Analysis Of Nonlinear Interaction Research Articles

Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation

In this paper we obtain the rate equations for Zeeman coherences in the broad-line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad-line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations in a straightforward way. We compare our approach with the perturbation-theory approach as given previously and show that our approach is more flexible for analyzing various experiments. Meanwhile we also show the validity and limitations of the application of the rate equations in experiments with coherent atomic excitation when either the broad-line approximation or steady-state conditions hold. Thus we have shown the basis for modeling the coherent atomic excitation experiments by using the relatively simple rate equations, provided that certain experimental conditions hold.

A meshless Hermite-Cloud method for nonlinear fluid-structure analysis of near-bed submarine pipelines under current

Through higher-order Hermite construction of the interpolation functions, a novel true meshless numerical technique—the Hermite-Cloud method is developed for the analysis of nonlinear fluid-structure interaction of near-bed submarine pipelines under a current. Following the development of the discrete point collocation technique throughout the computational domains, the present method constructs the approximations of both the unknown functions and their first-order derivatives based on the classical reproducing kernel particle method, except that a fixed reproducing kernel approximation is employed instead. For partial differential equations with boundary conditions, certain auxiliary conditions are required due to the use of the Hermite theorem. After validation of the presently developed Hermite-Cloud method by several two-dimensional elasticity examples, the method is used for the failure analysis of a near-bed submarine pipeline under a horizontal current with consideration of a nonlinear fluid–structure interaction effect. The numerical result indicates that the distance from the pipelines to seabed and the current velocity have remarkable influences on the deformation behavior of the pipelines. It also shows that various critical current velocities corresponding to different failure patterns exist, and the presently simulated relation of the critical velocities agrees with the results in the previous publications.

Statistical analysis of nonlinear wave interactions in simulated Langmuir turbulence data

Abstract. We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identify two and three wave processes in the data, and the Volterra model was furthermore employed to evaluate the direction and magnitude of energy transfer between the wave modes in the case of Langmuir wave decay. We demonstrate that these methods allow one to determine the relative importance of strongly and weakly turbulent processes. The statistical validity of the results was thoroughly tested using surrogated data set analysis.Key words. Space plasma physics (wave-wave interactions; experimental and mathematical techniques; nonlinear phenomena)

Three-Dimensional Analysis of Nonlinear Interaction Between Water Waves and Vertical Permeable Breakwater

This paper investigates the wave-induced flow field and water particle movement inside and around a vertical permeable structure, which is affected by the interaction between water waves and porous media. A three-dimensional fully nonlinear numerical model is developed to study the interaction between water waves and permeable structures. Modified resistance terms inside the equations of motion are proposed, which are able to consider the size of porous material directly inside the governing equations. It is understood that the wave-induced flow field and water particle movement inside and around the permeable structure are strongly influenced by the wave period or relative width of the permeable structure (structure width to wavelength ratio). Other parameters such as porous material size, porosity, and resistance coefficients affect the flow field. However, their degree of influence differs depending on the wave period.

The coupled finite element and boundary element analysis of nonlinear interactions between waves and bodies

A coupled finite element (FEM) and boundary element (BEM) method is developed to analyse the nonlinear interaction between bodies and water waves. The former is used away from the body while the latter is used in a region near body. The combination is based on consideration of the efficiency of FEM and BEM in computation and mesh generation, respectively. Results for wave/body interactions are obtained by using auxiliary functions to decouple the mutual dependence of the body acceleration and the wave force.

Quantitative analysis of cardiovascular interactions in patients with cardiomyopathy and after myocardial infarct

The aim of this study was to detect pathological changes of the complex autonomous regulation of ecg, blood pressure and respiration (synchronously recordings of 30 minutes) in patients with cardiac diseases. We investigated the cardiovascular and cardiorespiratory linear and nonlinear interactions in 10 patients with dilative cardiomyopathy (dcm) and in 10 patients after myocardial infarction (mi). We compared results from the classical linear correlation function analysis with results from the mutual information method (transinformation) for analysis of nonlinear and linear interactions. Both methods yield high significant parameters (p < 0.01). Thus, we found both linear and nonlinear interactions with partly different specificity in patients with dcm and mi compared to healthy subjects (ref).

Projection operators for time-symmetrized states in Fock space

Projection operators associated with antiunitary time-reversal symmetry differ from the usual orthogonal projections encountered in Hilbert space. Operators that act in Fock space and project parts of a single-mode state of the electromagnetic field that can be identified as its quadratures are defined and their properties are verified by consideration of their action on single-mode coherent states. The fact that their construction involves, in an essential way, not one but two parameters is discussed and a weakened form of orthogonal projection that is specialized to a particular Fock state superposition is identified. The question of whether or not such orthogonal projections are universal is raised. In passing, it is noted that the possibility of classifying states as well as operators according to their time-reversal symmetry properties is relevant to the analysis of nonlinear wave interactions between waves with rationally related frequencies.

Nonlinear analysis of 3D seismic interaction of soil–pile–structure systems and application

To investigate more precisely the seismic response of interactive soil–pile–structure systems, a three-dimensional finite element subsystem methodology with an advanced plasticity-based constitutive model for soils has been developed. The structure subsystem is represented by space frame elements while the pile–soil subsystem is idealized as an assemblage of solid elements. By means of the δ*-version of the hierarchical single surface (HiSS) modelling approach for cyclic behavior of soft clays, tangent matrices of the soil properties are formulated with distinct constitutive laws for individual stress–strain regimes such as virgin loading, unloading, and reloading. A successive-coupling, incremental solution scheme in the time domain is created to take account of both inertial and kinematic soil–pile–structure interactions simultaneously. The seismic inputs can be any combination of three-dimensional motions. The proposed methodology may be used to analyse the seismic responses of structures for different support excitations such as rigid ground motion, interactive pile-foundation motion, and, for long span structures, non-uniform free-field motion.

Three-dimensional non-linear soil-building interaction analysis in the lakebed zone of Mexico city during the hypothetical Guerrero earthquake

The 1985 Michoacan earthquake (M=8·1) caused very severe damage to mid-rise buildings in the lakebed zone of Mexico City, which is approximately 400 km from the epicentre in the Pacific Ocean. In the present study, we perform a three-dimensional (3-D) non-linear soil–building interaction analysis for several types of low- to high-rise buildings during the hypothetical Guerrero earthquake, and try to understand the real cause of heavy damage to mid-rise buildings in the lakebed zone during the 1985 Michoacan earthquake. We make a reasonable estimation of the input earthquake motions and the local site effects. The non-linear soil-building interaction analysis explains the damage pattern observed during the 1985 earthquake, although other analyses do not. We realize that all the factors from the earthquake source to the building superstructure must be taken into account adequately. © 1998 John Wiley & Sons, Ltd.

Analysis of nonlinear interaction of flexural modes of round cylindrical shells under periodic excitation

The processes occurring during the nonlinear interaction of flexural modes of round cylindrical shells under radial oscillating pressure, distributed unevenly over the lateral surface, are studied.

Elasto-plastic coupled analysis of buried structure and soil medium by perturbational semi-analytic method

In this paper, an effective numerical method for physically nonlinear interaction analysis is studied, in which the elasto-plastic problem of coupled analysis between the structure and medium may be transformed into several linear problems by mean of the perturbation technique, then, the finite strip method and finite layer method are used to analyse the underground structure and rock medium, respectively, for their corresponding linear problems, so the purpose of simplifing the calculation can be achieved. This kind of method has made use of the twice semi-analytical technique: the perturbation and semi-analytic solution function to simplify 3-D nonlinear coupled problem into 1-D linear numerical one. In addition, this method is a new advance of semi-analytical method in the application to nonlinear problems by means of combinating with the analytical perturbation method, and it is also a branch of the perturbational numerical method developed in last years.

Pointwise convergence to shock waves for viscous conservation laws

We are interested in the pointwise behavior of the perturbations of shock waves for viscous conservation laws. It is shown that, besides a translation of the shock waves and of linear and nonlinear diffusion waves of heat and Burgers equations, a perturbation also gives rise to algebraically decaying terms, which measure the coupling of waves of different characteristic families. Our technique is a combination of time-asymptotic expansion, construction of approximate Green functions, and analysis of nonlinear wave interactions. The pointwise estimates yield optimal Lp convergence of the perturbation to the shock and diffusion waves, 1 ≤ p ≤ ∞. The new approach of obtaining pointwise estimates based on the Green functions for the linearized system and the analysis of nonlinear wave interactions is also useful for studying the stability of waves of distinct types and nonclassical shocks. These are being explored elsewhere. © 1997 John Wiley & Sons, Inc.

Cross‐bispectral analysis of the electromagnetic field in a beam‐plasma interaction

The use of bicoherence has proved its efficiency in the analysis of nonlinear wave interactions. The method has been adapted to interpret the results of a simulation of the beam‐plasma interaction, in a case of broadband spectra, where many unstable modes can be suspected to couple. As the interacting waves exhibit different polarizations (electrostatic and electromagnetic), the bicoherence has been modified into a cross bicoherence in order to test the coupling of different field components. The visualization of the result has been designed in order to evidence the couplings in terms of efficiency (high bicoherence) and energy (high power). The application of this method to the simulation results shows that quadratic wave interactions are effective; new helpful information is stressed in order to interpret the observed growth of large‐scale magnetic fluctuations.

Theory of nonlinear multiple-grating interaction in diffusion-dominated photorefractive media: errata

Using a new model based on the so-called perturbational approach, we present a theoretical analysis of nonlinear multiple-grating interaction in diffusion-dominated photorefractive materials. This process appears when more than one grating at a time is induced in a photorefractive crystal. The interaction is caused by the nonlinear terms in the band-transport equations, and it is highly dependent on the intensity ratios of the writing beams. We show that, in a three-wave mixing scheme in which one reference beam and two nearly coincident object beams are incident upon a photorefractive crystal, one holographic grating is strongly influenced by the presence of the other. It appears that higher harmonic gratings, together with so-called sideband gratings, have a significant influence on the primary gratings. We show, for the first time to our knowledge, that in the transient case the temporal grating buildup exhibits a much more complex behavior compared with the linear case, in which only one grating is present. We also show that in the steady state one grating can experience everything ranging from total extinction to an enhancement of more than 50% when a second grating is induced. Our theoretical results are in good agreement with previously presented experimental results.

Theory of nonlinear multiple-grating interaction in diffusion-dominated photorefractive media

Using a new model based on the so-called perturbational approach, we present a theoretical analysis of nonlinear multiple-grating interaction in diffusion-dominated photorefractive materials. This process appears when more than one grating at a time is induced in a photorefractive crystal. The interaction is caused by the nonlinear terms in the band-transport equations, and it is highly dependent on the intensity ratios of the writing beams. We show that, in a three-wave mixing scheme in which one reference beam and two nearly coincident object beams are incident upon a photorefractive crystal, one holographic grating is strongly influenced by the presence of the other. It appears that higher harmonic gratings, together with so-called sideband gratings, have a significant influence on the primary gratings. We show, for the first time to our knowledge, that in the transient case the temporal grating buildup exhibits a much more complex behavior compared with the linear case, in which only one grating is present. We also show that in the steady state one grating can experience everything ranging from total extinction to an enhancement of more than 50% when a second grating is induced. Our theoretical results are in good agreement with previously presented experimental results.

Theoretical analysis of nonlinear interaction of intense electromagnetic wave and plasma waves in the ionosphere

AbstractIt is well known that refraction, Faraday rotation, scintillation and absorption of microwaves take place when a microwave passes through an ionospheric plasma. However, when the amplitude of the microwave is large, nonlinear interactions occur with plasma in addition to these plasma interactions with a small signal microwave. Various phenomena not conceivable for weak microwaves used in communication can take place. Especially, it is predicted that the three‐wave resonance, which is the most fundamental nonlinear wave‐wave interaction, can be applied to the nonlinear wave‐wave interaction between the plasma and a large signal microwave.In this paper, the generating condition of the electrostatic plasma wave phenomena excitated in the plasma medium by a large signal electromagnetic wave is theoretically investigated and the nonlinear coupling coefficient between the large signal electromagnetic wave and the electrostatic plasma wave is derived.

Three-wave non-linear interaction in a three-dimensional compressible boundary layer

A perturbation method for analysis of non-linear wave interaction in three-dimensional compressible boundary layer is developed. The method is based on a biorthogonal eigenfunction system for three-dimensional compressible boundary layers. It is assumed that characteristic space and time scales of the disturbances are much less than space and time scales of non-linear development and an averaging technique in intermediate scales may be applied. The method is a generalization of Zelman's results for two-dimensional incompressible boundary layer. As an example, a three-wave interaction is considered. A numerical example for so-called Tollmien — Schlichting wave interaction shows the possibility of amplification for rather broad packets without an exact resonance synchronizm for three-wave interaction.

Observation of equatorially trapped waves in the Pacific using Geosat altimeter data

A spatial integration filtering method is applied to process 4.5 years of Geosat altimeter sea level anomalies(SLA) recorded from 1 April 1985 to 17 September 1989. The integral limits are chosen as ±1.5° latitude centered at the equator and ±4° longitude centered at the each central longitude. These limits are chosen in order to eliminate the random noise and to enhance the equatorially trapped wave signals. The spatial-integration-filtered SLA time series show periodical signals with different time scales. Processing the SLA time series with a Short Time Fourier Transform (STFT) yields the time-frequency spectra of the SLA which show a frequency spectral splitting-combining phenomenon in the periods during and after the 1986–1987 El Niñio-Southern Oscillation (ENSO) event. Analysis of non-linear wave-wave interaction indicates that this phenomenon results from amplitude modulation of the short period oscillations in the 60–100 day band by a long period oscillation with a period of about 500 days. The wave components of the short period oscillations are further analysed using the equatorial wave modes to fit the meridional distribution of the SLA. The results indicate that the downwelling Kelvin wave mode before and during the peak phase of 1986–1987 ENSO and the upwelling Kelvin wave mode during the 1988 La Niña are the dominant components. The first and second Rossby wave modes play important roles for entire time series and occasionally become the dominant components. The mean phase speed of Kelvin wave mode during the 1986–1987 ENSO is 3.0 m s −1 which is 25% higher than those in non-ENSO periods.

Nonlinear transient dynamic analysis of soil-pavement interaction under moving load: a coupled BEM-FEM approach

The nonlinear transient dynamic analysis of a 3-D linear elastic pavement placed on an elastoplastic soil medium, subject to a moving load, is presented. The time domain nonlinear boundary element method for the soil medium is combined with the finite element method for the pavement. The nonlinear BEM is based on an initial stress approach. The accuracy of the algorithm is verified by comparison with available analytical solutions and published numerical results.

Comment on Z. G. Chen and Döring analysis of nonlinear beam-wave interaction of gyro-peniotron at harmonics

Comment on Z. G. Chen and Döring analysis of nonlinear beam-wave interaction of gyro-peniotron at harmonics