Stretched Non-negative Matrix Factorization

An algorithm is described and tested that carries out a non negative matrix factorization (NMF) ignoring any stretching of the signal along the axis of the independent variable. This extended NMF model is called StretchedNMF. Variability in a set of signals due to this stretching is then ignored in the decomposition. This can be used, for example, to study sets of powder diffraction data collected at different temperatures where the materials are undergoing thermal expansion. It gives a more meaningful decomposition in this case where the component signals resemble signals from chemical components in the sample. The StretchedNMF model introduces a new variable, the stretching factor, to describe any expansion of the signal. To solve StretchedNMF, we discretize it and employ Block Coordinate Descent framework algorithms. The initial experimental results indicate that StretchedNMF model outperforms the conventional NMF for sets of data with such an expansion. A further enhancement to StretchedNMF for the case of powder diffraction data from crystalline materials called Sparse-StretchedNMF, which makes use of the sparsity of the powder diffraction signals, allows correct extractions even for very small stretches where StretchedNMF struggles. As well as demonstrating the model performance on simulated PXRD patterns and atomic pair distribution functions (PDFs), it also proved successful when applied to real data taken from an in situ chemical reaction experiment.Comment: 39 pages, 16 figure

A thermal‐gradient approach to variable‐temperature measurements resolved in space

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155923/1/jcr2te5056.pd

Effects of numerical methods on comparisons between experiments and simulations of shock-accelerated mixing.

We consider the detailed structures of mixing flows for Richtmyer-Meshkov experiments of Prestridge et al. [PRE 00] and Tomkins et al. [TOM 01] and examine the most recent measurements from the experimental apparatus. Numerical simulations of these experiments are performed with three different versions of high resolution finite volume Godunov methods. We compare experimental data with simulations for configurations of one and two diffuse cylinders of SF{sub 6} in air using integral measures as well as fractal analysis and continuous wavelet transforms. The details of the initial conditions have a significant effect on the computed results, especially in the case of the double cylinder. Additionally, these comparisons reveal sensitive dependence of the computed solution on the numerical method

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

A Pressure Relaxation Closure Model for One-Dimensional

Abstract. Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framewor

How do numerical methods effect the statistical details of Richtmyer-Meshkov instabilities

Over the past several years we have presented a less than glowing experimental comparison of hydrodynamic codes with the gas curtain experiment. Here, we discuss the manner in which the various details of the hydrodynamic integration techniques conspire to produce poor results. This also includes some progress in improving the results and agreement with experimental results. Our results are based upon the gas curtain, Richtmyer-Meshkov experiments conducted by Rightley et al. (Rightley et al. 1999) at Los Alamos. We also examine the results of a gas cylinder experiment conducted more recently by Prestridge and Zoldi which includes velocity data obtained via a PIV technique. Traditionally, the integral width of the mixing layer is used as a yardstick to measure the Richtmyer-Meshkov instability. This is also used when investigating the performance of numerical methods. Our focus has been on the details of the mixing below the integral scale. Because the flow is hydrodynamically unstable, we employ statistical measures in our comparisons. This is built upon a parallel effort by the experimentalists investigating the statistical nature of the mixing induced by shock waves. The principle tools we use to measure the spectral structure of the images of these flows are the fractal dimension and the continuous wavelet spectrum. The bottom line is that all the higher order methods used to simulate the gas curtain compare poorly with the experimental data when quantified with these spatial statistics. Moreover, the comparisons degrade under mesh refinement. This occurs despite the fact that the the integral scale comparison is acceptable and consistent with the expectations from this class of methods. The most surprising result is that a first-order Godunov method does produce a good comparison relative to the assumed to be higher-order methods. We have examined a broad variety of methodologies associated with the high-order methods to illuminate this problematic result. In the next section we briefly describe the experiments. In Section the quantitative measures applied to the images are detailed; the results of these analyses are discussed in Section refsec:compare. The consideration of the relation between turbulence models and numerical methods was inspired by these results and is discussed