Comprehensive Analysis of Arkansas Teacher Salaries: State, Region, and District

School funding has been an area of contention in the courts of nearly every state. Many of these court cases have challenged the constitutionality of state funding formulas, arguing the funding system was inadequate or inequitable because poor urban or rural districts often faced a disadvantage in garnering tax dollars for education. Specific to Arkansas, in the 1983 decision Dupree v. Alma School District, the Arkansas Supreme Court declared the state’s funding system was not meeting its constitutional requirements

High performance interior point methods for three-dimensional finite element limit analysis

The ability to obtain rigorous upper and lower bounds on collapse loads of various structures makes finite element limit analysis an attractive design tool. The increasingly high cost of computing those bounds, however, has limited its application on problems in three dimensions. This work reports on a high-performance homogeneous self-dual primal-dual interior point method developed for three-dimensional finite element limit analysis. This implementation achieves convergence times over 4.5× faster than the leading commercial solver across a set of three-dimensional finite element limit analysis test problems, making investigation of three dimensional limit loads viable. A comparison between a range of iterative linear solvers and direct methods used to determine the search direction is also provided, demonstrating the superiority of direct methods for this application. The components of the interior point solver considered include the elimination of and options for handling remaining free variables, multifrontal and supernodal Cholesky comparison for computing the search direction, differences between approximate minimum degree [1] and nested dissection [13] orderings, dealing with dense columns and fixed variables, and accelerating the linear system solver through parallelization. Each of these areas resulted in an improvement on at least one of the problems in the test set, with many achieving gains across the whole set. The serial implementation achieved runtime performance 1.7× faster than the commercial solver Mosek [5]. Compared with the parallel version of Mosek, the use of parallel BLAS routines in the supernodal solver saw a 1.9× speedup, and with a modified version of the GPU-enabled CHOLMOD [11] and a single NVIDIA Tesla K20c this speedup increased to 4.65×

The cost of continuity: performance of iterative solvers on isogeometric finite elements

In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using $C^0$ B-splines, which span traditional finite element spaces, and $C^{p-1}$ B-splines, which represent maximum continuity. We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size $h$ and polynomial order of approximation $p$. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most \slfrac{33p^2}{8} times more expensive for the more continuous space, although for moderately low $p$, this number is significantly reduced. Moreover, if static condensation is not employed, this number further reduces to at most a value of 8, even for high $p$. Preconditioning options can be up to $p^3$ times more expensive to setup, although this difference significantly decreases for some popular preconditioners such as Incomplete LU factorization

Production of methyl ethyl ketone from biomass using a hybrid biochemical/catalytic approach

The recent demand for sustainable routes to fuels and chemicals has led to an increased amount of research in conversion of natural resources. A potential approach for conversion of biomass to fuels and chemicals is to combine biochemical and chemical processes. This research used microbial fermentation to produce 2,3-butanediol, which was then converted to methyl ethyl ketone by dehydration over a solid acid catalyst. The fermentation process was performed using the bacteria Klebsiella oxytoca (K.O). 2,3-butanediol then dehydrated to form methyl ethyl ketone on a solid acid catalyst, the proton form of ZSM-5, and heat. The goal was to determine the reaction kinetics of 2,3-butanediol dehydration over ZSM-5, and to demonstrate the hybrid biochemical/thermochemical approach for synthesizing chemicals from biomass. It was found that ZSM-5 produced methyl ethyl ketone with high selectivity (greater than 90%), and could convert fermentative 2,3-butanediol to methyl ethyl ketone. The reaction order of 2,3-butanediol dehydration was found to be slightly large than one, and an activation energy of 32.3 kJ/mol was measured

Expansion-limited aggregation of nanoclusters in a single-pulse laser-produced plume

Formation of carbon nanoclusters in a single-laser-pulse created ablation plume was studied both in vacuum and in a noble gas environment at various pressures. The developed theory provides cluster radius dependence on combination of laser parameters, properties of ablated material, and type and pressure of an ambient gas in agreement with experiments. The experiments were performed on carbon nanoclusters formed by laser ablation of graphite targets with 12 picosecond 532 nm laser pulses at MHz-range repetition rate in a broad range of ambient He, Ar, Kr, and Xe gas pressures from 2× 10-2 to 1500 Torr. The experimental results confirmed our theoretical prediction that the average size of the nanoparticles depends weakly on the type of the ambient gas used, and is determined exclusively by the single laser pulse parameters even at the repetition rate as high as 28 MHz with the time gap 36 ns between the pulses. The most important finding relates to the fact that in vacuum the cluster size is mainly determined by hydrodynamic expansion of the plume while in the ambient gas it is controlled by atomic diffusion in the gas. We demonstrate that the ultrashort pulses can be used for production of clusters with the size less than the critical value, which separates the particles with properties drastically different from those of a material in a bulk. The presented results of experiments on formation of carbon nanoclusters are in close agreement with the theoretical scaling. The developed theory is applicable for cluster formation from any monatomic material, such as silicon for example