Additional Nonlinear Interaction Research Articles

The role of nonlinear interactions in the onset of drag increase in flow over riblets

Characterizing the mechanisms that contribute to the onset of drag increase over micro-grooves (riblets) as the spacing increases is critical to design strategies for riblet-based drag reduction. This study decomposes the roughness function to investigate different mechanisms associated with the breakdown of drag reduction as riblet spacing is increased. We obtain the roughness function through direct numerical simulations (DNS) in a minimal channel and restricted nonlinear (RNL) models. Both the traditional RNL decomposition and an augmented RNL (ARNL) model that includes additional nonlinear interactions are employed as computationally tractable, reduced order representations of the flow field. RNL and ARNL results are compared to those of DNS in minimal channels to investigate the role of the different scale-dependent nonlinear interactions contributing to the roughness function. A comparison of the co-spectra arising from the minimal channel DNS with that from RNL and ARNL simulations indicates that general trends are captured by both reduced order models. However, the additional nonlinearity introduced in the ARNL model produces closer correspondence in the observed structural features of the DNS results. In particular, the ARNL better captures the signatures of the dispersive flow and the texture-coherent fluctuations. There is also a noticeable improvement observed in the profiles of the added stress contributions obtained with the ARNL model versus the RNL model.

Interplay between Raman self-frequency shift and cross-phase modulation in the vector-soliton of a birefringent fiber

Competition between cross-phase modulation (XPM) interaction and Raman-induced red-frequency shift is observed in the orthogonally polarized components (in the form of optical pulses) of a vector-soliton propagating in the fundamental mode of a birefringent fiber exhibiting negative third-order dispersion and group velocity birefringence. Both pulses experience opposite frequency shifts due to XPM, which reinforces the Raman self-frequency shift of one pulse while it hinders the self-frequency shift of the other. A large redshift in one of the pulses of the vector-soliton suggests transfer of a greater part of its energy to the dispersive radiation, leading to an asymmetry in the longitudinal evolution of the amplitudes as well as the frequencies of both the pulses of the vector-soliton. To support our analysis, an analytical approach is developed in order to understand the interplay between the Raman effect and XPM. The findings of the analytical approach are in good qualitative agreement with the numerical results, which is consistent with the results of Phys. Rev. E70, 016615 (2004)PLEEE81063-651X10.1103/PhysRevE.70.016615. The derived analytical relations accommodate additional nonlinear interactions originating from the XPM, as well as mutual Raman interaction, which makes our approach much superior to that used in Phys. Rev. E70, 016615 (2004)PLEEE81063-651X10.1103/PhysRevE.70.016615. It is also possible to understand the interaction between two frequency-shifted solitons in a true single-mode fiber or other waveguide system exhibiting negative third-order dispersion by a slight modification of our theoretical approach.

Intermittency measurement in two-dimensional bacterial turbulence.

In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β-limitation. A dual-power-law behavior separated by the viscosity scale ℓ_{ν} was observed for the qth-order Hilbert moment L_{q}(k). This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R, e.g., the bacterial body length. The measured scaling exponents ζ(q) of both the small-scale (k>k_{ν}) and large-scale (k<k_{ν}) motions are convex, showing the multifractality. A log-normal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are μ_{S}=0.26 and μ_{L}=0.17, respectively, for the small- and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f(α) versus α. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation.

General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters

Using the technique of classical r-matrices and quantum Lax operators, we construct the most general form of the quantum integrable “n-level, many-mode” spin-boson Jaynes-Cummings-Dicke-type hamiltonians describing an interaction of a molecule of N n-level atoms with many modes of electromagnetic field and containing, in general, additional non-linear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spin-boson analogs of the generalized Gaudin hamiltonians and prove their quantum commutativity. We investigate symmetries of the obtained models that are associated with the geometric symmetries of the classical r-matrices and construct the corresponding algebra of quantum integrals. We consider in detail three classes of non-skew-symmetric classical r-matrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and Jaynes-Cummings-Dicke-type hamiltonians depending on the considered r-matrix.

Interaction of a Two-Level Atom with the Morse Potential in the Framework of Jaynes–Cummings Model

A theoretical study of the dynamical behaviors of the interaction between a two-level atom with a Morse potential in the framework of the Jaynes–Cummings model (JCM) is discussed. We show that this system is equivalent to an intensity-dependent coupling between the two-level atom and the non-deformed single-mode radiation field in the presence of an additional nonlinear interaction. We study the dynamical properties of the system such as, atomic population inversion, the probability distribution of cavity-field, the Mandel parameter and atomic dipole squeezing. It is shown how the depth of the Morse potential can be affected by non-classical properties of the system. Moreover, the temporal evolution of the Husimi-distribution function is explored.

Greenberger-Horne-Zeilinger–type andW-type entangled coherent states: Generation and Bell-type inequality tests without photon counting

We study Greenberger-Horne-Zeilinger--type (GHZ-type) and $W$-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for $W$-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate $W$-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the $W$-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

Sudden or smooth transitions in porous media natural convection

In porous media isothermal flow a transition from the Darcy regime, via an inertia dominated regime, towards turbulence is anticipated. In porous medium natural convection the transition to turbulence follows a different route. The first transition from a motionless-conduction regime to steady natural convection is followed by a direct second transition to a non-steady (time dependent) and non-periodic regime (referred to as weak turbulent), prior to the amplitude of the convection reaching such large values as to involve inertial, non-Darcy effects. The latter is due to an additional non-linear interaction that appears in natural convection as a result of the coupling between the equations governing the fluid flow and the energy equation. The present paper deals with identifying whether the transitions are sudden or possibly smooth. The latter is accomplished by using a truncated Galerkin representation of the natural convection problem in a porous layer heated from below (an extended Darcy model) leading to the familiar Lorenz equations for the evolution of the convection amplitudes with time. Two different formulations (named the “original” and the “modified” systems) are being used in an anticipation to obtaining a smooth transition in the form of an imperfect bifurcation from the “modified” system formulation. The results show that the transition remains sudden and the accuracy of the “modified” system results is being tested in comparison with the “original” system showing a sufficiently high degree of accuracy.

Purification of entangled coherent states

We suggest an entanglement purification scheme for mixed entangled coherent states using 50-50 beam splitters and photodetectors. This scheme is directly applicable for mixed entangled coherent states of the Werner type, and can be useful for general mixed states using additional nonlinear interactions. We apply our scheme to entangled coherent states decohered in a vacuum environment and find the decay time until which they can be purified.

Purification of entangled coherent states

We suggest an entanglement purification scheme for mixed entangled coherent states using 50-50 beam splitters and photodetectors. This scheme is directly applicable for mixed entangled coherent states of the Werner type, and can be useful for general mixed states using additional nonlinear interactions. We apply our scheme to entangled coherent states decohered in a vacuum environment and find the decay time until which they can be purified.