Luoyi Tao

In this work we establish a link between a Reynolds averaged turbulence modeling methodology, containing interactions up to the second order correlations between the velocity fluctuations at various scales, and a multi-objective optimization problem with the constraints expressed in terms of equality and inequality, imposed by the given boundary conditions and the positive semi-definiteness of the Reynolds stress tensor, etc. The information unavailability and uncertainty associated with the boundary conditions for the fluctuation correlations of various orders is delineated, and the information from the Navier-Stokes equations is utilized to the extent allowed by the available input data necessary for simulations; turbulence from the perspective of systems simulation is explored and some objective functions are proposed. Finally, the challenges faced by the formulation and the issues yet to be resolved are discussed. © 2009.

We investigate the applicability of Poincaré's and the quantum recurrence theorems to the physical systems such as a container filled with a gas from a physical perspective. We discuss certain difficulties with regard to the definition of the Hamiltonian for such systems and the existence of one-to-one mappings as solutions to the equations of motion. We examine a typical proof of Poincaré's recurrence theorem and notice that a key part of the proof appeals to the motion of a neighborhood of finite volume in a phase space and this neighborhood possesses infinite kinetic energy, raising another question concerning the applicability of the theorem to physical systems. The same situations also present themselves in the application of Liouville's theorem. © 2008 Elsevier B.V. All rights reserved.