scholarly journals Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions

1996 ◽  
Vol 95 (6) ◽  
pp. 1079-1096 ◽  
Author(s):  
S. Mano ◽  
H. Suzuki ◽  
E. Takasugi
Keyword(s):  
Low Frequency ◽  
Analytic Solutions ◽  
Teukolsky Equation

A theory for Langmuir solitons

1982 ◽  
Vol 27 (1) ◽  
pp. 95-120 ◽  
Author(s):  
N. Nagesha Rao ◽  
Ram K. Varma
Keyword(s):  
Mach Number ◽  
A Priori ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Smooth Transition ◽  
Langmuir Waves ◽  
Method Of Solution ◽  
Mach Numbers ◽  
Ion Waves ◽  
Langmuir Solitons

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ = 0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

scholarly journals Analytic Solutions of the Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

1999 ◽  
Vol 102 (2) ◽  
pp. 253-272 ◽  
Author(s):  
Hisao Suzuki ◽  
Eiichi Takasugi ◽  
Hiroshi Umetsu
Keyword(s):  
Analytic Solutions ◽  
De Sitter ◽  
Teukolsky Equation

Analytical Solution to Excited Waveform of Bias Control on Electro-Hydraulic Vibration Exciter

2010 ◽  
Vol 44-47 ◽  
pp. 1729-1733
Author(s):  
Yan Ren ◽  
Jian Ruan ◽  
Ji Yan Yi
Keyword(s):  
Analytical Solution ◽  
Low Frequency ◽  
Experimental System ◽  
Analytic Solutions ◽  
Slide Valve ◽  
Central Position ◽  
Vibration Exciter ◽  
Sinusoidal Waveform ◽  
The Mathematical Model ◽  
Single Slide

For precisely controlling the bias position of an electro-hydraulic vibration exciter, a scheme of a parallel mechanism of a two-dimensional valve (2D valve) and a servo valve is proposed. In the low frequency section, the mathematical model of the electro-hydraulic vibration exciter is simplified reasonably. A vibration central position is first analytically derived by assuming that 2D valve connected with parallel valve is equivalent to a single slide valve with neutral positive opening and the time-average flow rate through them is identical. And then the analytic solutions to excited waveforms superimposed on the bias position are further obtained. Finally, the experimental system is built to verify the theoretical analysis. The results reveal that this approximate analytical solution could describe excited waveform of bias control on electro-hydraulic vibration exciter. When the opening area of 2D valve is a constant, the bias position follows a linear relation with the throttling areas of the parallel valve which is no more than the maximum position. The excited waveform is close to the sinusoidal waveform. At the same opening area of the parallel valve, the bias position is reduced as the area coefficient of 2D valve increases. The proposed scheme not only ensures the frequency and the amplitude to be controlled independently but also the bias position to be adjusted precisely.

scholarly journals Oscillatory superfluid Ekman pumping in helium II and neutron stars

2015 ◽  
Vol 783 ◽  
pp. 251-282 ◽  
Author(s):  
C. Anthony van Eysden
Keyword(s):  
Neutron Stars ◽  
Low Frequency ◽  
Line Tension ◽  
Outer Core ◽  
Oscillation Period ◽  
Analytic Solutions ◽  
Ekman Pumping ◽  
Helium Ii ◽  
Tension Parameter ◽  
Pumping Mode

The linear response of a superfluid, rotating uniformly in a cylindrical container and threaded with a large number of vortex lines, to an impulsive increase in the angular velocity of the container is investigated. At zero temperature and with perfect pinning of vortices to the top and bottom of the container, we demonstrate that the system oscillates persistently with a frequency proportional to the vortex line tension parameter to the quarter power. This low-frequency mode is generated by a secondary flow analogous to classical Ekman pumping that is periodically reversed by the vortex tension in the boundary layers. We compare analytic solutions to the two-fluid equations by Chandler & Baym (J. Low Temp. Phys., vol. 62, 1986, pp. 119–142) with the spin-up experiments by Tsakadze & Tsakadze (J. Low Temp. Phys., vol. 39, 1980, pp. 649–688) in helium II and find that the frequency agrees within a factor of four, although the experiment is not perfectly suited to the application of linear theory. We argue that this oscillatory Ekman pumping mode, and not Tkachenko modes, provides a natural explanation for the observed oscillation. In neutron stars, the oscillation period depends on the pinning interaction between neutron vortices and flux tubes in the outer core. Using a simplified pinning model, we demonstrate that strong pinning can accommodate modes with periods of days to years, which are only weakly damped by mutual friction over longer time scales.

scholarly journals The Vertical Structure of Low-Frequency Motions in the Nearshore. Part II: Theory

2016 ◽  
Vol 46 (12) ◽  
pp. 3713-3727 ◽  
Author(s):  
Thomas C. Lippmann ◽  
Anthony J. Bowen
Keyword(s):  
Vertical Structure ◽  
Vertical Mixing ◽  
Low Frequency ◽  
Companion Paper ◽  
Analytic Solutions ◽  
Shear Stresses ◽  
Low Frequencies ◽  
Shear Structure ◽  
Oscillating Motion ◽  
Bidirectional Flow

AbstractField observations from a vertical stack of two-component current meters obtained from the 1994 Duck94 nearshore field experiment (presented in a companion paper by Lippmann, et al.) show significant vertical structure in energy, phase, and rotation of motions at low frequencies around 0.005 Hz. Low-frequency motions are typically modeled in the surfzone with the shallow-water (depth averaged) momentum equations that do not allow for any vertical structure. Following work from the shelf tidal community (Prandle), this study shows that the observations are consistent with the depth-varying momentum equations including shear stresses induced by a bottom boundary layer described by a constant eddy viscosity νt and bottom friction given by a constant drag coefficient and depth-averaged velocity . The bidirectional flow field is solved over arbitrary depth profiles varying only in the cross-shore direction h(x) in the presence of a vertically uniform mean alongshore current with cross-shore shear structure V(x). Analytic solutions are found to depend on νt, cd, h, ∂V/∂x, and the parameter , where σ and k are the radian frequency and alongshore wavenumber of the oscillating motion. Model behavior is explored by plotting solutions for a given parameter space as functions of the nondimensional depth H = λh and dimensionless friction parameter that combines the effects of bottom drag and vertical mixing. The behavioral changes in amplitude, phase shift, and rotational structure over the water column are qualitatively similar to those observed in the field.

scholarly journals Multiscale Atmosphere–Ocean Interactions and the Low-Frequency Variability in the Equatorial Region

2017 ◽  
Vol 74 (8) ◽  
pp. 2503-2523 ◽  
Author(s):  
Enver Ramirez ◽  
Pedro L. da Silva Dias ◽  
Carlos F. M. Raupp
Keyword(s):  
El Niño ◽  
Time Scale ◽  
El Nino ◽  
Intraseasonal Variability ◽  
Low Frequency ◽  
Coupled Model ◽  
Analytic Solutions ◽  
Equatorial Region ◽  
Synoptic Scale ◽  
Atmospheric Variability

Abstract In the present study a simplified multiscale atmosphere–ocean coupled model for the tropical interactions among synoptic, intraseasonal, and interannual scales is developed. Two nonlinear equatorial β-plane shallow-water equations are considered: one for the ocean and the other for the atmosphere. The nonlinear terms are the intrinsic advective nonlinearity and the air–sea coupling fluxes. To mimic the main differences between the fast atmosphere and the slow ocean, suitable anisotropic multispace/multitime scalings are applied, yielding a balanced synoptic–intraseasonal–interannual–El Niño (SInEN) regime. In this distinguished balanced regime, the synoptic scale is the fastest atmospheric time scale, the intraseasonal scale is the intermediate air–sea coupling time scale (common to both fluid flows), and El Niño refers to the slowest interannual ocean time scale. The asymptotic SInEN equations reveal that the slow wave amplitude evolution depends on both types of nonlinearities. Analytic solutions of the reduced SInEN equations for a single atmosphere–ocean resonant triad illustrate the potential of the model to understand slow-frequency variability in the tropics. The resonant nonlinear wind stress allows a mechanism for the synoptic-scale atmospheric waves to force intraseasonal variability in the ocean. The intraseasonal ocean temperature anomaly coupled with the atmosphere through evaporation forces synoptic and intraseasonal atmospheric variability. The wave–convection coupling provides another source for higher-order atmospheric variability. Nonlinear interactions of intraseasonal ocean perturbations may also force interannual oceanic variability. The constrains that determine the establishment of the atmosphere–ocean resonant coupling can be viewed as selection rules for the excitation of intraseasonal variability (MJO) or even slower interannual variability (El Niño).

scholarly journals Exact Symmetric Solutions of MHD Casson Fluid Using Chemically Reactive Flow with Generalized Boundary Conditions

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6243
Author(s):  
Syed Tauseef Saeed ◽  
Muhammad Bilal Riaz ◽  
Jan Awrejcewicz ◽  
Hijaz Ahmad
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Low Frequency ◽  
Strong Shock ◽  
High Sensitivity ◽  
Analytic Solutions ◽  
Casson Fluid ◽  
The Laplace Transform ◽  
Shock Resistance ◽  
Generalized Boundary Conditions

Dynamic analysis of magnetic fluids with the combined effect of heat sink and chemical reactions based on their physical properties demonstrates strong shock resistance capabilities, low-frequency response, low energy consumption, and high sensitivity. Therefore, the applied magnetic field always takes diamagnetic, ferromagnetic, and paramagnetic forms. The influence of radiation is considered in the temperature profile. This manuscript investigates an analytic solution of incompressible and magnetic Casson fluid in Darcy’s medium subjected to temperature and concentration dependence within a porous-surfaced plate with generalized boundary conditions. The substantial mathematical technique of the Laplace transform with inversion is invoked in the governing equations of the magnetic Casson fluid. The analytic results are transformed into a special function for the plate with a constant velocity, a plate with linear velocity, a plate with exponential velocity, and a plate with sinusoidal velocity. Graphical illustrations of the investigated analytic solutions at four different times are presented. Our results suggest that the velocity profile decreases by increasing the value of the magnetic field, which reflects the control of resistive force. The Nusselt number remains constant at a fixed Rd and is reduced by raising the Rd value.

Elastic waves in finely layered sediments: The equivalent medium and generalized O’Doherty‐Anstey formulas

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1282-1300 ◽  
Author(s):  
Sergei A. Shapiro ◽  
Peter Hubral
Keyword(s):  
Phase Velocity ◽  
Multiple Scattering ◽  
Random Media ◽  
Plane Waves ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Seismic Velocities ◽  
Statistical Parameters ◽  
Practical Applications ◽  
Backus Averaging

We study the influence of elastic 1-D inhomogeneous random media (e.g., finely layered media with variable density and shear and compressional velocities) on the kinematics and dynamics of the transmitted obliquely incident P‐ and SV‐plane waves. Multiple scattering (resulting in localization and spatial dispersion of the elastic wavefield) is the main physical effect controlling the properties of the wavefield in such media. We analyze the wave propagation assuming the fluctuations of velocities and density to be small (of the order of 20% or smaller). We obtain explicit analytic solutions for the attenuation coefficient and phase velocity of the transmitted waves. These solutions are valid for all frequencies. They agree very well with results of numerical modeling. Our theory shows that fine elastic multilayering is characterized by a frequency‐dependent anisotropy. At typical acquisition frequencies this anisotropy differs significantly from the low‐frequency anisotropy described by the well‐known Backus averaging. The increase of the phase velocity with frequency is quantified. It can partly explain the difference between well‐log‐derived velocities and lower frequency seismic velocities [e.g., vertical seismic profiling (VSP) velocities] in terms of localization. The low‐ and high‐frequency asymptotical results for the phase velocity agree with those of Backus averaging and ray approximation, respectively. The theory describes the angle‐dependent attenuation caused by multiple scattering. The proposed formulas are simple enough to be used in many practical applications as, e.g., in an amplitude variation with offset (AVO) analysis. They can be implemented for taking into account the angle dependence of transmission effects, or they can be used in an inversion for statistical parameters of sediments.

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