Engineering Commons^™

A Bayesian Nonparametric Multiple Testing Procedure For Comparing Several Treatments Against A Control, Luis Gutiérrez, Andrés Barrientos, Jorge González, Daniel Taylor-Rodríguez

Mathematics and Statistics Faculty Publications and Presentations

We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.

Reconsidering The Foundations Of Thermodynamics From An Engineering Perspective, Terry Bristol

Mathematics and Statistics Faculty Publications and Presentations

Currently, there are two approaches to the foundations of thermodynamics. One, associated with the mechanistical Clausius-Boltzmann tradition, is favored by the physics community. The other, associated with the post-mechanical Carnot tradition, is favored by the engineering community. The bold hypothesis is that the conceptual foundation of engineering thermodynamics is the more comprehensive. Therefore, contrary to the dominant consensus, engineering thermodynamics (ET) represents the true foundation of thermodynamics. The foundational issue is crucial to a number of unresolved current and historical issues in thermodynamic theory and practice. ET formally explains the limited successes of the ‘rational mechanical’ approaches as idealizing special …

Shift-Symmetric Configurations In Two-Dimensional Cellular Automata: Irreversibility, Insolvability, And Enumeration, Peter Banda, John S. Caughman Iv, Martin Cenek, Christof Teuscher

Mathematics and Statistics Faculty Publications and Presentations

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.

Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of “non-symmetric” tasks regardless of the transition function. By using a compact enumeration formula and bounding the number …

A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity, Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi

Mathematics and Statistics Faculty Publications and Presentations

We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts …

Determination Of The Electric Field Intensity And Space Charge Density Versus Height Prior To Triggered Lightning, Christopher J. Biagi, Martin A. Uman, Jay Gopalakrishnan, J. D. Hill, Vladimir A. Rakov, T. Ngin, Douglas M. Jordan

Mathematics and Statistics Faculty Publications and Presentations

We infer the vertical profiles of space charge density and electric field intensity above ground by comparing modeling and measurements of the ground-level electric field changes caused by elevating grounded lightning-triggering wires. The ground-level electric fields at distances of 60 m and 350 m were measured during six wire launches that resulted in triggered lightning. The wires were launched when ground-level electric fields ranged from 3.2 to 7.6 kV m⁻¹ and the triggering heights ranged from 123 to 304 m. From wire launch time to lightning initiation time, the ground-level electric field reduction at 60 m ranged from 2.2 …

Polynomial Extension Operators. Part Iii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space H(div) is proven constructively. Specifically, on any tetrahedron K, given a function w on the boundary ∂K that is a polynomial on each face, the extension operator applied to w gives a vector function whose components are polynomials of at most the same degree in the tetrahedron. The vector function is an extension in the sense that the trace of its normal component on the boundary ∂K coincides with w. Furthermore, the extension operator is …

On The Intrinsic Evolution Of Material Inhomogeneities, Marek Elźanowski, Marcelo Epstein

Mathematics and Statistics Faculty Publications and Presentations

The evolution of a distribution of material inhomogeneities (defects, dislo-cations, etc.) is investigated. Adopting our recently developed model of the anelastic evolution law of a defective solid crystal body and using the classical methods of the theory of hyperbolic waves we analyze such phenomena as the long-term relaxation of defects and the dislocation pile-up.