Hindu-Arabic Numerical System

The decimal number system, an integral part of daily life, traces its origins back to 6th-century India. Characterized by the digits zero through nine, revolutionized numerical computation and record-keeping, setting the stage for advancements in mathematics, science, and commerce. Despite its apparent simplicity and utility to the contemporary observer, the widespread adoption of this system …

Diophantine Equations

Contributions of Diophantus of Alexandria hold a distinguished place. His seminal work, Arithmetica, unveiled in the 3rd century CE, is a key in the study of number theory, particularly in the realm of integers. This ancient text, encapsulating 130 equations, laid the foundation for what are now known as Diophantine equations—equations constrained to integer solutions. …

An Improbable Life by D.C. Wilcox, and the $k-\omega$ Model

I just finished reading the autobiography of D. C. Wilcox. He wrote a number of books that were published through his own company. One of the most popular is on fluid dynamics. A less known book is on turbulence modeling. He was famous for a particular two-equation turbulence model in the form of $k-\omega$. It …

On Algorithm

An algorithm, a concept rooted in 9th-century Arabic scholarship, is a methodical procedure for problem resolution, eliminating the need for trial-and-error. This term, reflecting centuries of intellectual endeavor, denotes the evolution from Euclid’s ancient formulations to Al-Khwarizmi’s systematic methods and Ada Lovelace’s 19th-century innovations, highlighting algorithms’ integral role in computational development.

Salome

It is my yearly tradition to listen to the opera Salome by Richard Strauss on Valentine’s Day. To celebrate, I treated the department staff to donuts. Working on my research while listening to the opera can be a bit distracting, but it makes for a perfect Valentine’s Day tradition. I first saw the opera while …

Remembering Professor Olga Alexandrovna Ladyzhenskaya Twenty Years On

It has been approximately twenty years since Professor Olga Alexandrovna Ladyzhenskaya passed away. An eminent mathematician and member of several Academies of Science, passed away in January 2004. Her distinguished career was marked by significant contributions to partial differential equations, particularly the Navier–Stokes equations and nonlinear elliptic and parabolic equations. Born in 1922 in Kologriv, …

AIAA SciTech 2024 – Parametric Study of the Hypersonic Near-Field and Sonic Boom from Waveriders using a Fully-Parabolized Approach

Citation: King, C. B., Shepard, C. T., and Miller, S. A. E., “Parametric Study of the Hypersonic Near-Field and Sonic Boom from Waveriders using a Fully-Parabolized Approach,” AIAA SciTech, Orlando, FL, Jan. 8-12, AIAA 2024-2106, 2024. DOI: 10.2514/6.2024-2106 Abstract: A parametric study is performed to understand the relationship between volume displace- ment, lift, near-field signature, …