Theory Of Nonlinear Interaction Research Articles

Multiphoton excitation and high harmonic generation in rectangular graphene quantum dot

The multiphoton excitation and high harmonic generation (HHG) processes are considered using the microscopic quantum theory of nonlinear interaction of strong coherent electromagnetic (EM) radiation with rectangular graphene quantum dot (RGQD). The dynamic Hartree–Fock approximation is developed for the consideration of the quantum dot-laser field nonlinear interaction at the nonadiabatic multiphoton excitation regime. The many-body Coulomb interaction is described in the extended Hubbard approximation. By numerical results, we show the significance of the RGQD lateral size, shape, and EM wavefield orientation in RGQD of the zigzag edge compear to the armchair edge in the HHG process allowing for increasing the cutoff photon energy and the quantum yield of higher harmonics. The differences via edge on the elongated side of the RGQD have been explained by the investigation of the dipole momentum in both cases. Numerical results have shown that the HHG spectra have a strong anisotropy depending on the orientation of the laser wave, and the cutoff photon energy shifts toward blue with an increase in the transverse size of the RGQD.

A New Mechanism for the Generation of Quasi‐6‐Day and Quasi‐10‐Day Waves During the 2019 Antarctic Sudden Stratospheric Warming

AbstractUsing the Modern‐Era Retrospective analysis for Research and Applications version 2 reanalysis and Aura Microwave Limb Sounder geopotential height and temperature observations, two unusual planetary waves (PWs) with westward zonal wavenumber 1 (W1) and periods of ∼6.0 and ∼9.6 days are identified during a rare Antarctic sudden stratospheric warming (SSW) event in September 2019, which follow a strong W1 PW with period of ∼7.4 days. It is found that the W1 ∼7.4‐day wave is actually the representation of the climatological W1 quasi‐6‐day wave before the September equinox, which peaks on September 10, 2019. Meanwhile, a strong zonally symmetric wave with period of ∼32.2 days occurs in the Southern Hemisphere with a maximum zonal wind amplitude of ∼27 m/s at 65°S and 48 km. Interestingly, the frequencies and zonal wavenumbers of the W1 ∼7.4‐day, ∼6.0‐day, ∼9.6‐day and zonally symmetric ∼32.2‐day waves exactly satisfy the nonlinear interaction theory between PWs. We thus proposed for the first time the occurrence of nonlinear interaction between a W1 ∼7.4‐day wave and a zonally symmetric ∼32.2‐day wave, which generates two W1 PWs with periods of ∼6.0 and ∼9.6 days. The Eliassen‐Palm flux diagnostics suggest that the zonally symmetric ∼32.2‐day wave also contributes to the wind deceleration during this SSW. Moreover, the baroclinic/barotropic instabilities related to the vertical shear in the zonal wind during the SSW considerably enhance the PW activities in the Antarctic stratosphere. The climatological variations of the instabilities and critical layers in the mesosphere can also influence the propagation of these three W1 PWs.

Higher Harmonic Generation of Coherent Sub-THz Radiation at Lifshitz Transition in Gapped Bilayer Graphene

The microscopic quantum theory of nonlinear interaction of strong coherent electromagnetic radiation with gapped bilayer graphene is used for consideration of the high harmonic generation at low-energy photon excitation Lifshitz transition. The Liouville–von Neumann equation for the density matrix is solved numerically at the nonadiabatic multiphoton excitation regime. By numerical solutions, we examine the rates of the second and third harmonics generation at the particle-hole annihilation at Lifshitz transitions in the linearly polarized coherent electromagnetic wave. The obtained results show that the gapped bilayer graphene can serve as an effective medium for the generation of even and odd high harmonics in the sub-THz domain of frequencies.

Theory of nonlinear interactions between x rays and optical radiation in crystals

We show that the nonlinear interactions between x rays and longer wavelengths in crystals depend strongly on the band structure and related properties. Consequently, these types of interactions can be used as a powerful probe for fundamental properties of crystalline bulk materials. In contrast to previous work that highlighted that these types of nonlinear interactions can provide microscopic information on the valence electrons at the atomic scale resolution, we show that these interactions also contain information that is related to the periodic potential of the crystal. We explain how it is possible to distinguish between the two contributions. Our work indicates on the possibility for the development of novel multi-dimensional pump-probe metrology techniques that will provide spectroscopic information combined with structural information including ultrafast dynamics at the atomic scale.

A Nonlinear Theory of Interaction between Electron Beams and High-Frequency Fields in Media with Complex Conductivity

Based on the Ovcharov–Solntsev wave approach, an approximate nonlinear theory is proposed for interaction between electron beams and high-frequency fields in media with complex conductivity.

Нелинейная теория взаимодействия трубчатого пучка заряженных частиц с поверхностными волнами в плазменном цилиндре

Нелинейная теория взаимодействия трубчатого пучка заряженных частиц с поверхностными волнами в плазменном цилиндре

A Theory of Nonlinear Interactions Between Signal and Amplified Spontaneous Emission Noise in Coherent Wavelength Division Multiplexed Systems

A general theory of nonlinear interactions between signal and amplified spontaneous emission noise in wavelength division multiplexed fiber-optic coherent transmission systems is presented. This theory is based on the regular perturbation treatment of the nonlinear Schrodinger equation, which governs the wave propagation in the optical fiber, and is exact up to the first order in the fiber nonlinear coefficient. It takes into account all cross-channel nonlinear four-wave mixing contributions to the total variance of nonlinear distortions, dependency on modulation format, erbium-doped fiber and backward Raman amplification schemes, heterogeneous spans, and chromatic dispersion to all orders; moreover, it is computationally efficient. This theory is used to estimate the impact of the signal-noise interaction on the unmitigated, as well as on the nonlinearity-mitigated systems with ideal multi-channel digital backpropagation, and to study the fundamental limits of zero-forcing nonlinear equalization of the fiber-optic coherent transmission systems.

Semi-Classical theory of Nonlinear interaction of circularly polarized optical vortex beam with plasma channel

A semiclassical approach of nonlinear interaction of intense circularly polarized optical vortex Laguerre-Gaussian (LG) beam modes with a plasma channel is analyzed theoretically and numerically. We study an exchange of angular momentum between the vortex beam and plasma channel. The transfer of angular momentum and the generated magnetic field are calculated. We have observed that both the generated magnetic field and angular momentum transfer depend on beam mode, intensity, and the polarization state of beam mode.

The magnetic hole as plasma inhomogeneity in the solar wind and related interplanetary medium perturbations

We considered magnetic hole-type plasma structures with a constant total pressure, which are often observed in the flux of the solar wind. The interaction between a linear magnetic hole and the front of the primary or bow shock wave before the Earth’s magnetosphere was studied, and the appearance of a fast shock wave in the magnetosheath and displacement of the bow shock front in the direction of the Earth’s magnetosphere is described. The magnetic hole in the scope of the MHD theory is considered a plasma inhomogeneity bounded by two tangential discontinuities: the front and rear boundaries. Based on the MHD theory of nonlinear interactions of solar wind discontinuity structures with a magnetic hole, the appearance of new automodel and MHD shock waves inside the magnetic hole is shown. The obtained results, which provide evidence of a change in the configuration of the magnetic hole and a displacement of the bow shock front due to the perturbation from the solar wind, are qualitatively verified in many aspects by observations performed earlier by the Cluster and ACE spacecrafts.

Исключение параметрических резонансных колебаний в движителе быстроходных гусеничных машин

The article contains a brief overview of the results of studies of elastic interaction of a caterpillar with a variety of soils and types of irregularities, forming a dynamic loading mover. The conclusion about the need to consider the periodic changes in the rigidity of the elastic interaction of tire road wheels with rubberized running track, which may lead to the appearance of parametric resonance. Based on the theory of nonlinear interaction of elastic elements are determined by the region of stability of parametric oscillations is determined by the minimum value of the modulation depth hardness of the elastic interaction, providing an exception parametric resonances at high speeds. The experimental validation of the developed mathematical model of the machine when driving on paved roads confirms the hypothesis of limited longevity of elements of caterpillar tracks. In accordance with the results of the study suggested embodiment of the caterpillars, which provides an exception parametric resonance. It shows the results of evaluating the effectiveness of the study.

A gentle stroll through EP flux theory

The celebrated 1960 paper by Eliassen & Palm (hereafter EP) put on record several brilliant discoveries in the theory of linear waves on shear flows for rotating stratified fluid systems. These discoveries opened up a new perspective on linear wave dynamics in the atmosphere and on the nascent theory of nonlinear interactions between the waves and the mean flow. Arguably, the most important discovery was that of their eponymous wave activity flux vector in the meridional plane and of the conditions under which this important flux was non-divergent.In this short paper we will retrace some of the steps of EP and explore how their path-breaking discoveries came to be understood in the light of subsequent theories. Of course, an endeavour like this runs the risk of looking patronizing, if only because of 50 years of hindsight, but this is not intended: it was the power of their original discoveries that inspired five decades of further research, with new results still coming out today.

A time-dependent nonlinear theory and simulation for gyroklystron amplifier

A time-dependent nonlinear theory for gyroklystron amplifier is presented. The theory includes a time-dependent description of the electromagnetic fields and a self-consistent analysis of the electrons. The generalized telegrapher equations represent the electromagnetic fields. The equations of motion of the electrons are described in the framework of the guiding-center approximation. All trajectories are calculated and used as current sources for the fields. The nonlinear theory of interaction is investigated in which mode coupling is taken into account in varying wall radius. Transverse velocity of the electrons from the gyroklystron amplifier satisfies Gaussian distribution. Distribution model of the velocity spread in the gyroklystron amplifier beam-wave interaction is established. A code for the self-consistent nonlinear beam-wave interaction is developed based on the presented theory. The electron beam-wave interaction of a Kα band gyroklystron amplifier is thoroughly studied and analyzed by the code. Numerical verification using MAGIC simulation is also given. The numerical results are in good agreement with the self-consistent nonlinear simulations.

CHAOTIC VIBRATIONS OF TWO-LAYERED BEAMS AND PLATES WITH GEOMETRIC, PHYSICAL AND DESIGN NONLINEARITIES

In this paper, the theory of nonlinear interaction of two-layered beams and plates taking into account design, geometric and physical nonlinearities is developed. The theory is mainly developed relying on the first approximation of the Euler–Bernoulli hypothesis. Winkler type relation between clamping and contact pressure is applied allowing the contact pressure to be removed from the quantities being sought. Strongly nonlinear partial differential equations are solved using the finite difference method regarding space and time coordinates. On each time step the iteration procedure, which improves the contact area between the beams is applied and also the method of changeable stiffness parameters is used. A computational example regarding dynamic interaction of two beams depending on a gap between the beams is given. Each beam is subjected to transversal sign-changeable load, and the upper beam is hinged, whereas the bottom beam is clamped. It has been shown that for some fixed system parameters and with an increase of the external load amplitude, synchronization between two beams occurs with the upper beam vibration frequency. Qualitative analysis of the interaction of two noncoupled beams is also extended to the study of noncoupled plates. Charts of beam vibration types versus control parameters {q0, ωp}, i.e. the frequency and amplitude of excitation are constructed. Similar and previously described competitions have been reported in the case of two-layered plates.

Stimulated second-order processes in the interaction of a spinless quantum particle beam with a self-consistent electromagnetic field

A nonlinear theory of interaction of two electromagnetic waves with a beam or a gas of spinless charged particles is developed. The effects of stimulated Compton scattering of electromagnetic waves and stimulated particle pair production (annihilation) during a collision of two electromagnetic quanta are investigated. Other stimulated processes that can occur only in a medium and decelerate electromagnetic waves are also considered. The relation between stimulated processes and various types of instabilities considered in classical electrodynamics of plasmas and plasmalike media is demonstrated.

A two scale nonlinear fractal sea surface model in a one dimensional deep sea

Using the theory of nonlinear interactions between long and short waves, a nonlinear fractal sea surface model is presented for a one dimensional deep sea. Numerical simulation results show that spectra intensity changes at different locations (in both the wave number domain and temporal-frequency domain), and the system obeys the energy conservation principle. Finally, a method to limit the fractal parameters is also presented to ensure that the model system does not become ill-posed.

Photon higher-order squeezing effects of the q analogue of a single-mode field interacting with a Ξ-type three-level atom

The nonlinear theory of interaction between the q analogue of a single-mode field and a Ξ-type three-level atom has been established. And the formal solution of the Schrödinger equation in the representation and its average number are obtained. Then, the photon squeezing effects are studied through numerical calculation. The results show that the q deformation nonlinear action has a lot of influence on the quantum coherence and quantum properties. When q approaches 1, the theory reduces to the common linear theory.

Nonlinear interaction of internal waves in the coastal zone of the Sea of Japan

Nonlinear interactions of the internal waves of a tidal period with low-frequency synoptic-scale internal waves are studied using instrumental measurements of the current in the coastal zone of the Sea of Japan. In the course of spectral analysis of the data of instrumental measurements, it is found that a maximum in the spectrum of the kinetic energy of coastal waters in the vicinity of the semidiurnal frequency ω0 is surrounded by satellite maxima whose frequencies obey the relation ωs = ω0 ± Ω, where Ω is the characteristic frequency of synoptic-scale internal waves. The spectrum of the anticyclonic current component has a similar structure in the vicinities of the frequency ω0 and its first and second harmonics. The general theory of nonlinear interactions of weakly dispersive waves is used to solve the problem of modulation and the parametric amplification of tidal internal waves in the coastal zone using low-frequency narrow-band internal waviness. As can be judged from the literature, the effect of parametric modulation of tidal internal waves by low-frequency synoptic-scale internal waves has been recorded in the coastal zone of a tidal sea for the first time.

A Numerical Study on Gravity Wave Excited Through Nonresonant Interaction

AbstractBy using a 2nd order operator‐splitting scheme and taking a fully nonlinear model, numerical simulation of gravity wave excited through nonresonant interaction in a compressible atmosphere is carried out. The results show that a downward propagating gravity wave packet is excited by two up‐going gravity wave packets owing to the nonresonant interaction. The energy of the excited wave is almost proportional to the energy of the primary wave, and increases slowly with initial energy of the secondary wave growing up, too. Wave energy tends to transfer mainly from the primary wave with highest frequency to other two waves, which isn't completely consistent with the resonant interaction. The characteristic time of the nonresonant interaction depends on the initial positions, wavelengths and frequencies of the primary and secondary wave, however, is independent of their initial amplitudes. The wave vector of the excited wave doesn't strictly satisfy the wave vector matching condition which is predicted by the weakly nonlinear interaction theory, and moreover, the wavelength and frequency of the excited wave are found to vary with time in the propagation. These indicate the weakly nonlinear interaction theory is limited to some extent for the nonresonant interaction.

Analytical study of nonlinear vibrations of a charged viscous liquid drop

The generatrix of a nonlinearly vibrating charged drop of a viscous incompressible conducting liquid is found by directly expanding the equilibrium spherical shape of the drop in the amplitude of initial multimode deformation up to second-order terms. A fact previously unknown in the theory of nonlinear interaction is discovered: the energy of an initially excited vibration mode of a low-viscosity liquid drop is gradually (within several vibrations periods) transferred to the mode excited by only nonlinear interaction. Irrespectively of the form of the initial deformation, an unstable viscous drop bearing a charge slightly exceeding the critical Rayleigh value takes the shape of a prolate spheroid because of viscous damping of all the modes (except for the fundamental one) for a characteristic time depending on the damping rates of the initially excited modes and the further evolution of the drop is governed by the fundamental mode. In a high-viscosity drop, the rate of rise of the unstable fundamental mode amplitude does not increase continuously with time, contrary to the predictions of nonlinear analysis in terms of the ideal liquid model: it first decreases to a value slightly differing from zero (which depends on the extent of supercriticality of the charge and viscosity of the liquid), remains small for a while (the unstable mode amplitude remains virtually time-independent), and then starts growing.

Sound interaction with moving vortices

This report is devoted to the nonlinear acoustic pressure of sound waves propagating in the vicinity of a rather general class of localized flows induced by the motion of spherically symmetric structures of the type of vortices in the liquid, say, biological, atmosphere, or ocean inhomogeneous environment. As a result expressions for cyclic and mean forces exerted on a vortex are derived. Conventional general expression for transport cross section derived in nonlinear theory of interaction of sound with rigid particles is proven to be incorrect for the vortex-sound interaction case. The absence of mean force is demonstrated for specific case of Hills vortex both in the traveling and standing sound wave fields. It is underlined, however, that the force could be observable if the distribution of mean sound energy in the incident sound field in the frames of vortex dimensions could be characterized by a nonzero spatial gradient. Instead of the previously used expression for mean radiation force exerted on a moving inhomogeneity valid for a solid particle based on its transport cross section, the correct generalized expression for force exerted on vortex structure is derived.