The numerical study of shock-induced hydrodynamic instability and mixing

Based on multi-fluid volume fraction and piecewise parabolic method (PPM), a multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and applied to the problems of shock-induced hydrodynamic interfacial instability and mixing. Simulations of gas/liquid interface instability show that the influences of initial perturbations on the fluid mixing zone (FMZ) growth are significant, especially at the late stages, while grids have only a slight effect on the FMZ width, when the interface is impulsively accelerated by a shock wave passing through it. A numerical study of the hydrodynamic interfacial instability and mixing of gaseous flows impacted by re-shocks is presented. It reveals that the numerical results are in good agreement with the experimental results and the mixing growth rate strongly depends on initial conditions. Ultimately, the jelly layer experiment relevant to the instability impacted by exploding is simulated. The shape of jelly interface, position of front face of jelly layer, crest and trough of perturbation versus time are given; their simulated results are in good agreement with experimental results.     

Evolution of nonlinear cosmological perturbations

We define fully nonperturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our nonlinear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first- and second-order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.     

Measurement of nonlinear coefficient of a highly nonlinear fiber based on peak four-wave mixing signal generation conditions

We introduce a new measurement method of the nonlinear coefficient (NC) of a highly nonlinear fiber based on a four-wave mixing (FWM) technique. The NC along with the fiber's zero-dispersion wavelength (ZDW) was determined from the precise measurement of the pump power dependent optimum pump frequency for peak FWM signal generation conditions. The measurement errors of the NC and ZDW values determined with this method were less than 4.6% and 0.051 nm, respectively.     

Strong perturbations in nonlinear systems

A novel case of probabilistic coupling for hybrid stochastic systems with chaotic components via Markovian switching is presented. We study its stability in the norm, in the sense of Lyapunov and present a quantitative scheme for detection of stochastic stability in the mean. In particular we examine the stability of chaotic dynamical systems in which a representative parameter undergoes a Markovian switching between two values corresponding to two qualitatively different attractors. To this end we employ, as case studies, the behaviour of two representative chaotic systems (the classic Rössler and the Thomas-Rössler models) under the influence of a probabilistic switch which modifies stochastically their parameters. A quantitative measure, based on a Lyapunov function, is proposed which detects regular or irregular motion and regimes of stability. In connection to biologically inspired models (Thomas-Rössler models), where strong fluctuations represent qualitative structural changes, we observe the appearance of stochastic resonance-like phenomena i.e. transitions that lead to orderly behavior when the noise increases. These are attributed to the nonlinear response of the system.     

Unitary parametrization of perturbations to tribimaximal neutrino mixing

Current experimental data on neutrino mixing are very well described by tribimaximal mixing. Accordingly, any phenomenological parametrization of the Maki-Nakagawa-Sakata-Pontecorvo matrix must build upon tribimaximal mixing. We propose one particularly natural parametrization, which we call "triminimal." The three small deviations of the Particle Data Group angles from their tribimaximal values, and the PDG phase, parametrize the triminimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical neutrinos. As no foreseeable experiment will be sensitive to more than second order in the small parameters, we expand these flavor probabilities to second order.     

Effects of viscosity on shock-induced damping of an initial sinusoidal disturbance

A lack of reliable data treatment method has been for several decades the bottleneck of viscosity measurement by disturbance amplitude damping method of shock waves.In this work the finite difference method is firstly applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in inviscid and viscous flow.When water shocked to 15 GPa is taken as an example,the main results are as follows:(1) For inviscid and lower viscous flows the numerical method gives results in good agreement with the analytic solutions under the condition of small disturbance(a0/λ=0.02);(2) For the flow of viscosity beyond 200 Pa s(η=κ) the analytic solution is found to overestimate obviously the effects of viscosity.It is attributed to the unreal pre-conditions of analytic solution by Miller and Ahrens;(3) The present numerical method provides an effective tool with more confidence to overcome the bottleneck of data treatment when the effects of higher viscosity in experiments of Sakharov and flyer impact are expected to be analyzed,because it can in principle simulate the development of shock waves in flows with larger disturbance amplitude,higher viscosity,and complicated initial flow.     

辐射驱动不对称性对靶球压缩的影响

定量评估了驱动不对称性对靶球压缩的影响。对于不随时间变化不对称性驱动内爆,2维数值模拟结果表明:收缩比越小,驱动不对称性对靶球压缩变形和中子产额的影响越小;如果靶球压缩变形度为2.0,则相应的中子产额较少30%。改变黑腔长度,可得到不同时空性质辐射流,当腔长为1 350μm时,后来的反向不均匀性能消除前期不对称压缩的影响,最后压缩接近球形,内爆中子产额也最高。靶球压缩X光成像数值分析表明,用成像图的半高全宽(FWHM)值来分析燃料压缩变形特性是合理的。该研究结果已成功地用于神光Ⅱ间接驱动内爆物理实验的理论设计和测量数据分析。     

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.     

Strongly nonlinear shear perturbations in discrete and continuous cubic nonlinear systems

Systems with constraints, the masses in which move only along guides, can execute strongly nonlinear vibrations. This means that nonlinear phenomena manifest themselves at arbitrary small deviations from equilibrium. The form of vibrations of a single mass is described by elliptical Jacobi functions. The spectrum of these vibrations is found. With an increase in amplitude, the period of vibrations decreases. We deduce equations of strongly nonlinear vibrations of a chain of connected masses. In the continuum limit, we obtain a new nonlinear equation in partial derivatives. We devise transformation of variables leading to linearization of this equation. We implemented a factorization procedure that decreases the order of the equation in partial derivatives from second to first. Exact solutions to the first-order equation describe the slow evolution of the displacement profile in a distributed system. In the absence of preliminary tension of elastic elements in the continued model, traveling waves cannot be achieved; however, time-oscillating solutions like standing waves are possible. We obtain an equation for a field of strongly nonlinear deformations. Its exact solution describes periodic movement in time and space. As well, the period of time oscillations decreases with an increase in amplitude, and the spatial period, in contrast, increases. The product of the vibration frequency multiplied by the spatial period is a constant that depends on the deformation energy. We propose a scheme of the mechanical system producing strongly nonlinear torsional vibrations. We experimentally measured the period of torsional vibrations of a single disc. We show that with an increase in amplitude in the process of vibration attenuation, an increase in the period occurs, which agrees with calculations. We measure the shapes of nonlinear vibrations of a chain of connected discs. A strongly nonlinear behavior of the chain is observed.     

Dynamics of the nonlinear four-wave mixing interaction

We present an analysis of the impulse response of four-wave mixing, in the case where the two-photon term of the nonlinear susceptibility is dominant. The nonlinear interaction itself will be considered to be steady state. The conditions of negligible pump depletion are considered first. It is shown that the reflected beam has only the character of perfect phase conjugation if the pulse length is longer than the medium length, and the latter is short compared to the characteristic distance of the problem. The weak-pulse approximation involving only two coupled equations is compared to the exact four-wave solution, when the medium thickness approaches the critical oscillation threshold. Finally, the stability and existence of steady-state solutions is analyzed for very long media (compared with the oscillation length).     

Asymptotical solutions of coupled nonlinear Schrodinger equations with perturbations

In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.     

辐射驱动不对称性对靶球压缩的影响

定量评估了驱动不对称性对靶球压缩的影响。对于不随时间变化不对称性驱动内爆,2维数值模拟结果表明：收缩比越小,驱动不对称性对靶球压缩变形和中子产额的影响越小;如果靶球压缩变形度为2.0,则相应的中子产额较少30%。改变黑腔长度,可得到不同时空性质辐射流,当腔长为1 350 μm时,后来的反向不均匀性能消除前期不对称压缩的影响,最后压缩接近球形,内爆中子产额也最高。靶球压缩X光成像数值分析表明,用成像图的半高全宽（FWHM）值来分析燃料压缩变形特性是合理的。该研究结果已成功地用于神光Ⅱ间接驱动内爆物理实验的理论设计和测量数据分析。     

Microbubble cloud characterization by nonlinear frequency mixing

In the frame of the fourth generation forum, France decided to develop sodium fast nuclear reactors. French Safety Authority requests the associated monitoring of argon gas into sodium. This implies to estimate the void fraction, and a histogram indicating the bubble population. In this context, the present letter studies the possibility of achieving an accurate determination of the histogram with acoustic methods. A nonlinear, two-frequency mixing technique has been implemented, and a specific optical device has been developed in order to validate the experimental results. The acoustically reconstructed histograms are in excellent agreement with those obtained using optical methods.     

What initial perturbations may be generated in inflationary cosmological models

Isothermal (isoinflaton) perturbations generated in cosmological models at the inflationary stage are discussed. The spectrum of such perturbations has been calculated for the example of a cosmological model with axion-type matter. The possibility of the cut-off of the spectrum at long wavelengths has been shown. This leads to the suppression of large-scale fluctuations of the temperature of the background radiation.     

Dynamics of the Manakov-typed bound vector solitons with random initial perturbations

Dynamics of the bound vector solitons with random initial perturbations is investigated for the Manakov model, which describes the propagation of the multimode soliton pulses in nonlinear fiber optics and two-component matter-wave solitons in the quasi-one-dimensional Bose–Einstein condensates (BECs) without confining potential. We review the analytic two-bound-vector-soliton solutions and give the three-bound-vector-soliton solutions. Breakup of the typical bound state is presented numerically when the symmetry and asymmetry random perturbations are added to the initial conditions. Relationship between the lifetime of the bound state and amplitude of the random perturbation is discussed. Meanwhile, existence of the symmetry-recovering is illustrated for the bound vector solitons with the asymmetry random perturbations. Discussions of this paper could be expected to be helpful in interpreting the dynamics of the Manakov-typed bound vector solitons when the random initial noises in nonlinear optical fibers or stochastic quantum fluctuations in the BECs are considered.     

Effect of counterintuitive time delays in nonlinear mixing

The effect of varying the relative arrival time of the two laser pulses employed in doubly resonant four-wave sum mixing, enhanced by induced transparency, is studied with the aim of optimizing the efficiency of vacuum-ultraviolet generation. With atomic hydrogen as the nonlinear medium, pulsed radiation with wavelengths of 243 and 656 nm and durations of 8 and 14 ns, respectively, is mixed to generate 103-nm coherent radiation. It is shown that by delaying the arrival time of the ground-state pump beam (243 nm) by 2.5-3.5 ns relative to the arrival of the upper-state coupling beam (656 nm), it is possible to enhance the generated intensity by a factor of 2 or more.     

Sum-frequency mixing of optical vortices in nonlinear crystals

Results of theoretical and experimental investigation of the influence of walk-off on sum-frequency mixing of optical vortices in nonlinear crystals are presented. Various phenomena of vortex interaction such as decay of higher order vortices into singly charged vortices, formation of aligned arrays of vortices perpendicular to walk-off direction, particle-like pulling and pushing of vortices, and appearance of pairs of vortices having opposite charges were observed.     

A built-in scale in the initial spectrum of density perturbations: Evidence from cluster and CMB data

We calculate the temperature anisotropies of the cosmic microwave background (CMB) for several initial power spectra of density perturbations with a built-in scale suggested by recent optical data on the spatial distribution of rich clusters of galaxies. Using cosmological models with different values of the spectral index, baryon fraction, Hubble constant, and cosmological constant, we compare the calculated radiation power spectrum with the CMB temperature anisotropies measured by the Saskatoon experiment. We show that spectra with a spike at 120h ⁻¹ Mpc are in agreement with the Saskatoon data. The combined evidence from cluster and CMB data favors the presence of a peak and a subsequent break in the initial matter power spectrum. Such a feature is similar to the prediction of an inflationary model wherein an inflaton field is evolving through a kink in the potential. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 373–378 (25 September 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.