Abstract: The scale invariant forms of the conservation equations will be applied to show that in the absence of convection the velocity field will be governed by non-homogenous diffusion equation similar to the density, the temperature, the pressure, and the vorticity fields. The similarities and the underlying connections between physical phenomena at various scales associated with geometric optics (Hamilton-Jacobi equation), electrodynamics (Schrodinger equation), statistical mechanics (Boltzmann equation), and hydrodynamics (Bernoulli equation) will be explored. In particular, the physical basis of quantum mechanics and the associated double-slit and the EPR problems will be addressed on the basis of a scale invariant description of Heisenberg matrix mechanics and Schrodinger equation. Furthermore, the nature of the connections between quantum versus continuum fields will be explored and its impact on the success of Fourier representation of generalized functions will be discussed. Finally, some of the implications of a scale-invariant model of statistical mechanics to the physical foundation of analysis, non-Euclidean geometry, and prime number theory will be addressed.

Brief Biography of the Speaker:
Siavash H. Sohrab received his PhD in Engineering Physics in 1981 from University of California, San Diego, his MS degree in Mechanical Engineering from San Jose State University in 1975, and his BS degree in Mechanical Engineering from the University of California, Davis in 1973. He then joined Northwestern University in 1982 as postdoctoral research assistant and became Visiting Assistant Professor in 1983, Assistant Professor of Mechanical Engineering in 1984, and since 1990 he is Associate Professor of Mechanical Engineering at the Northwestern University. From 1975-1978 he worked as a scientist doing research on fire protection and turbulent combustion at NASA Ames research center in California. His research interests have been on combustion, fluid dynamics, thermodynamics, and statistical and quantum mechanics.