Filtering by
The first class includes linear coupled PDEs with one spatial variable. Parabolic, elliptic or hyperbolic PDEs with Dirichlet, Neumann, Robin or mixed boundary conditions can be reformulated in order to be used by the framework. As an example, the reformulation is presented for systems governed by Schr¨odinger equation, parabolic type, relativistic heat conduction PDE and acoustic wave equation, hyperbolic types. The second form of PDEs of interest are scalar-valued with two spatial variables. An extra spatial variable allows consideration of problems such as local stability of fluid flows in channels and dynamics of population over two dimensional domains.
The approach does not involve discretization and is based on using Sum-of-Squares (SOS) polynomials and positive semi-definite matrices to parameterize operators which are positive on function spaces. Applying the parameterization to construct Lyapunov functionals with negative derivatives allows to express stability conditions as a set of LinearMatrix Inequalities (LMIs). The MATLAB package SOSTOOLS was used to construct the LMIs. The resultant LMIs then can be solved using existent Semi-Definite Programming (SDP) solvers such as SeDuMi or MOSEK. Moreover, the proposed approach allows to calculate bounds on the rate of decay of the solution norm.
The methodology is tested using several numerical examples and compared with the results obtained from simulation using standard methods of numerical discretization and analytic solutions.
The purpose of this project is to assess how well today’s youth is able to learn new skills<br/>in the realm of engineering through online video-conferencing resources. Each semester of this<br/>last year, a class of students in both 3rd and 6th grade learned about computer-aided design (CAD)<br/>and 3D printing through their laptops at school. This was done by conducting online lessons of<br/>TinkerCAD via Zoom and Google Meet. TinkerCAD is a simple website that incorporates easy-to-learn skills and gives students an introduction to some of the basic operations that are used in<br/>everyday CAD endeavors. In each lesson, the students would learn new skills by creating<br/>increasingly difficult objects that would test both their ability to learn new skills and their overall<br/>enjoyment with the subject matter. The findings of this project reflect that students are able to<br/>quickly learn and retain new information relating to CAD. The group of 6th graders was able to<br/>learn much faster, which was expected, but the class of 3rd graders still maintained the<br/>knowledge gained from previous lessons and were able to construct increasingly complicated<br/>objects without much struggle. Overall, the students in both classes enjoyed the lessons and did<br/>not find them too difficult, despite the online environment that we were required to use. Some<br/>students found the material more interesting than others, but in general, the students found it<br/>enjoyable to learn about a new skill that has significant real-world applications
0° spoilers reduced the wake area behind the car, decreasing pressure drag but also decreasing underbody flow, causing a reduction in drag and downforce. Angled spoilers increased the wake area behind the car, increasing pressure drag but also increasing underbody flow, causing an increase in drag and downforce. Longer spoilers increased these effects compared to shorter spoilers, and short spoilers at different angles did not create significantly different effects. 0° spoilers would be best suited for cases that prioritize fuel economy or straight-line acceleration and speed due to the drag reduction, while angled spoilers would be best suited for cars requiring downforce. The angle and length of spoiler would depend on the downforce needed, which is dependent on the track.