For analytical simplicity, most research to date on RT and RM instabilities has focused on planar geometries. Such a simplified design is very helpful in easing the diagnostic requirements for laboratory experiments. However, in our limited observations of Chapter 15, we have already witnessed that other geometric configurations may alter the mixing layer growth significantly. In a variety of important applications, one must deal with imploding/exploding flows, the prime examples of which are inertial confinement fusion implosions (convergent geometry) and supernova explosions (divergent geometry). In these configurations, the flows are radially accelerated/decelerated. In contrast to planar geometry, where only RM growth is expected to occur, converging/diverging shock-accelerated interfaces can be RT unstable as they geometrically contract or expand. In the experiments and analytical modeling in this chapter, the amplitude growth depends on the convergence history in a complicated way.

The structure of diatomic molecules is discussed in this chapter. The electronic structure of diatomic molecules is then discussed in detail. The coupling of the orbital and spin angular momenta of electrons and the angular momentum associated with nuclear rotation are discussed, with an emphasis on Hund’s cases (a) and (b). The rotational wavefunctions for diatomic molecules in the limits of Hund’s cases (a) and (b) and in the case intermediate between Hund’s cases (a) and (b) are then discussed in detail. For molecules that are of importance in combustion diagnostics, such as OH, CH, CN, and NO, the electronic levels are intermediate between Hund’s cases (a) and (b). We use Hund’s case (a) as the basis wavefunctions, and linear combinations of these wavefunctions are used to represent wavefunctions for electronic levels intermediate between cases (a) and (b). The choice of case (a) wavefunctions as the basis set is typical in the literature although case (b) wavefunctions can also be used as a basis set.

Describes a range of physical techniques that can be applied to bacterial biophysics including sample culture, flow cytometry, microscopy, photonics, NMR, mass spectrometry and electrophoresis.

Introduces the physical action of antibiotics and antiseptics including penetration through biofilms, persister cells, surface activity, physical sterilization and antibiofilm molecules.

Raman scattering spectroscopy is widely used in analytical chemistry, for structural analysis of materials and molecules and, most importantly for our purposes, as a gas-phase diagnostic technique. Raman scattering is a two-photon scattering process, and the mathematical treatment of Raman scattering is very similar to the mathematical treatment of two-photon absorption. Many of the molecules of interest for quantitative gas-phase spectroscopy are diatomic molecules with non-degenerate 1Σ ground electronic levels, including N2, CO, and H2. In this chapter, the theory of Raman scattering is developed based on Placzek polarizability theory and using irreducible spherical tensor analysis. Herman–Wallis effects are discussed in detail. The chapter concludes with detailed examples of Raman scattering signal calculations.

Considers diffusion and statistical models for bacterial motility from the perspective of anomalous transport.

Turbulent flow is a notoriously difficult topic in its own right because it is a truly multi-scale problem with strong nonlinearities. However, in this chapter, I will provide a framework for the key concepts, statistical measurements, and implications for the mixing process, so that the reader can better understand this issue. Both the classic engineering treatment of turbulence as well as the modern statistical closure theories will be introduced and brought together to show the reader how they can be synthesized to describe turbulence mixing induced by hydrodynamic instability driven flows. Some of the key concepts that I will elaborate on include energy transfer and interacting scales. The energy spectrum, and its applicability to RMI and RTI flow, is discussed.

Due to the time-consuming nature of fully 3D simulations of turbulence mixing induced by hydrodynamic instabilities, it is desirable to run computations in 2D when possible. But does 2D turbulence resemble 3D turbulence? The relevance of idealized 2D turbulence to certain aspects of atmospheric motion has been emphasized in many works. Yet molecular mixing occurs at the interfaces of the fluids, and the ratios of area-to-volume in three dimensions are very different than the length-to-area ratios in two dimensions. This has prompted some well-known scientists to claim that "two-dimensional turbulence, ... is a consequence of the construction of large computers." I will investigate this issue in detail and point out that the large-scale structures evolve over a similar time scale in 2D and 3D, indicating that 2D simulations are useful for providing some indication of the amount of instability growth at an interface.