Artificial light at night (ALAN) puts major pressure on the natural environment. There are five main ways of mitigating its biological impacts: avoidance of using ALAN, minimizing ALAN use, restoring or rehabilitating areas from ALAN, and offsetting the use of ALAN. Their potential effectiveness can be better understood through careful consideration of how organisms respond to light. Here we focus particularly on responses to altering recurring natural periods of light and darkness that affect the internal clock of organisms. All clocks are light sensitive and, depending on the photoreceptors of the organism, they show maximal responsiveness to different wavelengths, from UV to near infrared. Moreover, they show a high light-sensitivity, with a threshold at about intensities occurring during full moon or even less. This suggests that minimizing the use of ALAN through dimming of emissions and reducing the daily periods for which those lamps are in use may provide valuable benefits. However, if the biological effects of ALAN are to be widely reduced additional measures will need to be taken, including strengthening protection of the remaining dark spaces, reducing numbers of existing lights and restoring darkness in previously lit areas, and extensive shielding of those lights that are retained.

The Fourier series is introduced as a very useful way to represent any periodic signal using a sum of sinusoidal (“pure”) signals. A display of the amplitudes of each sinusoid as a function of the frequency of that sinusoid is a spectrum and allows analysis in the frequency domain. Each sinusoidal signal of such a complex signal is referred to as a partial, and all those except for the lowest-frequency term are referred to as overtones. For periodic signals, the frequencies of the sinusoids will be integer multiples of the lowest frequency; that is, they are harmonics. Pitch is a perceived quantity related to frequency, and it may have a complicated relationship to the actual frequencies present in terms of the series. For periodic signals, changes in the relative phase of the partials do not change the perception of sounds that are not too loud.

A minimal introduction to Nuclear Magnetic Resonance and to the two main types of contributions (dipolar and quadrupolar) to the spin Hamiltonian employed in studies of liquid crystals and obtainable from computer simulations.

In this note, we construct a higher-dimensional version of the chromatic fracture square. We then categorify the resulting chromatic fracture cubes obtaining a decomposition of the category of E(n)-local spectra into monochromatic pieces.

The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational toral G-spectra for arbitrary compact Lie groups. This chapter provides an introduction to the subject in two parts. The first discusses rational G-Mackey functors, the action of the Burnside ring and change of group functors. It gives a complete proof of the well-known classification of rational Mackey functors for finite G. The second part discusses the methods and tools from equivariant stable homotopy theory needed to obtain algebraic models for rational G-spectra. It gives a summary of the key steps in the classification of rational G-spectra in terms of a symmetric monoidal algebraic category. Having these two parts in the same place allows one to see clearly the analogy between the algebraic and topological classifications.

After explaining the mechanism producing double diffusion, its representation analytically is developed and applied to linear stability analysis to determine conditions for double diffusion to occur. Laboratory observations of salt fingers are summarized.

In the crudest sense, stable homotopy theory is the study of those homotopy invariant constructions of spaces which are preserved by suspension. In this chapter, we show how there are naturally occurring situations which exhibit stable behaviour. We will discuss several historic attempts at constructing a “stable homotopy category” where this stable behaviour can be studied, and we relate these to the more developed notions of spectra and the Bousfield–Friedlander model structure. Of course, if one only wants to perform calculations of stable homotopy groups, to have certain spectral sequences or similar, then one does not need much of the formalism of model categories of spectra. But as soon as one wishes to move away from those tasks and consider other stable homotopy theories (such as G–equivariant stable homotopy theory for some group G) or to make serious use of a symmetric monoidal smash product in the context of “Brave New Algebra”, then the advantages of the more formal setup become overwhelming.

In this chapter, we introduce symmetric spectra and orthogonal spectra along with their associated stable model structures. These versions of spectra have various technical advantages over sequential spectra. Furthermore, they are Quillen equivalent to the category of sequential spectra (equipped with its stable model structure). Hence, one may choose between these models according to their relative strengths. The primary advantage of symmetric and orthogonal spectra is that these model categories are symmetric monoidal models for the stable homotopy category. We will examine these monoidal structures further later on and show that symmetric spectra and orthogonal spectra are monoidally Quillen equivalent. Several other models of spectra also exist, and we will give short introductions to these later in this chapter. We end the chapter with a result that, roughly speaking, says that any model for the stable homotopy category will be Quillen equivalent to sequential spectra.

Bousfield and Friedlander defined the stable homotopy category in terms of the homotopy category of a model category of spectra. We will construct this model category following an approach similar to Mandell-May-Schwede-Shipley based on sequential spectra. A sequential spectrum is a sequence of pointed topological spaces (and structure maps), thus, a natural candidate for an analogue of weak homotopy equivalences are those maps of spectra inducing a weak homotopy equivalence at every level. However, we will see that these levelwise weak homotopy equivalences are not sufficient to define a class of weak equivalences leading to a meaningful stable homotopy theory. A key ingredient is the definition of homotopy groups of spectra and their isomorphisms. This generalises the notion of stable homotopy groups of topological spaces that we encountered earlier. Making these isomorphisms the weak equivalences of sequential spectra will give us a construction of our desired stable homotopy category. We end the chapter with an introduction to the Steenrod algebra and the Adams spectral sequence.