Partial differential equations govern the universe, and most of these equations are nonlinear. This poses a challenge to engineers because nonlinear equations are difficult to solve. In many cases, there is no explicit formula for a solution and it often takes several pages of mathematical arguments to prove whether or not a solution even exists. However, with some clever … [Read more...] about First-Order Nonlinear Partial Differential Equations and the Method of Characteristics
Editor Blogs
Buffy the Vampire Slayer: Season 2 Episode 22 Allegory on Queerness and the Coming Out Experience
Buffy the Vampire Slayer is a famous American TV show that aired from 1997 to 2003 for seven seasons. The show follows the main character Buffy Summers, a high school student who is also a chosen vampire slayer. She has been given the power and responsibility to fight against vampires, demons, and other supernatural beings that threaten the world. Buffy and her friends navigate … [Read more...] about Buffy the Vampire Slayer: Season 2 Episode 22 Allegory on Queerness and the Coming Out Experience
Eyewitness Testimony – Part 2
In the last blog, I elucidated factors in the acquisition and storage of memories that can impact their accuracies. In this blog, I intend to discuss factors in memory retrieval that can lead to false memories. A very well-known incident of mistaken identity is Jennifer Thomson’s identification of Ronald Cotton as her rapist (The Perfect Witness). After giving police a … [Read more...] about Eyewitness Testimony – Part 2
Face Filters: Augmenting or Losing Reality?
After acquiring Looksery, a specialized face-tracking technology from Ukraine, Snapchat introduced the first widely used set of “Lenses”- AR face filters that merged the user’s real world with the digital world inside their phone. They have since been pioneers in the AR filter scene, and even democratized filter creation with the release of their desktop app Lens Studio in … [Read more...] about Face Filters: Augmenting or Losing Reality?
Finding Reduced-Order Models for Nonlinearizable Dynamical Systems using Spectral Submanifolds
A fundamental theme throughout this blog series has been partial differential equations (PDEs). The reason for this is that PDEs are a language through which we can describe the world around us, from the smallest scales, to the very largest. Many PDEs, moreover, involve time derivatives. This makes sense, as phenomena such as fluid flows, beam vibrations, and gravitational … [Read more...] about Finding Reduced-Order Models for Nonlinearizable Dynamical Systems using Spectral Submanifolds