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
Editor Blogs
Nature vs. Nurture
One of the biggest questions for psychologists revolves around the idea of innate or learned traits. Are our behaviors and personality traits influenced by our genetics (nature), or do we learn them as we grow (nurture)? How we answer this question will greatly impact the types of treatments we provide for psychological disorders. The answer is still up for debate, but here are … [Read more...] about Nature vs. Nurture
The Fundamental Solution of Laplace’s Equation and its Importance in Physics
Welcome back. Today, we will explore a concept that is central to the study of linear partial differential equations: that of the fundamental solution. As its name suggests, a fundamental solution is a very special solution to a PDE that serves as a building block for more general solutions. In this blog, my goal is to derive the fundamental solution to Laplace’s … [Read more...] about The Fundamental Solution of Laplace’s Equation and its Importance in Physics
Eyewitness Identification – Part 1
Eyewitnesses are one of the most relied upon pieces of evidence in the trial process. Most jury members do not understand the limitations of eyewitness testimony, and they rely upon it as “fact”. Memory doesn’t function like a video camera: it is malleable and can be influenced by a lot of outside factors. Unlike eyewitness testimony, DNA is conclusive. The Innocence Project … [Read more...] about Eyewitness Identification – Part 1
Reviewing Altspace VR: One of the First of its Kind
Nowadays, the elusive term “The Metaverse” isn’t so foreign to most people anymore. It’s the concept of a virtual world in parallel to our actual reality. There are many ways for people to engage with this world- but by far the most immersive is through VR. You’re in the virtual world- a participant, rather than an observer. The most popular Metaverse “worlds” you can visit are … [Read more...] about Reviewing Altspace VR: One of the First of its Kind