The Renaissance, a period of significant intellectual, artistic, and cultural rebirth, marked the combination of art and science, especially through the application of geometric principles in artistic representation. This era witnessed the pioneering development of linear perspective, a technique that revolutionized the way depth and three-dimensional objects were portrayed on two-dimensional surfaces. The mathematical foundation …

# Category Archives: Mathematics

## Additional Thoughts on Half-Equation Model of Johnson and King

The Johnson King turbulence model represented a significant advancement in the understanding and modeling of turbulent flows. Introduced amidst the exploration of first and second equation models, the Johnson King model distinguished itself through the innovative concept of a half-equation model, emphasizing the critical role of memory in turbulence phenomena. The early stages of turbulence …

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## 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 …

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## 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.

## 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, …

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## Analytical Closed-Form Solution of the Navier-Stokes Equations for the Aerodynamic Near-field and Sonic Boom from Axisymmetric Bodies

I completed my Acoustical Society work and returned to the United States. Abstract: An analytical closed-form solution is presented for the aerodynamic near-field and ground signature from an axisymmetric body with a low thickness ratio. The Navier-Stokes equations are formulated as a boundary value problem that incorporates the incoming ambient flow-field and the aerodynamic properties …

## Toward Exascale Computation for Turbomachinery Flows

Citation: Yuhang Fu, Weiqi Shen, Jiahuan Cui, Yao Zheng, Guangwen Yang, Zhao Liu, Jifa Zhang, Tingwei Ji, Fangfang Xie, Xiaojing Lv, Hanyue Liu, Xu Liu, Xiyang Liu, Xiaoyu Song, Guocheng Tao, Yan Yan, Paul Tucker, Steven Miller, Shirui Luo, Seid Koric, and Weimin Zheng, “Toward Exascale Computation for Turbomachinery Flows,” Gordon Bell, High Performance Computing, …

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## DARPA Director’s Fellow

I am very fortunate to be awared the 2023-2024 DARPA Director’s Fellowship. The linked article from my department is at the following link: https://mae.ufl.edu/2023/08/09/darpa-directors-fellowship-awarded-to-steven-a-e-miller/ The article text is below Associate Professor Steven A. E. Miller, Ph.D., is awarded the Director’s Fellowship from the Defense Advanced Research Projects Agency (DARPA) for 2023-2024. The award recognizes technical …