Airborne viruses, bacteria, or toxins are dangerous because of the nature of the human transmission pathway through breathing. However, every airborne component must conform to the laws of physics governing atmospheric propagation. Given the fact that most atmospheric flows, at both ground level and throughout the atmosphere, are highly turbulent, the mechanisms of turbulence can be employed to understand the propagation of such components. In this paper, the problem of harmful airborne pathogen transmission is considered in the context of atmospheric turbulence and wall-bounded flow theory. Two approaches are considered: one of them relies on singular measurements of building boundary distances and morphology, and the other relies on constant temperature measurement. The theoretical and practical potential of these approaches is then discussed and explained in a larger urban context.
The nature of chaos is elusive and disputed, however it can be connected to sensitivity to initial conditions caused by nonlinearity of the equations describing chaotic phenomena. A nowhere-near comprehensive list of such equations can still be shown: the Boltzmann equation, Ginzburg-Landau equation, Ishimori equation, Korteweg-de Vries equation, Landau-Lifshitz-Gilbert equation, Navier-Stokes equation, and many more. This disproportionality between input and output creates an analytically-difficult situation, one that is complicated both algebraically and numerically – however, the study of equations that are both simple and chaotic may yield useful connections between algebraic complexity and chaos. Such connections can be used to determine the simplest possible chaotic function, which can be used as a “chaotic operator” for various non-chaotic or chaotic functions, thus reducing the problem of chaos to one based strictly on algebra.
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