Ishwarabroto Mridha
Amplitude Equations for Modelling Electromagnetically Induced Flows
Electromagnetically induced flows, that is a fluid motion caused by the interaction between a magnetic field and an electric current passing through the fluid, are ubiquitous in both natural and industrial processes. This interaction can stir fluids, create turbulence, and enhance mixing without the use of mechanical devices making it a valuable tool for various applications. This research aims to develop a simplified mathematical model to better understand and predict the associated complex fluid behaviors. We will consider the fluid motion as a combination of distinct patterns, or modes, that evolve in time. The amplitude evolution of such modes can be described by ordinary differential equations of Landau type. The research seeks to capture the interactions between these modes through a system of coupled equations. The six-week project begins with an in-depth review of existing theories on electromagnetically driven flows. Building on this foundation, the next phase will involve deriving amplitude equations that accurately describe the non-linear interactions between different flow modes. Subsequently, these equations will be analysed to reveal how the fluid behaves under varying conditions. The insights gained from this work are envisaged to serve the purpose of improving industrial processes. By enhancing the understanding of electromagnetically induced flows this research will inform better engineering designs and practical advancements across a range of scientific and industrial fields such as pharmaceutical micro-mixing.
Ishwarabroto Mridha
Swinburne University of Technology
Ishwarabroto recently graduated from Swinburne University of Technology with a Bachelor of Science, majoring in Applied Mathematics. He aspires to pursue a Master of Research, focusing on Dynamical Systems and Ergodic Theory. When not dreaming of winning a Fields Medal, he enjoys watching films and writing critiques, often in the form of essays. In fact, it was after watching Good Will Hunting that he decided to pursue mathematics—and that journey has brought him here today.
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