When nodes share features we can combine those features in many possible ways. One standard way is to base relationships on shared features. But there are other possibilities. Here we will apply a number of approaches to investigate the concept of distinctiveness. Distinctiveness is how easy it is to discriminate one thing from another thing. In an important sense distinctiveness is therefore a hypothesis about how the mind works. We say two things are distinctive because a mind can distinguish them. But what makes something distinctive? In this chapter, I will introduce some of the theory behind distinctiveness and then demonstrate how we can use network science to investigate distinctiveness in children’s abilities to learn words. This takes a multilayer network approach, in which we will examine many different edge types constructed of various combinations of shared and unshared features. By examining these edge types will discover how best to combine features and which feature combinations best predict early word learning.

In this chapter, we will focus on the statistical spectral dynamics which are paramount to understanding the development of the integrated mixing quantities described in Chapter 5. Reynolds flow averaging and the turbulent kinetic energy are introduced. In addition, I will discuss how the energy of the flows is transferred from large scale to small scale modes, as well as the impact of the shockwave and gravity on the isotropy of the flows. The flow spectra allow several important length scales to be defined. Numeric simulations and experimental data will be offered to provide insights on the mixing processes.

This chapter will provide a detailed presentation of the basic structure of the supernova and its core collapse process to illustrate the roles that RMI, RTI, and KHI play in the different stages of these processes. During the explosions, the shockwave passing through the onion-like supernova core will generate both RMI and RTI. The RTI is the key physical process creating the filament structures observed in the Crab Nebula. MHD RT instabilities will be presented to show how they can further improve the comparison between simulations and observations. Several additional applications where hydrodynamic instability plays an important role will also be examined. Geophysics and solar physics also present effective lenses to view the importance of hydrodynamic instabilities. In the case of solar physics, I will describe how RTI’s impact can be viewed through various phenomena, such as the plumes that rise from low density bubbles as well as eruptions that occur as material returns to the solar surface. Once again, MHD RT instabilities are relevant.

After the RM instability grows from a first shock, it can be hit by a second shock. These reshock scenarios have been found in the key applications of inertial confinement fusion implosions or supernova explosions. In this chapter, I will introduce the efforts to model the growth of the mixing layer induced by the first shock and subsequent reshock and describe how the turbulence kinetic energy and anisotropy might be affected by the reshock events. Data from shock tube experiments and numeric simulations will also be introduced to provide insight into the reshock RM induced flows.

Structure matters for understanding behavior. This chapters introduces the main theme of the book, provides a number of stories about the importance of structure, and outlines the main structure of the book.

There are a number of microphysics and transport processes that can be extremely important to suppress or enhance the growth of these instabilities. I will provide a detailed description of how the hydrodynamic instability evolutions can be modified by incorporating the viscosity, surface tension, diffuse interface, and compressibility of the flows into the governing equations and growth rates.