Game-environment feedback dynamics in growing population: Effect of finite carrying capacity.

The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in conjunction with a phenomenological equation for the state of the shared resource to gain insight into the influence of the games on the TOC. The replicator equation, by construction, models a fixed infinite population undergoing microevolution. Thus, it is unable to capture any effect of the population growth and the carrying capacity of the population although the TOC is expected to be dependent on the size of the population. Therefore, in this paper, we present a mathematical framework that incorporates the density dependent payoffs and the logistic growth of the population in the eco-evolutionary dynamics modeling the game-resource feedback. We discover a bistability in the dynamics: a finite carrying capacity can either avert or cause the TOC depending on the initial states of the resource and the initial fraction of cooperators. In fact, depending on the type of strategic game-theoretic interaction, a finite carrying capacity can either avert or cause the TOC when it is exactly the opposite for the corresponding case with infinite carrying capacity.

Evaporation dynamics of pure and binary mixture drops on dry and lubricant coated slippery surfaces.

HYPOTHESIS: Lubricating fluid coated slippery (LCS) surfaces offer a new scope to study the evaporation of sessile drops due to pinning free motion of the three-phase contact line (TPCL). This work aims to experimentally demonstrate the different evaporation behavior of water and binary mixture drops on dry and LCS surfaces. EXPERIMENTS: Evaporation study on dry and LCS surfaces is performed by capturing top and side views of evaporating drops to extract various parameters which are subsequently used to distinguish between different evaporation modes. FINDINGS: Formation of a wetting ridge and cloaking of water drops on LCS surfaces affect the overall evaporation process and make it different compared to that on dry surfaces. Evaporation dynamics on LCS surfaces reveal that wetting ridge height of an evaporating drop varies non-monotonically compared to the drop height. Diffusion based theoretical model is used to predict the role of various system parameters on the evaporation process. In contrast to dry solid surfaces, where coffee ring effects are commonly observed towards the end of the evaporation process, LCS surfaces show the formation of a wrinkle like pattern of the lubricating fluid which disappears at long times.