In this chapter, we explore the basics of fluid mechanics. We will think about how to describe fluids and look at the kinds of things they can do.

Unusually, and a little defensively, the title of this chapter highlights what we won’t talk about, rather than what we will. Fluids have a property known as viscosity. This is an internal friction force acting within the fluid as diferent layers rub together. It is crucially important in many applications. In spite of its importance, we will start our journey into the world of fluids by ignoring viscosity altogether. Such flows are called inviscid. This will allow us to build intuition for the equations of fluid mechanics without the complications that viscosity brings. Moreover, the flows that we find in this section will not be wasted work. As we will see later, they give a good approximation to viscous flows in certain regimes where the more general equations reduce to those studied here.

The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.

Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important.

The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.

In this chapter, we present the microscopic (Langevin equation) and macroscopic (Fokker–Planck equation) descriptions of Brownian motion and confirm their consistency. Furthermore, we provide a detailed introduction to the Poisson process, which forms the foundation of chemical reactions. Subsequently, we introduce the chemical Langevin equation and its corresponding Fokker–Planck equation, which are utilized in modeling molecular number fluctuations in chemical reactions. We also explain stochastic differential equations with both the Ito and Stratonovich types of integrals. Exploring mechanisms arising from the presence of noise, we discuss noise-induced transitions and attractor selection and adaptation in dynamical systems, elucidating their functional significance in cells. Finally, as an advanced topic, we introduce adiabatic elimination in stochastic systems.

Rare or extreme fluctuations beyond the Gaussian regime are treated through large deviation theory for the nonequilibrium steady state of discrete systems and of systems with Langevin dynamics. For both classes, we first develop the spectral approach that yields the scaled cumulant-generating function for state observables and currents in terms of the largest eigenvalue of the tilted generator. Second, we introduce the rate function of level 2.5 that can be determined exactly. Contractions then lead to bounds on the rate function for state observables or currents. Specialized to equilibrium, explicit results are obtained. As a general result, the rate function for any current is shown to be bounded by a quadratic function which implies the thermodynamic uncertainty relation.

In 1896, Edward Charles Pickering, Director of the Harvard College Observatory (HCO), reported in a trio of publications on the observation of “peculiar spectra” of the southern star ζ Puppis, which he attributed to an “element not yet found in other stars or on earth.” Supported by laboratory spectra obtained by Alfred Fowler, Niels Bohr showed in 1913 that this “element” was ionized helium. Its spectrum has become known as the Pickering series, even though Pickering credited Williamina Fleming (1857−1911), one of HCO’s “computers” and the future curator of the Astronomical Photographic Glass Plate Collection, for the discovery. The series of spectral lines associated with Pickering’s name played a unique role on the path to quantum mechanics,serving as a proving ground for Bohr’s model of the atom. Our examination of the discovery of the Pickering series relied on the records held at the Center for Astrophysics | Harvard & Smithsonian, especially the notebooks and diaries of Fleming, and on the center’s glass plate collection. Glimpses of the “peculiar sociology” of a research institution, half of whose staff were women employed on grossly unequal terms with men, are also given.

This chapter examines the contributions to quantum physics made by Lídia Salgueiro (1917–2009) and a team of women researchers at the Laboratory of Physics of the University of Lisbon. Between 1929 and 1947, the Lisbon laboratory rose to prominence as a successful research school in atomic and nuclear physics. The 1947 political purge by the dictatorial regime of the Estado Novo, however, led to a drastic reorganization, including the ousting of one of its leaders, Manuel Valadares. The right-wing physicist Julio Palacios was then appointed director. We here analyze how these institutional changes impacted Salgueiro’s agency. While Palacios opted for a new research agenda on electrochemistry, Salgueiro and women researchers gathered around her took responsibility for continuing research along the lines previously set up by Valadares. This group of women successfully extended their research into quantum physics to the study of radiation emitted at the atomic and nuclear levels, with a particular emphasis on X-ray spectroscopy. They asserted themselves as a relevant group within the Portuguese emerging research community in the field, participating in the many avenues asserting experimental atomic and nuclear physics on a global scale.

The efficiency of classical heat engines is bounded by the Carnot efficiency leading to vanishing power. Efficiency at maximum power is often related to the Curzon–Ahlborn efficiency. As a paradigm for a periodic stochastic heat engine, a Brownian particle in a harmonic potential is sequentially coupled to two heat baths. For a simple steady-state heat engine, a two-state model coupled permanently to two heat baths leads to transport against an external force or against an imposed electrochemical potential. Affinities and Onsager coefficients in the linear response regime are determined. The identification of exchanged heat in the presence of particle transport is shown to be somewhat ambiguous.

Spanish physicist Maria Lluïsa Canut (1924–2005) specialized in the application of X-ray diffraction to the determination of molecular crystal structures, a field at the intersection of crystallography and quantum mechanics. She completed her PhD at the University of Barcelona under the supervision of José Luís Amorós (1920–2001). After becoming a couple, the two developed joint research projects. In the 1960s, they moved to Southern Illinois University, where she notably built computing programs to analyze molecular structures from X-ray diffraction patterns. In parallel, Canut became involved in the struggle for pay parity at the university. This participation in the US second feminist wave sparked her interest in science policy. After the couple moved back to Madrid in the 1970s, Amorós continued with crystallographic research, whereas Canut became involved in American–Spanish scientific cooperation and computing systems applied to university libraries. This chapter analyzes Canut’s scientific contributions against the backdrop of her gender and across the changing contexts of her career, including the role played by scientific couples in the research enterprise.

Take an electric charge and shake it and it will produce light. The purpose of this chapter is to explain how this works.

The Hamiltonian plays the starring role in the standard formulation of quantum mechanics. But, back in the classical world, there are two equivalent ways to write down a theory, one using the Hamiltonian and the other using the Lagrangian. It’s natural to wonder if there might also be another formulation of quantum mechanics, where things are written in terms of the Lagrangian. Happily, there is. And it’s lovely. Its called the path integral

The main ideas are introduced in a historical context. Beginning with phase retrieval and ending with neural networks, the reader will get a sense of the book’s broad scope.

There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like.

This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.