High-repetition-rate combustion thermometry with two-line atomic fluorescence excited by diode lasers

We report on kilohertz-repetition-rate flame temperature measurements performed using blue diode lasers. Two-line atomic fluorescence was performed by using diode lasers emitting at around 410 and 451 nm to probe seeded atomic indium. At a repetition rate of 3.5 kHz our technique offers a precision of 1.5% at 2000 K in laminar methane/air flames. The spatial resolution is better than 150 mu m, while the setup is compact and easy to operate, at much lower cost than alternative techniques. By modeling the spectral overlap between the locked laser and the probed indium lines we avoid the need for any calibration of the measurements. We demonstrate the capability of the technique for time-resolved measurements in an acoustically perturbed flame. The technique is applicable in flames with a wide range of compositions including sooting flames

Van der Waals interactions of parallel and concentric nanotubes

For sparse materials like graphitic systems and carbon nanotubes the standard density functional theory (DFT) faces significant problems because it cannot accurately describe the van der Waals interactions that are essential to the carbon-nanostructure materials behavior. While standard implementations of DFT can describe the strong chemical binding within an isolated, single-walled carbon nanotube, a new and extended DFT implementation is needed to describe the binding between nanotubes. We here provide the first steps to such an extension for parallel and concentric nanotubes through an electron-density based description of the materials coupling to the electrodynamical field. We thus find a consistent description of the (fully screened) van der Waals interactions that bind the nanotubes across the low-electron-density voids between the nanotubes, in bundles and as multiwalled tubes.Comment: 6 pages, 4 figures (5 figure files

Large deviations for weighted empirical measures arising in importance sampling

Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted empirical measure, where the weights are given by the likelihood ratio between the original distribution and the sampling distribution. In this paper the efficiency of an importance sampling algorithm is studied by means of large deviations for the weighted empirical measure. The main result, which is stated as a Laplace principle for the weighted empirical measure arising in importance sampling, can be viewed as a weighted version of Sanov's theorem. The main theorem is applied to quantify the performance of an importance sampling algorithm over a collection of subsets of a given target set as well as quantile estimates. The analysis yields an estimate of the sample size needed to reach a desired precision as well as of the reduction in cost for importance sampling compared to standard Monte Carlo

Tail probabilities for infinite series of regularly varying random vectors

A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to the sequence $(Z_j)$. The distribution of $Z_1$ is assumed to be multivariate regular varying. Moment conditions on the matrices $(A_j)$ are determined under which the distribution of $X$ is regularly varying and, in fact, `inherits' its regular variation from that of the $(Z_j)$'s. We compute the associated limiting measure. Examples include linear processes, random coefficient linear processes such as stochastic recurrence equations, random sums and stochastic integrals.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ125 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes

We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$. For predictable integrands with a finite $(\alpha+\delta)$-moment, for some $\delta>0$, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving L\'{e}vy process and we determine its limit measure associated with regular variation on the space of c\`{a}dl\`{a}g functions.Comment: Published at http://dx.doi.org/10.1214/009117906000000548 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measurements of the indium hyperfine structure in an atmospheric-pressure flame by use of diode-laser-induced fluorescence

We report on what we believe is the first demonstration of laser-induced fluorescence (LIF) in flames by use of diode lasers. Indium atoms seeded into an atmospheric-pressure flame at trace concentrations are excited by a blue GaN laser operating near 410 nm. The laser is mounted in an external-cavity configuration, and the hyperfine spectrum of the 5(2)P(1/2) → 6(2)S(1/2) transition is captured at high resolution in single-wavelength sweeps lasting less than one tenth of a second. The research demonstrates the potential of diode-based LIF for practical diagnostics of high-temperature reactive flows