Perturbation Growth and Structure in Uncertain Flows. Part II

Perturbation Growth and Structure in Uncertain Flows. Part II

Perturbation growth in uncertain systems associated with fluid flow is examined concentrating on deriving, solving, and interpreting equations governing the ensemble mean covariance. Covariance evolution equations are obtained for fluctuating operators and illustrative physical examples are solved. Stability boundaries are obtained constructively in terms of the amplitude and structure of opera...

Perturbation Growth and Structure in Uncertain Flows. Part I

Perturbation growth in uncertain systems is examined and related to previous work in which linear stability concepts were generalized from a perspective based on the nonnormality of the underlying linear operator. In this previous work the linear operator, subject to an initial perturbation or a stochastic forcing distributed in time, was either fixed or time varying, but in either case the ope...

Perturbation Growth and Structure in Time-Dependent Flows

Asymptotic linear stability of time-dependent flows is examined by extending to nonautonomous systems methods of nonnormal analysis that were recently developed for studying the stability of autonomous systems. In the case of either an autonomous or a nonautonomous operator, singular value decomposition (SVD) analysis of the propagator leads to identification of a complete set of optimal pertur...

Part II Linguistic Structure

Modeling Growth Stocks ( Part Ii )

Continuing the previous work on growth stocks, we propose a diffusion model for growth stocks. Since growth stocks tend to have low or even negative earnings and high volatility, it is a great challenge to derive a meaningful mathematical model within the traditional valuation framework. The diffusion model not only has economic interpretations for its parameters, but also leads to some interes...