Late Lunch Talk Double Feature: Bubbles and the Lotka-Volterra predator-prey model
Late Lunch Talk by Vikash Pandey from CEES
1) A tale of "coupled" bubbles
A bubble is a gas trapped within a medium of denser material which is often a liquid. These two phase (gas-liquid) media are often born from chance and usually end their short life violently in the union with the nearly infinite! The scientific aesthetics attached with bubbles can be inferred from the fact that their investigation has attracted great minds such as Leonardo da Vinci, George Gabriel Stokes, and Lord Rayleigh. Bubbles often come into existence in huge clusters of bubble-clouds that could have varying population of individual bubbles, from few of tens to millions! Such a cloud of bubbles have known to tear apart steel, cement, human tissue, and so much more! The two-bubble case constitutes the simplest form of such a complex bubble-cloud dynamics. Interestingly, the behavior of a two-bubble system is similar to that of a human-couple. Sometimes the bubbles may come close, but they may also tend to distance away from one another. But nevertheless, their collective behavior is always coupled, i.e., the response of a bubble is determined by the response from the bubble in its immediate vicinity. On the one hand, a complete understanding of bubbles is pivotal for many industrial applications such as turbomachinery, biomedical ultrasound, shock wave lithotripsy, material processing, and seismic exploration. On the other hand, even though bubbles are easily amenable to our imagination, they are notoriously difficult for scientific investigation. In this talk, I will qualitatively explain the physics of bubble dynamics, the two-bubble case, and why we should study them. Some really cool facts about bubbles will be mentioned too.
2) The more the merrier, is not always true. Deriving new insights from Lotka-Volterra predator-prey model
At CEES, I am working in collaboration with Prof. Nils Christian Stenseth and others in the micro-macro project. The project aims to mathematically model and relate micro-evolutionary processes with macro-evolutionary processes, and also examine the role of feedback between ecology and evolutionary processes. The mathematical models form the foundation of modern ecological theory as they are not only useful in generating immediately testable quantitative predictions, but they also serve as a tool to elaborate empirically-derived biological patterns. However, these models must also provide proof-of-concept, as they are necessary to test the validity of verbal chains of logic by laying out the specific assumptions mathematically. The accuracy of the mathematical expressions is critical, but once they are established, the resulting mathematical analysis could reduce the possibility of logical error in the understanding of evolutionary processes which are inherently complex. In this talk, I will discuss an intermediate result that I have arrived at along with one of my project collaborators Prof. Jan Martin Nordbotten (UiB). The result is related to the well-established Lotka-Volterra predator-prey model. It will be shown that the mathematical rigor when followed along with dimensional consistency requirements from physics can lead to interesting interpretation of the parameters that govern the mathematical models.