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Method of Lines Transpose: High Order L-Stable {O}(N) Schemes for Parabolic Equations Using Successive Convolution
Get PDFWe present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a one-dimensional heat equation solver that uses fast convolution. This fundamental solver has arbitrary order of accuracy in space and is based on the use of the Green\u27s function to invert a modified Helmholtz equation. Higher orders of accuracy in time are then constructed through a novel technique known as successive convolution (or resolvent expansions). These resolvent expansions facilitate our proofs of stability and convergence, and permit us to construct schemes that have provable stiff decay. The multidimensional solver is built by repeated application of dimensionally split independent fundamental solvers. Finally, we solve nonlinear parabolic problems by using the integrating factor method, where we apply the basic scheme to invert linear terms (that look like a heat equation), and make use of Hermite--Birkhoff interpolants to integrate the remaining nonlinear terms. Our solver is applied to several linear and nonlinear equations including heat, Allen--Cahn, and the FitzHugh--Nagumo system of equations in one and two dimensions
2016 Draft Statement
No full textA Draft Statement presenting the findings of the recent evaluation by the Engineering Accreditation Commission of ABET
2016 Draft Statement
No full textA Draft Statement presenting the findings of the recent evaluation by the Engineering Accreditation Commission of ABET
When and Where to Use Probability Distributions with Periodic Failure Rates
No full textWe discuss situations in real life where probability distributions with periodic failure rates should be considered. This discussion leads us to a new class, called Almost-Lack-of-Memory (ALM) probability distributions. We explain the structure of these distributions, and list some of their important properties. One of the main properties is its periodic failure rate. Throughout this article we notice some areas of possible applications of these distributions, and relate applications to the properties of these distributions
Paired vehicle occupant analysis indicates age and crash severity moderate likelihood of higher severity injury in second row seated adults in frontal crashes
No full textThe majority of advances in occupant protection systems for motor vehicle occupants have focused on occupants seated in the front row of the vehicle. Recent studies suggest that these systems have resulted in lower injury risk for front row occupants as compared to those in the second row. However, these findings are not universal. In addition, some of these findings result from analyses that compare groups of front and second row occupants exposed to dissimilar crash conditions, raising questions regarding whether they might reflect differences in the crash rather than the front and second row restraint systems. The current study examines factors associated with injury risk for pairs of right front seat and second row occupants in frontal crashes in the United States using paired data analysis techniques. These data indicate that the occupant seated in the front row frequently experiences the more severe injury in the pair, however there were no significant differences in the rate of occurrence of these events and events where the more severe injury occurs in the second row occupant of the pair. A logistic regression indicated that the likelihood of the more severe injury occurring in the second row seated occupant of the pair increased as crash severity increased, consistent with data from anatomic test dummy (ATD) tests. It also indicated that the second row occupant was more likely to have the more severe injury in the pair if that occupant was the older occupant of the pair. These findings suggest that occupant protection systems which focus on providing protection specifically for injuries experienced by older occupants in the second row in higher severity crash conditions might provide the greatest benefit