Decay of weak turbulence

Weak turbulence fields generated by single and multiple stage grids covering Reynolds numbers between 7 and 70 showing decay of energy spectr

Prototype selection for parameter estimation in complex models

Parameter estimation in astrophysics often requires the use of complex physical models. In this paper we study the problem of estimating the parameters that describe star formation history (SFH) in galaxies. Here, high-dimensional spectral data from galaxies are appropriately modeled as linear combinations of physical components, called simple stellar populations (SSPs), plus some nonlinear distortions. Theoretical data for each SSP is produced for a fixed parameter vector via computer modeling. Though the parameters that define each SSP are continuous, optimizing the signal model over a large set of SSPs on a fine parameter grid is computationally infeasible and inefficient. The goal of this study is to estimate the set of parameters that describes the SFH of each galaxy. These target parameters, such as the average ages and chemical compositions of the galaxy's stellar populations, are derived from the SSP parameters and the component weights in the signal model. Here, we introduce a principled approach of choosing a small basis of SSP prototypes for SFH parameter estimation. The basic idea is to quantize the vector space and effective support of the model components. In addition to greater computational efficiency, we achieve better estimates of the SFH target parameters. In simulations, our proposed quantization method obtains a substantial improvement in estimating the target parameters over the common method of employing a parameter grid. Sparse coding techniques are not appropriate for this problem without proper constraints, while constrained sparse coding methods perform poorly for parameter estimation because their objective is signal reconstruction, not estimation of the target parameters.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS500 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices

This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using basic ideas from probability theory and builds upon an algorithm from discrete Morse theory with a strong mathematical foundation. While a formal proof is only hinted at, we do provide a thorough numerical evaluation of our method and compare it to established algorithms.Comment: 17 pages, 7 figure

Tangling clustering of inertial particles in stably stratified turbulence

We have predicted theoretically and detected in laboratory experiments a new type of particle clustering (tangling clustering of inertial particles) in a stably stratified turbulence with imposed mean vertical temperature gradient. In this stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, that results in formation of a gradient of the mean particle number density, \nabla N, and generation of fluctuations of the particle number density by tangling of the gradient, \nabla N, by velocity fluctuations. The mean temperature gradient, \nabla T, produces the temperature fluctuations by tangling of the gradient, \nabla T, by velocity fluctuations. These fluctuations increase the rate of formation of the particle clusters in small scales. In the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter 10 microns and Reynolds numbers Re =250. Our theoretical predictions are in a good agreement with the obtained experimental results.Comment: 16 pages, 4 figures, REVTEX4, revised versio