Forthcoming

To understand what the Maxwell equations are telling us, it’s useful to dissect them piece by piece. The simplest piece comes from looking at stationary electric charges and how they give rise to electric fields. A consequence of this is the Coulomb force law between charges. This, and much more, will be described in this chapter.

The chapter then goes on to explore many other different kinds of waves that arise in different situations, from the atmosphere, to supersonic aircraft to traffic jams.

Theres a lot of interesting physics to be found if you subject an atom to an electric or magnetic field. This chapter explores this physics. It covers the Stark effect and the Zeeman effect and Rabi oscillations. it also looks at what happens when coherent states of photons in a cavity interact with atoms.

In this chapter, we ease in gradually by thinking about a quantum particle moving along a line. This provides an opportunity for us to learn about the properties of the wavefuntion and how it encodes properties such as the position and momentum of the particle. We will also see how the physics of a system is described by the Schrodinger equation.

Sonja Ashauer (1923–1948) trained as a physicist at the University of São Paulo in Brazil and obtained a PhD in theoretical and mathematical physics from the University of Cambridge, under the guidance of Paul Dirac. Acknowledged as the first Brazilian woman with a physics PhD, her life was brief: She passed away six months after defending her thesis. In her few contributions, she explored the non-physical consequences of classical equations for point electrons, reformulated by Dirac in the late 1930s to address divergence issues in quantum electrodynamics. This chapter traces Ashauer’s journey from São Paulo, where she collaborated with a small and enthusiastic group of young researchers around the Italian–Russian physicist Gleb Wataghin and focused on cosmic ray physics research, to Cambridge, where she found a more secluded research environment.

The reflect-reflect-relax (RRR) algorithm is derived from basic principles. Local convergence is established and the flow limit is introduced to better understand the global behavior.

A qubit is the classical version of a bit in the sense that it can take one of two values. But the key idea of the quantum world is that it can, in fact, take both values at the same time. Here we explore the physics of the qubit and use it as a vehicle to better understand some of the stranger features of quantum mechanics.

The size of the intersection of A and B tells us if we should expect many solutions, or if we should be surprised to find even one. The latter case implies a conspiracy and is the most interesting.

In this chapter, we introduce various modeling approaches capable of addressing pattern formation by cell populations. Firstly, we discuss the Delta–Notch system as an example of pattern formation by local interaction. We then explore the Kessler–Levin model, which combines cellular automaton and continuous system approaches, illustrating the evolution of cAMP waves in cellular slime molds. Next, our attention turns to methodologies requiring active consideration of cellular arrangements and deformations, including models involving cell proliferation and movement. We present reaction–diffusion systems that explain structures formed in bacterial colonies resembling Diffusion Limited Aggregation (DLA). Additionally, we introduce the cellular Potts model to investigate pattern formation among moving cells, incorporating variations in cellular adhesion force. The cell-vertex model represents a cell population as a collection of vertices of a polygon or polyhedron. We also discuss the phase field model, employing partial differential equations to depict relatively simple morphological changes in complex structures. By employing these modeling techniques, we can capture the characteristics of various pattern formations orchestrated by cell populations.

The chapter illustrates what it meant for Carolyn Beatrice Parker (1917–1966) to be a Black woman physicist in the US during the Jim Crow era. Her father, a physician, and her mother, a teacher, shepherded her into Fisk University, an historically Black college. As a physics major she studied infrared spectroscopy with the Black physicist Elmer Imes, graduating with a BS in 1938. She later attended the University of Michigan, obtaining an MA in physics in 1941. But like many Black women, she spent time before and after graduate school teaching in the K–12 system. In 1943, she became a research physicist at the Aircraft Radio Laboratory in Dayton, Ohio, where she stayed for four years. Although she co-authored a governmental report about her work on signal attenuation in coaxial cables, her name only appeared in the acknowledgments of the ensuing academic publications, thus partly obscuring her contributions. In 1947, Fisk University welcomed Parker on the faculty, but she soon after enrolled in a nuclear physics PhD program at the Massachusetts Institute of Technology. After dropping out, she worked as a laboratory technician until she grew too ill and died a short time later.

When a quantum system has some external time dependence, some rather special things happen. This chapter explores this subject. Among the topics that we cover are the adiabatic theorem, Berry phase, the sudden approximation, and time-dependent perturbation theory.

There are two great equations of classical physics: one is Einstein’s equation of general relativity, the other the Navier-Stokes equation that describes how fluids flow. In this chapter, we meet Navier-Stokes.

This equation differs from the Euler equation by the addition of a viscosity term. This is not a small change and makes solutions to the Navier-Stokes equation much richer and more subtle than those of the Euler equation. In this chapter, we begin our exploration of these solutions.

Active particles self-propel through some intrinsic mechanism. First, a simple one-dimensional model is introduced for which the density profile between confining walls and the pressure exerted on these walls can be calculated analytically. In three dimensions, run-and-tumble particles, active Brownian particles, and active Ornstein–Uhlenbeck particles constitute three classes of models that can be described by Langevin equations. The identification of entropy production in the steady state is shown to be ambiguous. The continuum limit of a thermodynamically consistent discrete model shows that Langevin descriptions contain some implicit coarse-graining which prevents the recovery of the full physical entropy production.