Welcome back. In today’s blog post, I am excited to discuss Koopman operator theory, which provides a mathematical framework for representing nonlinear dynamics as a linear system. This theory was originally developed by Columbia University professor Bernard Koopman in 1931 [1], but remained in relative obscurity until the 2000s, when modern computers allowed it to be applied … [Read more...] about Linear Embeddings of Nonlinear Dynamics with the Koopman Operator
Archives for January 2025
The Groutfit: Fashion in Grayscale
The “groutfit,” a portmanteau of “gray” and “outfit,” has emerged as a unique and sometimes controversial trend in modern fashion. This head-to-toe gray ensemble, while simple, has sparked conversations about comfort and style, particularly among young adults and college students. The groutfit first gained recognition in the late 2000s, when it was humorously defined … [Read more...] about The Groutfit: Fashion in Grayscale
How Spider Silk is Revolutionizing Modern Materials
Scientists have spent decades trying to replicate spider silk's properties in synthetic materials. Unlike silkworms, which can be farmed, spiders are territorial and cannibalistic, making large-scale silk production impractical. This challenge has led to innovative approaches, including: Genetically modified bacteria that produce spider silk proteinsSynthetic polymers that … [Read more...] about How Spider Silk is Revolutionizing Modern Materials
The Changing Beauty Consumer: Rise of Sustainability
Over 120 billion pieces of cosmetic packaging is created each year. As the vanity is filled in, bathroom counters lined up, and drawers crammed with products, what happens to them after they are finished? Beauty has been a staple in today’s society with individuals wanting to feel their best selves, in their own way. However, the beauty industry is no longer just about what it … [Read more...] about The Changing Beauty Consumer: Rise of Sustainability
Hydrodynamic Stability: Three-Dimensional Linear Stability and Input-Output Analysis of Parallel Shear Flows
Introduction: Welcome back. Today, I am excited to return to our series on hydrodynamic stability. In previous blogs, we considered the stability of two-dimensional parallel shear flows. Now, we will derive the governing equations for stability analysis of three-dimensional parallel shear flows. Our mathematical work here will give us the tools to consider oblique modes and … [Read more...] about Hydrodynamic Stability: Three-Dimensional Linear Stability and Input-Output Analysis of Parallel Shear Flows