Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an explicit formula for the wave speed. The key step in our approach is the derivation of an asymptotic ODE for the appropriately rescaled strain profile.Comment: revised version with corrected typos; 25 pages, several figure

To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case

In parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters. Interpolation in the parameters is an obvious possibility, in this context often labeled as a collocation method. In the frequent situation where one has a "solver" for the equation for a given parameter value - this may be a software component or a program - it is evident that this can independently solve for the parameter values to be interpolated. Such uncoupled methods which allow the use of the original solver are classed as "non-intrusive". By extension, all other methods which produce some kind of coupled system are often - in our view prematurely - classed as "intrusive". We show for simple Galerkin formulations of the parametric problem - which generally produce coupled systems - how one may compute the approximation in a non-intusive way

May 2010 - Digital Minute Issue 2

This issue features information about global repositories, as well as visits to our Digital Commons by country

Sparse bayesian polynomial chaos approximations of elasto-plastic material models

In this paper we studied the uncertainty quantification in a functional approximation form of elastoplastic models parameterised by material uncertainties. The problem of estimating the polynomial chaos coefficients is recast in a linear regression form by taking into consideration the possible sparsity of the solution. Departing from the classical optimisation point of view, we take a slightly different path by solving the problem in a Bayesian manner with the help of new spectral based sparse Kalman filter algorithms

Near real-time stereo vision system

The apparatus for a near real-time stereo vision system for use with a robotic vehicle is described. The system is comprised of two cameras mounted on three-axis rotation platforms, image-processing boards, a CPU, and specialized stereo vision algorithms. Bandpass-filtered image pyramids are computed, stereo matching is performed by least-squares correlation, and confidence ranges are estimated by means of Bayes' theorem. In particular, Laplacian image pyramids are built and disparity maps are produced from the 60 x 64 level of the pyramids at rates of up to 2 seconds per image pair. The first autonomous cross-country robotic traverses (of up to 100 meters) have been achieved using the stereo vision system of the present invention with all computing done onboard the vehicle. The overall approach disclosed herein provides a unifying paradigm for practical domain-independent stereo ranging

Beyond Surveys: Analyzing Software Development Artifacts to Assess Teaching Efforts

This Innovative Practice Full Paper presents an approach of using software development artifacts to gauge student behavior and the effectiveness of changes to curriculum design. There is an ongoing need to adapt university courses to changing requirements and shifts in industry. As an educator it is therefore vital to have access to methods, with which to ascertain the effects of curriculum design changes. In this paper, we present our approach of analyzing software repositories in order to gauge student behavior during project work. We evaluate this approach in a case study of a university undergraduate software development course teaching agile development methodologies. Surveys revealed positive attitudes towards the course and the change of employed development methodology from Scrum to Kanban. However, surveys were not usable to ascertain the degree to which students had adapted their workflows and whether they had done so in accordance with course goals. Therefore, we analyzed students' software repository data, which represents information that can be collected by educators to reveal insights into learning successes and detailed student behavior. We analyze the software repositories created during the last five courses, and evaluate differences in workflows between Kanban and Scrum usage