Molecular motors that transform chemical energy into mechanical motion can be modeled in different ways. Thermodynamically consistent ratchet-type models lead to transport against an external force in a periodic potential that switches between different shapes. In a second class of models, the motor is described by a set of internal states that leads to discrete steps along a filamentous track. In the class of hybrid models, the motor cycles through internal states while pulling a cargo particle that follows a Langevin dynamics. For these motors, the first and second laws and the thermodynamic efficiency are discussed and illustrated with experimental data for a rotary motor, the F1-ATPase.

Cells regulate their proliferation, differentiation, and motility in response to external stimuli. Often, these responses involve a complex interplay of association, dissociation, and catalytic reactions, characterized by highly specific intermolecular interactions. This chapter examines cellular responses arising from such chemical reactions from a mathematical standpoint. As examples of input–output relationships, we introduce the Hill equation, Adair equation, and the MWC model concerning allosteric regulation, which describe cooperative behaviors. We discuss the Michaelis–Menten equation in enzyme reactions, covering activation, inactivation, push–pull reactions, zero-order ultrasensitivity, and positive feedback switches. Furthermore, we present the formation of a bell-shaped input–output curve by feed-forward loops, and the mechanisms of adaptation and fold-change detection utilizing feed-forward loops, or negative feedback. We explore bacterial chemotaxis mechanisms through models such as the Asakura–Honda model and the Barkai–Leibler model.

Ana María Cetto Kramis (born 1946) studied physics at Universidad Nacional Autónoma de México and biophysics at Harvard University. As a faculty member back in Mexico, she spent over half a century delving into the fundamentals of quantum physics, with a singular focus on its stochastic interpretation. In addition to her theoretical work, she founded Latindex and has become a key figure in the open access movement. She has also had a long and influential contribution to international scientific cooperation. Her professional and personal journeys culminate with the dynamization of the International Year of Quantum Science and Technologies 2025, aiming to shed light on her understanding of quantum science and of science as a whole. This chapter is mostly based on an oral history, which is here also revisited as a historiographical methodology from its early use at the origins of the history of quantum physics.

In recent years, Grete Hermann (1901–1984) has been rediscovered as a principal figure in the history and philosophy of quantum physics. In particular, her criticism of Johann von Neumann’s so-called “no hidden variables” proof is a focal point of interest. Did she really find a mistake in this proof? We argue that the whole debate is misleading. It fits too well with the image of a forgotten woman who disproved a result of a mathematical genius, but it is neither historically nor systematically justified. Despite Hermann’s challenging thoughts on quantum physics, her impressive and important achievements were in ethics and politics. We offer a new and broader reading of Hermann’s interpretation of quantum physics and try to build a bridge between her works on quantum physics and ethics. In doing so, we focus on her interpretation of Heisenberg’s cut as a methaphorical device to argue against Leonard Nelson’s theory of free will and for freedom and responsibility as cornerstones of any democratic society.

We all know what a wave is. But you may not know just how many different kinds of waves there are and what strange and interesting properties they have. We start this chapter with something very familiar from everyday life: waves on the surface of an ocean. While they may be familiar, their mathematical description is surprisingly subtle. This can be traced, like so many other things in fluid mechanics, to the boundary conditions.

The fundamentals of electromagnetism are simple. Moving electric charges set up electric and magnetic fields. In turn, these fields make the charges move. This dance between charges and fields is described by the Maxwell equations. This brief chapter describes how this comes about. It is, in a sense, everything you need to know about electromagnetism, enshrined in these simple equations. The rest of the book is mere commentary.

The laws of classical mechanics are valid in so-called inertial frames. Roughly speaking, these are frames that are at rest. But what if you, one day, find yourself in a frame that is not in- ertial? For example, suppose that every 24 hours you happen to spin around an axis which is 2500 miles away. What would you feel? Or what if every year you spin around an axis 36 million miles away? Would that have any effect on your everyday life? In this chapter, we describe what happens if you sit in a rotating reference frame and the effects of the resulting centrifugal and Coriolis forces.

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.