The AMS this month has a wonderful article on Euclid’s work and journey through the east. The famous mathematical text ‘Euclid’s Elements’ has a long and fascinating translation history in China. In the early 1600s, Italian priest Matteo Ricci brought a copy to China and collaborated with scholar Xu Guangqi to translate the first six …

# Category Archives: Mathematics

## AIAA Paper: Fully-Parabolized Prediction of Hypersonic Sonic Boom

Abstract: Hypersonic flight-vehicles create shock and expansion waves that propagate through the atmosphere and are observed on the ground as sonic booms. We present a methodology to predict the near-field aerodynamic pressure and sonic boom signature using approximately 1% of the computational cost relative to fully-nonlinear computational fluid dynamics and state-ofthe-art sonic boom propagation solvers. …

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## Aeroacoustic and Aerodynamic Interaction Effects Between eVTOL Rotors

My student presented his MS thesis on the aerodynamics and aeroacoustics of rotors. Abstract: Electric vertical take-off and landing (eVTOL) aircraft are characterized by their unconventional wing and electric rotor configurations, which involve both side-by-side and tandem rotor configurations. These configurations create unique aerodynamic and aeroacoustic flow-fields. We numerically investigate the interaction effects between rotor …

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## On Infinity by Euler

We may here deduce from it a few consequences that are extremely curious, and worthy of attention. The fraction $\frac{1}{\infty}$ represents the quotient resulting from the division of the dividend 1 by the divisor $\infty$. Now, we know, that if we divide the dividend 1 by the quotient $\frac{1}{\infty}$, which is equal to nothing, we …

## Teller on Uncertainty

… we have a radioactive substance that emits, on the average, a particle, an alpha particle, once every second on the average. Now, here I have a counter, and I close that counter, so it won’t count, except that I open it for half a second. If, in that half a second, a particle arrives, …

## Chairing Turbulence Theory at APS Division of Fluid Dynamics – Highlight of the year

All our presenters were present and traveled internationally. DNS is the tool of choice for numerical simulations. Theory emerged from results, and I hope that new relations will guide those making turbulence models today. High-order inertial range scaling exponents in incompressible turbulence using generalized extended self-similarityPresenter: Sualeh Khurshid, Massachusetts Institute of Technology, Author: Sualeh Khurshid, …

## APS Presentation – Alternative Analytical Solution for Planar Oblique Shock Waves

Abstract: One now famous analytical solution for shock waves was developed by Dr. Theodore Meyer within his Ph.D. dissertation under advisement of Professor Ludwig Prandtl. The original solution relies on analysis via control volume of the equations of motion. This approach has limited future development of analytical solutions for more complex flow-fields. In this presentation, …

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## APS Presentation – A New Course: Modeling Inhomogeneous Turbulence with a Historic Perspective

Abstract: A new graduate class is developed at the University of Florida called Modeling Inhomogeneous Turbulence with a Historical Perspective. The course covers in-depth concepts of the science and mathematics of turbulence modeling. Major topics of the class include statistics for modeling, the Russian school, law of the wall, chaos, compressible Navier-Stokes equations, mean kinetic …

## The prediction of cross-spectra from first mode instability waves within high-speed flow over sharp and blunt cones with plasma actuation

Abstract: Leading edge geometries, such as cones, moving at high-speed undergo intense loading due to the growth of instability waves and turbulent transition. These instability waves are highly spatially coherent. Aerodynamic loading related to instability waves and transition cause large-amplitude vibrations within the underlying structure, which may lead to flight-vehicle failure. We examine the effect …

## On Challenges in Turbulent Flow Theory and Experiment

Research in macroscopic classical physics, such as fluid dynamics or aspects of condensed matter physics, continues to confront baffling challenges that are by no means less demanding than those at the post-Newtonian frontiers of physics that have been explored since the beginning of this century. This is so even though the basic equations of macroscopic …

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