Harikrishnan S
School of Mathematics
Indian Institute of Science Education and Research
Thiruvananthapuram
Posts
Reynolds Transport Theorem (RTT): A Fundamental Relation Between System and Control Volume Analyses
The Reynolds Transport Theorem is a foundational principle in fluid mechanics and thermodynamics that provides a bridge between the Lagrangian (system) and Eulerian (control volume) descriptions of fluid motion. It allows us to relate the rate of change of an extensive property for a system (a fixed quantity of matter) to the behavior of that property within a control volume (a specified region in space) and across its control surfaces.
September 21, 2024
Reinhardt Domains Examples and Counter Examples
Introduction In the realm of complex analysis, the study of domains within complex spaces is fundamental to understanding the behavior of holomorphic functions. Complex numbers, which can be represented geometrically as points on a plane, extend naturally into higher dimensions as complex vectors in $ \mathbb{C}^n $. This geometric perspective allows for the exploration of intricate structures and symmetries within these spaces. One particularly interesting type of domain is the Reinhardt domain.
July 14, 2024
Master Stability Function
The master stability function is a simple concept with a wide range of applications, primarily in determining the stability of the synchronised state of coupled dynamical systems. I am assuming that you are unfamiliar with the master stability function, chaotic oscillators, and coupled dynamical systems. Understanding Chaos: An Example Imagine a hypothetical point particle in motion in 3D space. How would you find the trajectory of this hypothetical point particle?
July 13, 2024