Welcome back. In today’s blog post, I am excited to discuss Lyapunov functions, which can prove the stability of equilibrium points of a broad class of dynamical systems, including nonlinear systems. Lyapunov functions generalize the concept of energy from mechanical systems. If a pendulum is damped, then its downward position is a stable equilibrium point, and its energy will … [Read more...] about Lyapunov Functions: Proving the Stability of Equilibrium Points of Dynamical Systems
Articles
Nanotechnology in Cosmetics: Revolution or Risk
When producing cosmetics, chemists are always searching for ways to make products with maximum efficiency. Better UV penetration, deeper color pigment, or smoother application, all of these factors are goals as new products come out. However, there is one branch of science that the beauty industry has started to invest in, to make this possible: nanotechnology. Nano refers to … [Read more...] about Nanotechnology in Cosmetics: Revolution or Risk
The Cult of Chrome Hearts
Chrome Hearts is a luxury brand that has captivated the hearts of fashion enthusiasts with its blend of Gothic aesthetics, rock-and-roll influences, and high-quality craftsmanship. Founded in 1988 in Los Angeles by Richard Stark, Leonard Kamhout, and John Bowman, the brand started as a niche label catering to motorcycle enthusiasts. Over the years, it has transformed into a … [Read more...] about The Cult of Chrome Hearts
Saving Ma Ganga: Investigating the Conflict Between Religious Purity and Bacterial Impurity of the Ganges River
The Ganges, or Ganga, is a river that extends nearly 1,680 miles from the base of the Himalayas to the Bay of Bengal. Like most major world rivers, it is an essential aspect of daily life for those who live along its banks, providing drinking water, irrigation for crops, and serving as an avenue for travel (McNeil). However, in addition to its practical significance, the Ganges … [Read more...] about Saving Ma Ganga: Investigating the Conflict Between Religious Purity and Bacterial Impurity of the Ganges River
Hydrodynamic Stability: 2D Stability Analysis in Primitive Variables
Welcome back. I hope everyone is having a wonderful first week after spring break and is doing well going into the final stretch of the semester. In today’s blog post, I want to discuss how we could perform linear stability analysis using primitive velocity and pressure variables instead of intricately-derived streamfunction or vorticity quantities. One downside of primitive … [Read more...] about Hydrodynamic Stability: 2D Stability Analysis in Primitive Variables