constructed in such a way that the structural properties of their kinetic energy are obtained. No restrictions on either the size or structure of the external force are required.

scholarly journals Отражение света слоем гиперболического метаматериала в случае распространения в нем особых неоднородных волн

2019 ◽  
Vol 126 (3) ◽  
pp. 319 ◽  
Author(s):  
Н.С. Петров ◽  
С.Н. Курилкина ◽  
А.Б. Зимин ◽  
В.Н. Белый
Keyword(s):  
Boundary Problem ◽  
Electromagnetic Waves ◽  
Total Reflection ◽  
Transmitted Light ◽  
Energy Characteristics ◽  
Hyperbolic Metamaterial ◽  
The Waves ◽  
Analytical Expressions

AbstractThe boundary problem of reflection of electromagnetic waves by a hyperbolic metamaterial layer under conditions of total reflection from the boundary with this layer in the absence of birefringence has been solved. In this case, so-called “special inhomogeneous electromagnetic waves” may propagate in the layer. Analytical expressions are obtained for the vector amplitudes of the waves reflected by the layer and transmitted through it and for the special inhomogeneous electromagnetic waves propagating in this layer. These expressions allows calculating the energy characteristics of reflected and transmitted light for an optically uniaxial metamaterial.

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