Welcome back. In this week’s blog, we will explore the Fourier transform, which is a valuable tool across engineering disciplines. Like most tools, its primary power is to make complicated problems simpler. To demonstrate this, we will first define the Fourier transform and establish some of its most important properties. We will then apply it to solve the one-dimensional heat … [Read more...] about The Fourier Transform and the Heat Equation
Editor Blogs
Continuation of Olfactory VR: A Historical Perspective
There are several main areas that scent-focused XR is tasked with addressing, the first of which being position tracking. In order to trigger appropriate smells at times that correspond with the storytelling in a virtual experience, it is important that the system is able to track where a user is in this digital environment, so that as they come upon scent-triggering elements, … [Read more...] about Continuation of Olfactory VR: A Historical Perspective
Soul: The Meaning of Life
Soul is a 2020 Pixar animated film that was directed by Pete Docter and Written by Pete Docter, Mike Jonas, and Kemp Powers. It follows Joe, a middle school band teacher, who dies suddenly, and doesn’t feel like he’s ready for his time to be up. He dies right before he’s able to perform at his dream gig. He had been doing on and off side gigs, but was never able to land his big … [Read more...] about Soul: The Meaning of Life
Consciousness
When pondering the mind, consciousness is a difficult problem to fully understand. Consciousness is defined as the quality or state of being aware, especially of something within oneself (www.merriam-webster.com). If a person, or organism, has a conscious experience, it means there is something it is like to be that kind of person or organism. To perceive your own … [Read more...] about Consciousness
Gradients and Potential Flow Part 2: Streamlines, Harmonics, and Analytic Functions
Last time, we learned that if we have a scalar function φ(x,y) that satisfies Laplace’s equation (∆φ = ∇ • ∇φ = 0), then its gradient can define the velocity field of a well-behaved fluid that is irrotational and has no sources or sinks. Today we will try to find equations for the streamlines that particles have as they move through the fluid flow defined by ∇φ. Here, we can … [Read more...] about Gradients and Potential Flow Part 2: Streamlines, Harmonics, and Analytic Functions