By necessity, experimental studies have been the key to advancement in fluid dynamics for centuries. However, with the rapid increase of computational capabilities, numerical approaches have become an acceptable surrogate for experiments. Calculations must resolve the Navier–Stokes equations or approximate methods constructed from them. I will discuss the pros and cons of various types of approaches used, including direct numerical simulations, subgrid models, and implicit grid-discretization-based large-eddy simulation.

This chapter contains a discussion of the coupling of a magnetic field, through the framework of magnetohydrodynamics (MHD), to the hydrodynamic body forces. This leads to an additional body force, namely the Lorentz force on electrical currents in the fluid. Due to their conductivity, this effect is especially important for ionized plasmas. The intuitive result is that the magnetic field lines follow the flow, and they have an effective tension that can stabilize the RTI. As with the RTI, the RMI can be suppressed by a magnetic field.

Is searching memory like searching space? William James once wrote that “We make search in our memory for a forgotten idea, just as we rummage our house for a lost object.” Both space and memory have structure and we can use that structure to zero in on what we are looking for. In searching space, this is easy to see. A person hunting for their lost keys is not unlike a starling scouring the garden for wayward insects. But in searching memory, what is the map? And by what means does a person move from one memory to the next? In this chapter I will lay out the similarities between foraging in space and mind and then describe a research approach inspired by an ecological model of animal forging. Using this approach, we will combine data from a memory production task with a cognitive map – a network representation – of memory derived from natural language. We will then use this to compare a suite of models aimed at teasing apart how memory search is similar to our garden starling.

Conspiracy theories explain anomalous events as the outcome of secret plots by small groups of people with malevolent aims. Is every conspiracy unique, or do they all share a common thread? That is, might conspiracy explanations stem from a higher-order belief that binds together a wide variety of overtly independent phenomena under a common umbrella? We can call this belief the conspiracy frame. Network science allows us to examine this frame at two different levels: by examining the structural coherence of individual conspiracies and by examining the higher-level interconnectivity of the conspiracy beliefs as a whole.

The challenge confronting researchers is significant in many ways. One can start by noting that multiple instabilities might exist simultaneously and interact with each other. As an example, oblique shocks generate all three instabilities: RT, RM, and KH. In this chapter, several combined instabilities are discussed: RTI and RMI, RTI and/or RMI with KHI.

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.

Chapter 7 sets out the key components of State responsibility under international law and then uses a series of case studies to demonstrate that responsibility in practice. Responsibility for a State’s negligent failure to prevent a terrorist attack looks at the acts and omissions of the Russian authorities with respect to the school siege at Beslan in 2003. Three cases have been chosen to exemplify the direct perpetration of terrorism by a State. The first case is the bombing by French agents of the Greenpeace boat, Rainbow Warrior, by French agents in New Zealand in 1985. The second involves certain acts of Syrian authorities following the protests related to the Arab Spring, in particular the widespread and systematic torture and summary execution of opponents of the regime. The third case is the conduct of Russian forces in Ukraine following its invasion on 24 February 2022. Examples of State responsibility as accomplices to acts of terrorism are the responsibility of Liberia for the actions of the Revolutionary United Front (RUF) in neighbouring Sierra Leone during the civil war and the potential responsibility of Syria for the murder of former Lebanese Prime Minister, Rafik Hariri, in Beirut on 14 February 2005.