Qualitative changes in bifurcation structure for soft vs hard impact models of a vibro-impact energy harvester.

Vibro-impact phenomena in engineering systems, considered an adverse effect in some settings, are an intrinsic part of the mechanism in others. In energy harvesting, a vibro-impact component is often intentionally introduced to increase the power output or the system's bandwidth. The impacts can be treated as "hard" for instantaneous impacts or "soft" for compliant materials.

Maximization of viability time in a mathematical model of cancer therapy.

In this paper, we study a dynamic optimization problem for a general nonlinear mathematical model for therapy of a lethal form of cancer. The model describes how the populations of cancer and normal cells evolve under the influence of the concentrations of nutrients (oxygen, glucose, etc.) and the applied therapeutic agent (drug).