A comprehensive model for the quantification of linear and nonlinear regime laser-induced fluorescence of OH under A2Σ+←X2Π(1,0) excitation

An analytic model termed the ‘integrated quasi-steady-state’ (IQSS) model for the comprehensive quantification of both linear and nonlinear regime laser-induced fluorescence (LIF) is presented. The IQSS model is optimized for the hydroxyl radical (OH), subject to nanosecond A²Σ⁺←X²Π(1,0) excitation at pressures close to atmospheric. The IQSS model is particularly relevant to experimental conditions where the LIF signal is both spectrally and temporally integrated, such as in planar laser-induced fluorescence experiments. The IQSS model is based around a quasi-steady-state solution to a four-level rate-equation approximation of the OH molecule; this quasi-steady-state solution is then integrated with a triangular functional form for both the spatial and temporal variations to produce an analytic solution. In order to accurately predict LIF in the nonlinear regime, it is shown that both the temporal and the spatial variations of the laser pulse—or ‘wings’ of the laser pulse—must be adequately accounted for in the LIF model formulation. The IQSS model is successfully verified against detailed numerical simulations for variations in the laser irradiance, quenching environment and temperature. Experimentally, the IQSS model is successfully validated by comparing the predicted and measured OH LIF vs. irradiance dependence in the product gases of a methane–air laminar flame.     

Equidistribution of Heegner points and the partition function

Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X ₀(6). We obtain a new asymptotic formula for p(n) with an effective error term which is O(n^-(\frac12+d)){O(n^{-(\frac{1}{2}+\delta)})} for some δ > 0. We then use this asymptotic formula to sharpen the classical bounds of Hardy and Ramanujan, Rademacher, and Lehmer on the error term in Rademacher’s exact formula for p(n).     

A General Data-Based Approach for Developing Reduced-Order Models of Nonlinear MDOF Systems

A general procedure is presented for analyzing dynamic response measurements from complex multi-degree-of-freedom nonlinear systems incorporating arbitrary types of nonlinear elements. The analysis procedure develops a reduced-order, nonlinear model whose format is convenient for numerical simulation studies. No information about the systems mass properties is needed, and only the applied excitations and corresponding response are needed to develop the model whose dimension is compatible with the number of available sensors. The utility of the approach is demonstrated by means of a three-degree-of-freedom system incorporating polynomial-type nonlinear features with hardening as well as softening characteristics.     

An improved method of data aquisition and reduction for laser raman-rayleigh and fluorescence scattering from Multispecies

We review the spontaneous Raman scattering process as applied to the determination of species concentration and thermometry in turbulent reactive flows. Comments on design improvements to the apparatus are made. We elaborate on a matrix formulation for data reduction that logically removes the following undesired sources of signal in Raman scattering systems: 1) cross-talk due to Raman scattering from other species, 2) laser induced fluorescence, 3) background flame chemiluminescence, and 4) noise in the data acquisition system.Research Supported by the Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences     

Theoretical study of acoustic waves supported by a film-substrate interface

By using the Green's function method, we study the dispersion of acoustic waves guided by an anisotropic film-substrate interface when the film thickness changes.     

A calculation of the intrinsic {111} surface states of the zinc blende ANB8−N compounds

The electronic structure of polar {111} faces of zinc blende A^NB^8?N compounds is studied using a LCAO approximation. Within a molecular model a selfconsistent solution is achieved, taking into account the charge accumulation near the surface necessary to stabilize the system. It is found that stabilization by intrinsic surface states associated with unreconstructed surfaces is easier in large gap systems, which is supported by experimental evidence. The gap between electronegative and electropositive surface states is found to be in agreement with recent photoemission measurements for GaAs.     

The effect of time-delayed feedback controller on an electrically actuated resonator

This paper presents a study of the effect of a time-delayed feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated as a resonator by DC and AC voltage loads. A linearization analysis is conducted to determine the stability chart of the linearized system equations as a function of the time delay period and the controller gain. Then the method of multiple-scales is applied to determine the response and stability of the system for small vibration amplitude and voltage loads. It is shown that negative time-delay feedback control gain can lead to unstable responses, even if AC voltage is relatively small compared to the DC voltage. On the other hand, positive time delay can considerably strengthen the system stability even in fractal domains. We also show how the controller can be used to control damping in MEMS, increasing or decreasing, by tuning the gain amplitude and delay period. Agreements among the results of a shooting technique, long-time integration, basin of attraction analysis with the perturbation method are achieved.     

The role of DME addition on the evolution of soot and soot precursors in laminar ethylene jet flames

Dimethyl ether (DME) has received considerable attention as a fuel additive to reduce the emission of particulate matter (PM) due to its low-temperature chemistry, molecularly bound oxygen atom and the absence of CC bonds. However, the effect of DME addition on the evolution of soot and particularly soot precursors is not entirely understood. This study aims to shed light on this issue by blending different proportions of DME with diffusion, E60, and partially premixed, PP12, base cases of laminar ethylene flames using the Yale benchmark burner. Laser-induced fluorescence (LIF) intensity and decay time are used to characterize the structure and evolution of soot precursors, while laser-induced incandescence (LII) is utilized to determine the soot volume fraction (SVF) and the effective primary particle diameter (D_p). For the diffusion flames, the addition of 10% DME increases the concentrations of both soot and soot precursors. With the further addition of DME to 20%, the SVF decreases to levels similar to those of E60 and then decreases further with 30% DME addition. All diffusion flames with DME addition exhibit higher concentrations of soot precursors than those of the reference E60 case. For PP12, the addition of 10% DME shows similar concentrations of soot precursors and a slight reduction in the SVF which continues to decrease with further increases in DME additions to the PP12 flame. The addition of DME seems to have little effect on the soot particle diameters for all the studied flames. Overall, the PP flames result in smaller mean particle diameters than the diffusion flame counterparts.