Nonlinear effects in the squeezing spectrum of a parametric amplifier

1988 ◽  
Vol 66 (10) ◽  
pp. 854-858 ◽  
Author(s):  
H. R. Zaidi
Keyword(s):  
Linear Theory ◽  
Nonlinear Theory ◽  
Nonlinear Effects ◽  
Parametric Amplifier

A general nonlinear theory is formulated for the calculation of the squeezing spectrum of a parametric amplifier. The lowest order nonlinear corrections are calculated for both modes below the threshold, and the results are compared with linear theory. The corrections to the spectrum are found to be significant.

The centrifugal instability of a Stokes layer: nonlinear theory

1977 ◽  
Vol 354 (1676) ◽  
pp. 119-126 ◽  
Keyword(s):  
Circular Cylinder ◽  
Linear Theory ◽  
Nonlinear Theory ◽  
Exponential Growth ◽  
Nonlinear Effects ◽  
Critical Value ◽  
Basic Flow ◽  
Supercritical Regime ◽  
Stokes Layer ◽  
Centrifugal Instability

It has recently been shown by Seminara & Hall (1976) th at a Stokes layer on an oscillating circular cylinder is unstable according to linear theory when the frequency of oscillation exceeds a certain critical value. In this paper it is shown how nonlinear effects prevent the exponential growth of disturbances when this frequency is exceeded. The flow obtained in the supercritical regime is found to be synchronous with the basic flow.

scholarly journals TSUNAMI GENERATION AND PROPAGATION

1972 ◽  
Vol 1 (13) ◽  
pp. 146
Author(s):  
Joseph L. Hammack ◽  
Frederic Raichlen
Keyword(s):  
Linear Theory ◽  
Source Region ◽  
Three Dimensional ◽  
Frequency Dispersion ◽  
Nonlinear Effects ◽  
Its Region ◽  
Experimental Results ◽  
Specific Class ◽  
Two Dimensional ◽  
Three Dimensional Models

A linear theory is presented for waves generated by an arbitrary bed deformation {in space and time) for a two-dimensional and a three -dimensional fluid domain of uniform depth. The resulting wave profile near the source is computed for both the two and three-dimensional models for a specific class of bed deformations; experimental results are presented for the two-dimensional model. The growth of nonlinear effects during wave propagation in an ocean of uniform depth and the corresponding limitations of the linear theory are investigated. A strategy is presented for determining wave behavior at large distances from the source where linear and nonlinear effects are of equal magnitude. The strategy is based on a matching technique which employs the linear theory in its region of applicability and an equation similar to that of Korteweg and deVries (KdV) in the region where nonlinearities are equal in magnitude to frequency dispersion. Comparison of the theoretical computations with the experimental results indicates that an equation of the KdV type is the proper model of wave behavior at large distances from the source region.

scholarly journals “Extraordinary” modulation instability in optics and hydrodynamics

2021 ◽  
Vol 118 (14) ◽  
pp. e2019348118
Author(s):  
Guillaume Vanderhaegen ◽  
Corentin Naveau ◽  
Pascal Szriftgiser ◽  
Alexandre Kudlinski ◽  
Matteo Conforti ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Stability Analysis ◽  
Linear Stability ◽  
Nonlinear Theory ◽  
Linear Stability Analysis ◽  
Water Waves ◽  
Modulation Instability ◽  
Nonlinear Effects ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

Nonlinear Rayleigh–Taylor instability in hydromagnetics

1976 ◽  
Vol 15 (2) ◽  
pp. 239-244 ◽  
Author(s):  
G. L. Kalra ◽  
S. N. Kathuria
Keyword(s):  
Magnetic Field ◽  
Power Generation ◽  
Growth Rate ◽  
Linear Theory ◽  
Nonlinear Theory ◽  
Taylor Instability ◽  
Rayleigh Taylor Instability ◽  
Image Position

Nonlinear theory of Rayleigh—Taylor instability in plasma supported by a vacuum magnetic field shows that the growth rate of the mode, unstable in the linear theory, increases if the wavelength of perturbation π lies betweenand 2πcrit. This might have an important bearing on the proposed thermonuclear MHD power generation experiments.

Nonlinear theory of surface-helical instability of a semiconductor plasma. III. Analysis of nonlinear effects

1980 ◽  
Vol 23 (5) ◽  
pp. 378-382
Author(s):  
F. G. Karavaev ◽  
B. A. Uspenskii ◽  
N. L. Chuprikov
Keyword(s):  
Nonlinear Theory ◽  
Nonlinear Effects ◽  
Semiconductor Plasma

Rayleigh–Taylor instability of a plasma in a magnetic field: nonlinear theory

1982 ◽  
Vol 27 (1) ◽  
pp. 129-134 ◽  
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Magnetic Field ◽  
Nonlinear Analysis ◽  
Linear Theory ◽  
Nonlinear Theory ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Taylor Instability ◽  
Rayleigh Taylor Instability ◽  
Linear Cut

Kaira & Kathuria used the method of multiple scales to develop nonlinear analysis of Rayleigh–Taylor instability of a plasma in a magnetic field. Their calculations remain valid only for wavenumbers k away from the linear cut-off value kc, and break down for wavenumbers near kc. The purpose of this paper is to treat the latter case. The solution uses the method of strained parameters. The results show the instability persists even at k = kc, despite the cut-off predicted by the linear theory.

scholarly journals A note on tsunamis: their generation and propagation in an ocean of uniform depth

1973 ◽  
Vol 60 (4) ◽  
pp. 769-799 ◽  
Author(s):  
Joseph L. Hammack
Keyword(s):  
Linear Theory ◽  
Linear Approximation ◽  
Frequency Dispersion ◽  
Nonlinear Effects ◽  
Solid Boundary ◽  
Far Field ◽  
Bed Deformation ◽  
Downstream Region ◽  
Generation Region ◽  
Block Section

The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion.Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion duringpropagationand the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and morerecently advocated by Ben jamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.

Nonlinear Ripple Formation in Sputter Erosion

1999 ◽  
Vol 585 ◽  
Author(s):  
A.-L. Barabási ◽  
B. Kahng ◽  
H. Jeong ◽  
S. Park
Keyword(s):  
Surface Morphology ◽  
Linear Theory ◽  
Characteristic Time ◽  
Nonlinear Effects ◽  
Morphological Features ◽  
Ripple Formation ◽  
Morphological Transitions ◽  
Sputter Erosion ◽  
Short Times

AbstractWe investigate the morphological features of sputter eroded surfaces, demonstrating that while at short times ripple formation is described by the linear theory, after a characteristic time the nonlinear terms determine the surface morphology. We also show that the morphological transitions induced by the nonlinear effects can be detected by monitoring the surface width and the erosion velocity.

Gurtin-Type Quasi-Variational Principle of Intelligent Structure Based on Nonlinear Theory

2010 ◽  
Vol 148-149 ◽  
pp. 1291-1295 ◽  
Author(s):  
Zong Min Liu ◽  
Hai Yan Song ◽  
Ji Ze Mao
Keyword(s):  
Variational Principle ◽  
Research And Development ◽  
Linear Theory ◽  
Nonlinear Theory ◽  
High Performance ◽  
Hot Spot ◽  
Large Strain ◽  
High Strength ◽  
Intelligent Structure ◽  
Intelligent Material

Intelligent structure is consistently identified as one of techniques getting much attention in the 21 century. With the research and development of intelligent material with large strain, high strength and high performance, the study on the non-linear theory of intelligent structure is a hot spot for research in the future. Based on nonlinear theory, Gurtin-type quasi-variational principle of nonlinear intelligent structure is established in this paper. Finally, some correlative problems are discussed.

Nonlinear thermal convection in an elasticoviscous layer heated from below

1977 ◽  
Vol 356 (1685) ◽  
pp. 161-176 ◽  
Keyword(s):  
Linear Theory ◽  
Nonlinear Effects ◽  
Horizontal Layer ◽  
Plane Poiseuille Flow ◽  
Elastic Parameters ◽  
Temperature Contrast ◽  
The Mean ◽  
Exchange Of Stability ◽  
Steady Convection ◽  
Adiabatic Temperature Gradient

The linear and nonlinear stabilities of a horizontal layer of an elasticoviscous fluid, whose stress-rate-of-strain relations are due to Oldroyd (1958), are studied. In the linear theory it is already shown that steady convection (the situation generally referred to as the exchange of stability) is preferred for all relevant values of the Prandtl number (which is the ratio of the kinematic viscosity to the thermal diffusivity). The study of nonlinear effects for slightly supercritical Rayleigh number (which measures the temperature contrast across the layer) shows that plane disturbances for the case where the exchange of stability is valid and plane or centred disturbances for the case of overstability are governed by equations similar to those derived by Hocking, Stewartson & Stuart (1972) for plane Poiseuille flow. The influence of elasticity is to give rise to a burst only when the principle of exchange of stability is valid and provided certain conditions relating to the elastic parameters of the fluid are satisfied. The effect of the adiabatic temperature gradient is also discussed. It is shown that it stabilizes the layer in the linear theory. However, in the nonlinear theory it can destabilize the layer if the ratio the mean temperature of the layer to the temperature difference across the layer is large enough. For most practical purposes it does not influence the conditions necessary for a burst to occur.

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