Perturbation Methods 
From the standpoint of physical modeling, perturbation methods are instrumental to most fields of engineering, particularly, to propulsion related subdisciplines such as acoustics, fluid dynamics, and combustion. For example, in seeking solutions to wave propagation in injectiondriven chambers, it is necessary to not only explore the mathematical ranges of asymptotic theory, but also to develop new original strategies that stand to capture the nonlinear scaling structure that underlies these problems. Such strategies have to be developed and validated, thus constituting important contributions of our research endeavor. Other contributions include applications of wave propagation theory to pulsatory flows in biologically inspired systems and the application of swirl driven flow modeling to plasma transport, meteorology (in modeling cyclonic motion), and industrial flow separation industries (where centrifuges and cyclone separators are used). In the
field of perturbation
theory, we have
developed a new method for solving boundary value problems that exhibit
nonlinear scales. This
approach, dubbed the GeneralizedScaling Technique (GST), applies to
specific classes of differential equations that arise in the context of
overlapping dispersive and dissipative mechanisms.
Such complexity characterizes acoustic (dispersive) oscillations that
are subject to shear (dissipative).
The new asymptotic technique enables us to predict the inner
variables (both linear and nonlinear) at the forefront of a
multiplescales analysis. It
should be noted that prediction of nonlinear scales was not possible
before. Some problems that
exhibit a nonlinear scaling structure (that is virtually impossible to
conjecture) are now tractable using the GST technique.
Applications of GST include many fields of science and
engineering that involve multiple scales.
