scholarly journals COMPLEX WAVE NUMBERS IN THE VICINITY OF THE SCHWARZSCHILD EVENT HORIZON

2008 ◽  
Vol 23 (09) ◽  
pp. 1417-1433 ◽  
Author(s):  
M. SHARIF ◽  
UMBER SHEIKH
Keyword(s):  
Event Horizon ◽  
Plasma Wave ◽  
Cold Plasma ◽  
Dispersion Relations ◽  
Wave Numbers ◽  
Complex Wave ◽  
And Behavior ◽  
Wave Properties

This paper is devoted to investigate the cold plasma wave properties outside the event horizon of the Schwarzschild planar analogue. The dispersion relations are obtained from the corresponding Fourier analyzed equations for nonrotating and rotating, nonmagnetized and magnetized backgrounds. These dispersion relations provide complex wave numbers. The wave numbers are shown in graphs to discuss the nature and behavior of waves and the properties of plasma lying in the vicinity of the Schwarzschild event horizon.

Wave Propagation and Instability in a Circular Semi-Infinite Liquid Jet Harmonically Forced at the Nozzle

1978 ◽  
Vol 45 (3) ◽  
pp. 469-474 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Wave Propagation ◽  
Radiation Condition ◽  
Liquid Jet ◽  
Propagation Characteristics ◽  
Frequency Spectra ◽  
One Dimensional ◽  
Wave Numbers ◽  
Complex Wave ◽  
The Stability ◽  
The Waves

The linearized form of the inviscid, one-dimensional Cosserat jet equations derived by Green [6] are used to study wave propagation in a circular jet with surface tension. The frequency spectra are shown for complex wave numbers for a complete range of Weber numbers. The propagation characteristics of the waves are studied in order to determine which branches of the frequency spectra to use in the semi-infinite jet problem with harmonic forcing at the nozzle. Two of the four branches are eliminated by a radiation condition that energy must be outgoing at infinity; the remaining two branches are used to satisfy the nozzle boundary conditions. The variation of the jet radius along its length is shown graphically for various Weber numbers and forcing frequencies. The stability or instability is explained in terms of the behavior of the two propagating phases.

Uncoupled Wave Systems and Dispersion in an Infinite Solid Cylinder

1989 ◽  
Vol 56 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Yoon Young Kim
Keyword(s):  
Cylindrical Surface ◽  
Wave Motion ◽  
Fourier Number ◽  
Large Wave ◽  
Surface Conditions ◽  
Asymptotic Nature ◽  
Wave Numbers ◽  
Complex Wave ◽  
Insight Into ◽  
Free Cylindrical Surface

In this study, it is shown that there exist uncoupled wave systems for general non-axisymmetric wave propagation in an infinite isotropic cylinder. Two cylindrical surface conditions corresponding to the uncoupled wave systems are discussed. The solutions of the uncoupled wave systems are shown to provide proper bounds of Pochhammer’s equation for a free cylindrical surface. The bounds, which are easy to construct for any Fourier number in the circumferential direction, can be used to trace the branches of Pochhammer’s equation. They also give insight into the modal composition of the branches of Pochhammer’s equation at and between the intersections of the bounds. More refined dispersion relations of Pochhammer’s equation are possible through an asymptotic analysis of the itersections of the branches of Pochhammer’s equation with one family of the bounds. The asymptotic nature of wave motion corresponding to large wave numbers, imaginary or complex, for Pochhammer’s equation is studied. The wave motion is asymptotically equivoluminal for large imaginary wave numbers, and is characterized by coupled dilatation and shear for large complex wave numbers.

Singularities of dispersion relations

1983 ◽  
Vol 95 (3-4) ◽  
pp. 301-316 ◽  
Author(s):  
G. Dangelmayr
Keyword(s):  
Catastrophe Theory ◽  
Bifurcation Theory ◽  
Normal Forms ◽  
Dispersion Relations ◽  
Bifurcation Parameter ◽  
Special Cases ◽  
Wave Numbers ◽  
Imperfect Bifurcation ◽  
Generic Singularities ◽  
Zero Frequency

SynopsisGeneric singularities occurring in dispersion relations are discussed within the framework of imperfect bifurcation theory and classified up to codimension four. Wave numbers are considered as bifurcation variables x =(x1,…, xn) and the frequency is regarded as a distinguished bifurcation parameter λ. The list of normal forms contains, as special cases, germs of the form ±λ +f(x), where f is a standard singularity in the sense of catastrophe theory. Since many dispersion relations are ℤ(2)-equivariant with respect to the frequency, bifurcation equations which are ℤ(2)-equivariant with respect to the bifurcation parameter are introduced and classified up to codimension four in order to describe generic singularities which occur at zero frequency. Physical implications of the theory are outlined.

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

scholarly journals The Exact Frequency Equations for the Euler-Bernoulli Beam Subject to Boundary Damping

2020 ◽  
Vol 25 (2) ◽  
pp. 183-189
Author(s):  
Angela Biselli ◽  
Matthew P. Coleman
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Methods ◽  
Bernoulli Beam ◽  
Boundary Damping ◽  
Numerical Examples ◽  
Wave Numbers ◽  
Complex Wave ◽  
Energy Conserving ◽  
Vibrating Beams ◽  
Euler Bernoulli Beam

The Euler-Bernoulli (E-B) beam is the most commonly utilized model in the study of vibrating beams. The exact frequency equations for this problem, subject to energy-conserving boundary conditions, are well-known; however, the corresponding dissipative problem has been solved only approximately, via asymptotic methods. These methods, of course, are not accurate when looking at the low end of the spectrum. Here, we solve for the exact frequency equations for the E-B beam subject to boundary damping. Numerous numerical examples are provided, showing plots of both the complex wave numbers and the exponential damping rates for the first five frequencies in each case. Some of these results are surprising.

Sign in / Sign up

Export Citation Format

Share Document