Two-Point Closure Strategy in the Mapping Closure Approximation Approach

A two-point closure strategy in mapping closure approximation (MCA) approach is developed for the evolution of the probability density function (PDF) of a scalar advected by stochastic velocity fields. The MCA approach is based on multipoint statistics. We formulate a MCA modeled system using the one-point PDFs and two-point correlations. The MCA models can describe both the evolution of the PDF shape and the rate at which the PDF evolves.

Effects of Noise and Detection Error in a Dynamic Adaptive Optics System

It is well known that noise and detection error can affect the performances of an adaptive optics (AO) system. Effects of noise and detection error on the phase compensation effectiveness in a dynamic AO system are investigated by means of a pure numerical simulation in this paper. A theoretical model for numerically simulating effects of noise and detection error in a static AO system and a corresponding computer program were presented in a previous article. A numerical simulation of effects of noise and detection error is combined with our previous numeral simulation of a dynamic AO system in this paper and a corresponding computer program has been compiled. Effects of detection error, readout noise and photon noise are included and investigated by a numerical simulation for finding the preferred working conditions and the best performances in a practical dynamic AO system. An approximate model is presented as well. Under many practical conditions such approximate model is a good alternative to the more accurate one. A simple algorithm which can be used for reducing the effect of noise is presented as well. When signal to noise ratio is very low, such method can be used to improve the performances of a dynamic AO system.

Mapping Closure Approximation for Reactive Scalars in Random Flows

The Mapping Closure Approximation (MCA) approach is developed to describe the statistics of both conserved and reactive scalars in random flows. The statistics include Probability Density Function (PDF), Conditional Dissipation Rate (CDR) and Conditional Laplacian (CL). The statistical quantities are calculated using the MCA and compared with the results of the Direct Numerical Simulation (DNS). The results obtained from the MCA are in agreement with those from the DNS. It is shown that the MCA approach can predict the statistics of reactive scalars in random flows.

First-passage time of Duffing oscillator under combined harmonic and white-noise excitations

The first-passage time of Duffing oscillator under combined harmonic and white-noise excitations is studied. The equation of motion of the system is first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. Numerical results for two resonant cases with several sets of parameter values are obtained and the analytical results are verified by using those from digital simulation.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

A delay model for noise-induced bi-directional switching

Many biological systems can switch between two distinct states. Once switched, the system remains stable for a period of time and may switch back to its original state. A gene network with bistability is usually required for the switching and stochastic effect in the gene expression may induce such switching. A typical bistable system allows one-directional switching, in which the switch from the low state to the high state or from the high state to the low state occurs under different conditions. It is usually difficult to enable bi-directional switching such that the two switches can occur under the same condition. Here, we present a model consisting of standard positive feedback loops and an extra negative feedback loop with a time delay to study its capability to produce bi-directional switching induced by noise. We find that the time delay in the negative feedback is critical for robust bi-directional switching and the length of delay affects its switching frequency.

Resolution and noise in ghost imaging with classical thermal light

The resolution and classical noise in ghost imaging with a classical thermal light are investigated theoretically. For ghost imaging with a Gaussian Schell model source, the dependences of the resolution and noise on the spatial coherence of the source and the aperture in the imaging system are discussed and demonstrated by using numerical simulations. The results show that an incoherent source and a large aperture will lead to a good image quality and small noise.

Effect of microcosmic optical parameters of dopants on the signal-to-noise ratio in doubly doped LiNbO3 crystals

We propose a united theory that describes the two-center recording system by taking scattering noise into account. The temporal evolution of the signal-to-noise ratio in doubly doped photorefractive crystals is described based on jointly solving material equations and coupled-wave equations with the fourth-order Runge-Kutta method. Roles of microcosmic optical parameters of dopants on the signal-to-noise ratio are discussed in detail. The theoretical results can confirm and predict experimental results. (c) 2005 Elsevier GmbH. All rights reserved.

Dynamic phase-mapping of domain nucleation on MgO : LiNbO3 crystal by digital holographic interferometry

The quantitative phase-mapping of the domain nucleation in MgO:LiNbO3 crystals is presented by using the digital holographic interferometry. An unexpected peak phase at the beginning of the domain nucleation is observed and it is lowered as the spreading of the domain nucleus. The existence of the nucleus changes the moving speed of the domain wall by pinning it for 3s. Such in-situ quantitative analysis of the domain nucleation process is a key to optimizing domain structure fabrication.

Phase mapping of domain kinetics in lithium niobate by digital holographic interferometry

The phase mapping of domain kinetics under the uniform steady-state electric field is achieved and investigated in the LiNbO3 crystals by digital holographic interferometry. We obtained the sequences of reconstructed three-dimensional and two-dimensional wave-field phase distributions during the electric poling in the congruent and near stoichiometric LiNbO3 crystals. The phase mapping of individual domain nucleation and growth in the two crystals are obtained. It is found that both longitudinal and lateral domain growths are not linear during the electric poling. The phase mapping of domain wall motions in the two crystals is also obtained. Both the phase relaxation and the pinning-depinning mechanism are observed during the domain wall motion. The residual phase distribution is observed after the high-speed domain wall motion. The corresponding analyses and discussions are proposed to explain the phenomena.

Gain and noise figure of a double-pass waveguide amplifier based on Er/Yb-doped phosphate glass

A waveguide amplifier is fabricated by Ag+-Na+ two-step ion exchange on Er/Yb-doped phosphate glass. The spectroscopic performance of glass and the properties of channel waveguide are characterized. A double-pass configuration is adopted to measure the gain and noise figure (NF) of the waveguide amplifier, and the comparison of gain and NF for the single and double-pass configuration of the waveguide amplifier is presented. The results show that the double-pass configuration can make the gain increase from 8.8dB (net gain 2.2dB/cm) of the single-pass one to 14.6 dB (net gain 3.65 dB/cm) for small input power at 1534 nm, and the NF are all lower than 5.5dB for both the configurations.