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

Combined space and time convergence analysis of a compressible flow algorithm

In this study, we quantify both the spatial and temporal convergence behavior simultaneously for various algorithms for the two-dimensional Euler equations of gasdynamics. Such an analysis falls under the rubric of verification, which is the process of determining whether a simulation code accurately represents the code developers description of the model (e.g., equations, boundary conditions, etc.). The recognition that verification analysis is a necessary and valuable activity continues to increase among computational fluid dynamics practicioners. Using computed results and a known solution, one can estimate the effective convergence rates of a specific software implementation of a given algorithm and gauge those results relative to the design properties of the algorithm. In the aerodynamics community, such analyses are typically performed to evaluate the performance of spatial integrators; analogous convergence analysis for temporal integrators can also be performed. Our approach combines these two usually separate activities into the same analysis framework. To accomplish this task, we outline a procedure in which a known solution together with a set of computed results, obtained for a number of different spatial and temporal discretizations, are employed to determine the complete convergence properties of the combined spatio-temporal algorithm. Such an approach is of particular interest for Lax-Wendroff-type integration schemes, where the specific impact of either the spatial or temporal integrators alone cannot be easily deconvolved from computed results. Unlike the more common spatial convergence analysis, the combined spatial and temporal analysis leads to a set of nonlinear equations that must be solved numerically. The unknowns in this set of equations are various parameters, including the asymptotic convergence rates, that quantify the basic performance of the software implementation of the algorithm