The verified integration of ranges of initial conditons through ODEs faces two major challenges, namely the precise representation of the flow over the short term, and the avoidance of unfavorable buildup of errors in the long term. We discuss the method of shrink wrapping for meeting the second of these challenges within the framework of Taylor model methods. Illustrative examples of the perfo...

Over the past century, plastics have infiltrated all aspects of human life. From the plastic shrink wrapping that protects food from bacteria and fungus, to the Styrofoam cup that keeps coffee hot and soft drinks cold, to the life-saving medical equipment found in hospitals and doctor’s offices, plastic is everywhere. However, the popularity of plastics comes at great cost. Most plastics are de...

Abstract Cell injection is a common clinical approach for therapeutic delivery into diseased and damaged tissues in order to achieve regeneration. However, cell retention, viability, engraftment at the site have generally been poor, driving need improved approaches. Here, we developed technique shrink-wrap micropatterned islands of corneal endothelial cells basement membrane-like layer extracel...

The thermal instability of polymer separators severely threatens the safety characteristics lithium-ion (Li-ion) batteries. Separators will melt, shrink, vaporize, and collapse under high temperatures, leading to internal short circuits runaway catastrophes cell. Therefore, amelioration battery challenges benefits from a fundamental understanding separator behaviors thermally abusive scenarios....

In this note, we outline one method to perform shrink wrapping to eliminate the remainder term of the Taylor model integration of ODEs. We point out that there are many variants of this approach, and while the one shown here is perhaps the simplest one to understand, it is not necessarily the optimal choice. More about other possibilities at the end of the section. After the n-th step of the in...

Students are most motivated and learn best when they are immersed in an environment that causes them to realize why they should learn. Perhaps nowhere is this truer than when teaching the biological sciences to engineers. Transitioning from a traditionally mathematics-based to a traditionally knowledge-based pedagogical style can challenge student learning and engagement. To address this, human...

Students are most motivated and learn best when they are immersed in an environment that causes them to realize why they should learn. Perhaps nowhere is this truer than when teaching the biological sciences to engineers. Transitioning from a traditionally mathematics-based to a traditionally knowledge-based pedagogical style can challenge student learning and engagement. To address this, human...