Introduction to the Special Issue on Perspectivesand Experiences on Mentoring Undergraduate Students in Research: Part II

Abstract

This issue is the second of a special PRIMUS two-part issue collecting articles on undergraduate research from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. This issue presents a collection of papers offering advice on a variety of specific topics important for leaders of undergraduate research programs. Issues of finding and designing appropriate and accessible research projects, assessing undergraduate research, and publicizing it in the media are addressed.     

Battle-outcome-prediction conditions for variable-coefficient Lanchester-type equations for area fire2

New important battle-outcome-prediction conditions are developed for combat between two homogeneous military forces modelled by variable-coefficient Lanchester-type equations for area fire. Such conditions are very significant in modern operations research for developing important insights into the dynamics of combat. However, similar differential-equation models do arise in other fields of science and technology such as mathematical ecology and epidemiology, and consequently our new mathematical results may also find application there. These new important “simple approximate” battle-outcome-prediction conditions depend on not only the combat-attrition model but also the battle-termination model, and they are developed for two different types of battle-termination conditions (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). They are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and a generalization of Lanchester’s famous linear law to variable-coefficient combat is involved in their development. Certain integrability properties of the Lanchester attrition-rate coefficients figure prominently in these results, and an important physical interpretation (relating to logistics considerations) is given for these properties.