Multi-ion Mach–Zehnder interferometer with artificial nonlinear interactions

We propose a method to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By manipulating the coupling strength between two involved internal states of the ions, we could achieve the beam splitting/recombination with NOON states. Using current techniques for manipulating trapped ions, we discuss the experimental feasibility of our scheme and analyze some undesired uncertainty under realistic experimental environment.

Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves are also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoreti- cal autocorrelation and spectral density functions of the first and the second orders are derived. The boundary conditions for the determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.

Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions

Recently, cavity optomechanics has become a rapidly developing research field exploring the coupling between the optical field and mechanical oscillation. Cavity optomechanical systems were predicted to exhibit rich and nontrivial effects due to the nonlinear optomechanical interaction. However, most progress during the past years have focused on the linearization of the optomechanical interaction, which ignored the intrinsic nonlinear nature of the optomechanical coupling. Exploring nonlinear optomechanical interaction is of growing interest in both classical and quantum mechanisms, and nonlinear optomechanical interaction has emerged as an important new frontier in cavity optomechanics. It enables many applications ranging from single-photon sources to generation of nonclassical states. Here, we give a brief review of these developments and discuss some of the current challenges in this field.

Numerical study of nonlinear interactions of bi-chromatic progressive deep-water waves

This paper proposes a 3-D non-hydrostatic free surface flow model with a newly proposed general boundary-fitted grid system to simulate the nonlinear interactions of the bi-chromatic deep-water gravity waves.First,the monochromatic bidirectional and bi-chromatic bidirectional waves of small wave steepness are successively simulated to verify the abilities of the numerical model.Then,a series of bi-chromatic progressive waves of moderate wave steepness and different crossing angles are simulated and analyzed in detail.It is found that if the crossing angle is close to or smaller than the resonant angle,apparent discrepancies are observed among the numerical results,the linear wave theory,and the steady third-order theory.Otherwise,the three solutions coincide well.Through analysis,it is concluded that the discrepancies are caused by the third-order quasi-resonant interactions between the bi-chromatic progressive waves.Such interactions not only could modify the wave spectrum,but could also change the wave shape patterns.

A Perspective on the Evolution of Atmospheric Blocking Theories:From Eddy-Mean flow Interaction to Nonlinear Multiscale Interaction

In this paper,we first review the research advancements in blocking dynamics and highlight the merits and drawbacks of the previous theories of atmospheric blocking.Then,the dynamical mechanisms of atmospheric blocking are presented based on a nonlinear multi-scale interaction(NMI)model.Previous studies suggested that the eddy deformation(e.g.,eddy straining,wave breaking,and eddy merging)might lead to the formation and maintenance of atmospheric blocking.However,the results were speculative and problematic because the previous studies,based on the time-mean eddy-mean flow interaction model,cannot identify the causal relationship between the evolution of atmospheric blocking and the eddy deformation.Based on the NMI model,we indicate that the onset,growth,maintenance,and decay of atmospheric blocking is mainly produced by the spatiotemporal evolution of pre-existing upstream synoptic-scale eddies,whereas the eddy deformation is a concomitant phenomenon of the blocking formation.The lifetime of blocking is mainly determined by the meridional background potential vorticity gradient(PVy)because a small PVyfavors weak energy dispersion and strong nonlinearity to sustain the blocking.But the zonal movement of atmospheric blocking is associated with the background westerly wind,PVy,and the blocking amplitude.Using this NMI model,a bridge from the climate change to sub-seasonal atmospheric blocking and weather extremes might be established via examining the effect of climate change on PVy.Thus,it is expected that using the NMI model to explore the dynamics of atmospheric blocking and its change is a new direction in the future.

A numerical study on matching relationships of gravity waves in nonlinear interactions

Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are discussed.In resonant interactions,the wavelengths of the excited wave are in good agreement with the values derived from sum or difference resonant conditions,and the frequencies of the three waves also satisfy the matching condition.Since the interacting waves obey the resonant conditions,resonant interactions have a reversible feature that for a resonant wave triad,any two waves are selected to be the initial perturbations,and the third wave can then be excited through sum or difference resonant interaction.The numerical results for nonresonant triads show that in nonresonant interactions,the wave vectors tend to approximately match in a single direction,generally in the horizontal direction.The frequency of the excited wave is close to the matching value,and the degree of mismatching of frequencies may depend on the combined effect of both the wavenumber and frequency mismatches that should benefit energy exchange to the greatest extent.The matching and mismatching relationships in nonresonant interactions differ from the results of weak interaction theory that the wave vectors are required to satisfy the resonant matching condition but the frequencies are permitted to mismatch and oscillate with amplitude of half the mismatching frequency.Nonresonant excitation has an irreversible characteristic,which is different from what is found for the resonant interaction.For specified initial primary and secondary waves,it is difficult to predict the values of the mismatching wavenumber and frequency for the excited wave owing to the complexity.

Nonlinear parametric interactions in ion-implanted semiconductor plasmas having strain-dependent dielectric constants

We report nonlinear parametric interactions using a hydrodynamic model of ion-implanted semiconductor plasmas having strain-dependent dielectric constants（SDDC）. High-dielectric-constant materials are technologically important because of their nonlinear properties. We find that the third-order susceptibility varies in the range 10^-14--10^-12m^2·V^-2 for ion-implanted semiconductor plasmas, which is in good agreement with previous results. It is found that the presence of SDDC in ion-implanted semiconductor plasma modifies the characteristic properties of the material.

Super-ballistic diffusion in a quasi-periodic non-Hermitian driven system with nonlinear interaction

We investigate the effects of nonlinear interactions on quantum diffusion in a quasi-periodic quantum kicked rotor system,featuring a non-Hermitian kicking potential.Remarkably,when the non-Hermitian driving strength is sufficiently strong,the energy diffusion follows a power law of time,characterized by an exponent that decreases monotonically with increasing the strength of nonlinear interactions.This demonstrates the emergence of super-ballistic diffusion(SBD).We find a distinct prethermalization stage in the time domain preceding the onset of SBD.The unique quantum diffusion phenomena observed in this chaotic system can be attributed to the decoherence effects generated by the interplay between nonlinear interactions and the non-Hermitian kicking potential.

Laboratory Study of the Nonlinear Transformation of Irregular Waves over A Mild Slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

We applied n-variable conserving nonlinear differential equations (n-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (1845-1921). Modeling external effects as perturbations to population dynamics, recovering and restorations from disintegrations (or extinctions), stability and survival strategies are discussed in terms of the conservation law inherent to dynamical interactions among species. The 2-variable conserving nonlinear interaction (2CNIs) is extended to 3, 4, ... n-variable conserving nonlinear interactions (n-CNIs) of species by adjusting minimum unknown parameters. The population cycle of species is a manifestation of conservation laws existing in complicated ecosystems, which is suggested from the CNDE analysis as a standard rhythm of interactions. The ecosystem is a consequence of the long history of nonlinear interactions and evolutions among life-beings and the natural environment, and the population dynamics of an ecosystem are observed as approximate CNIs. Physical analyses of the conserving quantity in nonlinear interactions would help us understand why and how they have developed. The standard rhythm found in nonlinear interactions should be considered as a manifestation of the survival strategy and the survival of the fittest to the balance of biological systems. The CNDEs and nonlinear differential equations with time-dependent coefficients would help find useful physical information on the survival of the fittest and symbiosis in an ecosystem.

Maximal and total skew information for a two-qubit system using nonlinear interaction models

Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.

Observation of interactions between internal tides and near-inertial waves after typhoon passage in the northern South China Sea

During the observational period of our study, Typhoon Hagupit passed over the mooring site and induced strong near-inertial waves （NIWs）, which provided an opportunity to investigate the interactions between internal tides （ITs） and NIWs. Based on the mooring data, we compared the current spectra during the typhoon period and non-typhoon period in the northern South China Sea, and found that the high- frequency waves （fD1 and fD2） were evident during the former. Moreover, the observations of the current revealed that fD1 and fD2 occurred near the depth of strong vertical shear in the NlWs. In order to confirm the generation mechanism of fD1 and fD2, we compared the positions of strong vertical shear in the NIWs and strong vertical velocity in the ITs. It was established that the vertical shear of the horizontal current of the NIWs and the vertical current of the ITs contributed to the generation of fDt and fD2.

Diurnal wind and nonlinear interaction between inertial and tidal currents in the South China Sea during the passage of Typhoon Conson

Diurnal wind （DW） and nonlinear interaction between inertial and tidal currents near the Xisha Islands of the South China Sea （SCS） during the passage of Typhoon Conson （2010） are investigated using observational data and a damped slab model. It is found that the DWs, which are dominated by clockwise wind components, are prominent at our observational site. The DWs increase after the passage of the typhoon from 1 to about 4 m/s, which may be due to the decrease of the sea surface temperature caused by the passage of the typhoon. Kinetic energy spectra and bicoherence methods reveal nonlinear interactions between the inertial currents and the 2MK3 tidal constituent at our observational site. The slab damped model reproduces the inertial currents successfully induced by the total observed winds, and it is shown that the inertial currents induced by DWs are positively proportional to the DWs speed. Even though the observed inertial currents are distinct, the proportion of inertial currents induced by DWs to those induced by the total observed winds is just 0.7%/4% before/after the passage of typhoon. This shows that the inertial currents induced by the DWs are unimportant near the Xisha Islands during the typhoon season.

Maximal and total skew information of three-qubit system obtained using nonlinear interaction models

Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.

The Nonlinear Interaction Process in the Wave Assimilation Model and Its Experiments

This paper presents a composite interaction formula based on the discrete-interaction operator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space was also analyzed preliminarily.

AN ANALYSIS OF SUBGRID-RESOLVED SCALE INTERACTIONS WITH USE OF RESULTS FROM DIRECT NUMERICAL SIMULATIONS

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range. By decomposing the subgrid energy transfer and nonlinear interaction into ‘forward’ and ‘backward’ groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.

Lateral Global Buckling of Submarine Pipelines Based on the Model of Nonlinear Pipe–Soil Interaction

With the increasing development and utilization of offshore oil and gas resources, global buckling failures of pipelines subjected to high temperature and high pressure are becoming increasingly important. For unburied or semi-buried submarine pipelines, lateral global buckling represents the main form of global buckling. The pipe–soil interaction determines the deformation and stress distribution of buckling pipelines. In this paper, the nonlinear pipe–soil interaction model is introduced into the analysis of pipeline lateral global buckling, a coupling method of PSI elements and the modified RIKS algorithm is proposed to study the lateral global buckling of a pipeline, and the buckling characteristics of submarine pipeline with a single arch symmetric initial imperfection under different pipe–soil interaction models are studied. Research shows that, compared with the ideal elastic–plastic pipe–soil interaction model, when the DNV-RP-F109 model is adopted to simulate the lateral pipe–soil interactions in the lateral global buckling of a pipeline, the buckling amplitude increases, however, the critical buckling force and the initial buckling temperature difference decreases. In the DNV-RP-F109 pipe–soil interaction model, the maximum soil resistance, the residual soil resistance, and the displacement to reach the maximum soil resistance have significant effects on the analysis results of pipeline global buckling.

Fully Nonlinear Time Domain Analysis for Hydrodynamic Performance of An Oscillating Wave Surge Converter

The hydrodynamic behaviour of an oscillating wave surge converter(OWSC) in large motion excited by nonlinear waves is investigated. The mechanism through which the wave energy is absorbed in the nonlinear system is analysed. The mathematical model used is based on the velocity potential theory together with the fully nonlinear boundary conditions on the moving body surface and deforming free surface. The problem is solved by the boundary element method. Numerical results are obtained to show how to adjust the mechanical properties of the OWSC to achieve the best efficiency in a given wave, together with the nonlinear effect of the wave height. Numerical results are also provided to show the behaviour of a given OWSC in waves of different frequencies and different heights.

Numerical Investigations on Transient Behaviours of Two 3-D Freely Floating Structures by Using a Fully Nonlinear Method

Two floating structures in close proximity are very commonly seen in offshore engineering. They are often subjected to steep waves and, therefore, the transient effects on their hydrodynamic features are of great concem. This paper uses the quasi arbitrary Lagrangian Eulerian finite element method （QALE-FEM）, based on the fully nonlinear potential theory （FNPT）, to numerically investigate the interaction between two 3-D floating structures, which undergo motions with 6 degrees of freedom （DOFs）, and are subjected to waves with different incident angles. The transient behaviours of floating structures, the effect of the accompanied structures, and the nonlinearity on the motion of and the wave loads on the structures are the main focuses of the study. The investigation reveals an important transient effects causing considerably larger structure motion than that in steady state. The results also indicate that the accompanied structure in close proximity enhances the interaction between different motion modes and results in stronger nonlinearity causing 2hal-order component to be of similar significance to the fundamental one.

Theoretical and Experimental Study on the Acoustic Wave Energy After the Nonlinear Interaction of Acoustic Waves in Aqueous Media

Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves＇ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.