Two-dimensional Z-scan method for the measurement of optical nonlinear effects

1997 ◽  
Author(s):  
Peilin Chen ◽  
Ivan V. Tomov ◽  
Peter M. Rentzepis ◽  
Masato Nakashima ◽  
Joseph F. Roach
Keyword(s):  
Nonlinear Effects ◽  
Two Dimensional

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 Nonlinear processes in the bunched electron beams of high-power klystrons and the limits of analytical and one-dimensional numerical models applicability for their analysis.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
V.Y. Rodyakin ◽  
◽  
V.M. Pikunov ◽  
V.N. Aksenov ◽  
◽  
...  
Keyword(s):  
Electron Beam ◽  
High Power ◽  
Numerical Models ◽  
Nonlinear Effects ◽  
Analytical Models ◽  
Modulation Amplitude ◽  
Two Dimensional ◽  
One Dimensional ◽  
Charge Parameter ◽  
Program Data

We present the results of a comparative theoretical analysis of the electron beam bunching in a single-stage klystron amplifier using analytical models, a one-dimensional disk program, and a two-dimensional program. Data on the influence of various one-dimensional and two-dimensional nonlinear effects on the efficiency of electron beam bunching at different values of the space charge parameter and the modulation amplitude are presented. The limits of applicability of analytical and one-dimensional numerical models for electron beam bunching analysis in high-power klystron amplifiers are found.

Nonlinear effects in dense two-dimensional exciton polariton system

2001 ◽  
Vol 44 (10S) ◽  
pp. 54-57
Author(s):  
V D Kulakovskii ◽  
A I Tartakovskii ◽  
D N Krizhanovskii ◽  
M S Skolnick
Keyword(s):  
Nonlinear Effects ◽  
Two Dimensional

Stripes or spots? Nonlinear effects in bifurcation of reaction—diffusion equations on the square

1991 ◽  
Vol 434 (1891) ◽  
pp. 413-417 ◽  
Keyword(s):  
Pattern Formation ◽  
General Pattern ◽  
Reaction Diffusion ◽  
Nonlinear Effects ◽  
Neural Nets ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Linearized Model ◽  
Selection Of

Bifurcation to spatial patterns in a two-dimensional reaction—diffusion medium is considered. The selection of stripes versus spots is shown to depend on the nonlinear terms and cannot be discerned from the linearized model. The absence of quadratic terms leads to stripes but in most common models quadratic terms will lead to spot patterns. Examples that include neural nets and more general pattern formation equations are considered.

Conditional Nonlinear Optimal Perturbations of a Two-Dimensional Quasigeostrophic Model

2006 ◽  
Vol 63 (6) ◽  
pp. 1587-1604 ◽  
Author(s):  
Mu Mu ◽  
Zhiyue Zhang
Keyword(s):  
Singular Vector ◽  
Nonlinear Evolution ◽  
Initial Perturbation ◽  
Nonlinear Effects ◽  
Two Dimensional ◽  
Physical Problems ◽  
Maximum Value ◽  
The Difference ◽  
Quasigeostrophic Model ◽  
The Cost

Abstract Conditional nonlinear optimal perturbations (CNOPs) of a two-dimensional quasigeostrophic model are obtained numerically. The CNOP is the initial perturbation whose nonlinear evolution attains the maximum value of the cost function, which is constructed according to the physical problems of interests with physical constraint conditions. The difference between the CNOP and a linear singular vector is compared. The results demonstrate that CNOPs catch the nonlinear effects of the model on the evolutions of the initial perturbations. These results suggest that CNOPs are applicable to the study of predictability and sensitivity analysis when nonlinearity is of importance.

Characterization of nonlinear effects in a two-dimensional dielectric elastomer actuator

2010 ◽  
Vol 19 (10) ◽  
pp. 105027 ◽  
Author(s):  
Y Jhong ◽  
D Mikolas ◽  
T Yeh ◽  
W Fang ◽  
D Shaw ◽  
...  
Keyword(s):  
Nonlinear Effects ◽  
Dielectric Elastomer ◽  
Two Dimensional ◽  
Dielectric Elastomer Actuator

Energy transfer in rotating turbulence

1997 ◽  
Vol 337 ◽  
pp. 303-332 ◽  
Author(s):  
CLAUDE CAMBON ◽  
N. N. MANSOUR ◽  
F. S. GODEFERD
Keyword(s):  
Energy Transfer ◽  
Rotation Axis ◽  
Physical Space ◽  
Nonlinear Effects ◽  
Spectral Energy ◽  
Rossby Number ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Plane Normal

The influence of rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime found in an RDT (rapid distortion theory) analysis, cannot affect a homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (direct numerical simulation) results are collected here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on turbulence.The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping of the energy transfer due to rotation. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Roω=ω′/(2Ω) – ratio of r.m.s. vorticity and background vorticity – as the relevant rotation parameter, in accordance with DNS and EDQNM results.In addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (RoL<1 and Roω>1), which is characterized by a macro-Rossby number RoL based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in the wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In addition, a polarization of the energy distribution in this slow two-dimensional manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral length-scales. Finally a generalized EDQNM (eddy damped quasi-normal Markovian) model is used to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space. The results from the model are compared to recent LES results and are shown to agree well. While the EDQNM2 model was developed to simulate ‘strong’ turbulence, it is shown that it has a strong formal analogy with recent weakly nonlinear approaches to wave turbulence.

Three-Dimensional Analysis of Continuously Reinforced Concrete Pavements

2000 ◽  
Vol 1730 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Seong-Min Kim ◽  
Moon C. Won ◽  
B. Frank McCullough
Keyword(s):  
Reinforced Concrete ◽  
Three Dimensional ◽  
Drying Shrinkage ◽  
Nonlinear Effects ◽  
Element Model ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Transverse Steel ◽  
Three Dimensional Finite Element

Continuously reinforced concrete pavement (CRCP) performance depends primarily on early-age cracks that result from changes in temperature and drying shrinkage. Presented is the behavior of the CRCP due to the temperature change obtained by using a three-dimensional finite element model. The nonlinear effects of the bond-slip between concrete and steel and between concrete and base have been studied. Modeling for the curling effect and for the viscoelastic material characteristics also has been considered. The results from the two-dimensional and three-dimensional models have been compared to verify the possibility of using a two-dimensional model. From this study, it was found that crack width and concrete stress are dependent on the transverse steel arrangement near the edge (longitudinal joint), but they are almost independent in the interior of the slab. The tensile stress occurring at the top of the edge on the transverse steel location can be higher than that occurring at the top of the slab center. This represents the possibility of forming a transverse crack from the edge on the transverse steel location. The twodimensional model with the plane stress element gives results very close to those of the three-dimensional model, except near the edge.

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