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Classical mechanics starts with Newtons three laws, among them the famous F=ma. But these laws are not quite as transparent as they may seem. In this chapter, we introduce the laws and provide some commentary. We will also learn about Galileos ideas of relativity, a precursor to the much more shocking ideas of Einstein that come later.
Laura M. Chalk (later, Laura Rowles, 1904−1996) was the first woman to complete a PhD in physics at McGill University in Montreal, Canada. Her doctoral research on the quantum phenomenon called the Stark effect, under the supervision of J. Stuart Foster, produced the earliest experimental test of Erwin Schrödinger’s wave mechanics. After a brief stint as a postdoctoral fellow at King’s College London, she chose to return home and dedicate herself to teaching and marriage. This paper aims to fully recover Chalk’s work and explore why the Foster−Chalk experiment was overlooked in physics historiography. It considers the Stark effect’s significance in quantum physics and the impact of gender on her personal trajectory. Shaped by personal choice, systemic discrimination, and acceptance of societal norms, Chalk Rowles’ story highlights the paradoxes faced by women in a culturally disembodied yet male-dominated field, and reflects broader themes of gender and identity in the history of women in physics.
Quantum particles, like happy families, are all the same. In fact, not only are they the same. They are literally indistinguishable. This has deep and important consequences that are fleshed out in this chapter.
The real fun of the Maxwell equations comes when we understand the link between electricity and magnetism. A changing magnetic flux can induce currents to flow. This is Faraday’s law of induction. We start this chapter by understanding this link and end this chapter with one of the great unifying discoveries of physics: that the interplay between electric and magnetic fields is what gives rise to light.
In this chapter, we explore how electric and magnetic fields behave inside materials. The physics can be remarkably complicated and messy but the end result are described by a few, very minor, changes to the Maxwell equations. This allows us to understand various properties of materials, such as conductors.
What is the essence of quantum mechanics? What makes the quantum world truly different from the classical one? Is it the discrete spectrum of energy levels? Or the inherent lack of determinism? The purpose of this chapter is to go back to basics in an attempt to answer this question. We will look at the framework of quantum mechanics in an attempt to get a better understanding of what we mean by a “state”, and what we mean by a “measurement”. A large part of our focus will be on the power of quantum entanglement.
In this chapter, we discuss dynamical system approaches for cellular differentiation. We explain how intracellular reaction dynamics can give rise to various attractors using a simple discrete-time and discrete-state reaction model known as a Boolean network. Subsequently, we outline the behavior of a simple stochastic differentiation model of stem cells, where the scaling law discovered therein aligns well with that observed in the distribution of clonal cell populations generated by epidermal stem cells. To integate both approaches, we introduce a theory wherein cell–cell interactions induce transitions between attractors, and stability at the cell-population level emerges through the regulation of these dynamic transitions. Such a circular relationship satisfies the consistency between the cell and the cell population. We expound on three types of differentiation processes, that by Turing instability, transition from an oscillatory state (limit-cycle) to a fixed point, and retaining oscillatory expression dynamics. Additionally, we analyze stability at the cell population level through the regulation of differentiation ratios and the differentiation dynamics of stem cells. Finally, we engage in a discussion of unresolved issues in the field.
Large temporal fluctuations or oscillations in cellular states are widely observed in biological systems, for instance, in neural firing, circadian rhythms, and collective motion of amoebae. These phenomena arise from the interplay between positive and negative feedback mechanisms, as discussed in previous chapters. In this chapter, we focus on such dynamic changes in cellular states. Using trajectories of oscillatory dynamics in phase planes such as the Brusselator, we provide detailed explanations of conditions for oscillation through the use of nullcline and Jacobian matrix analyses. We confirm the existence of two mechanisms: the activator-inhibitor system and the substrate-depletion system. Furthermore, we extensively introduce the Hodgkin–Huxley equations concerning membrane potential and excitability, which represent a significant milestone in the fields of biophysics, theoretical biology, and electrophysiology. Through quantitative comparison with experimental data, we elucidate the mechanisms underlying its dynamics, which are explained by the reduction of variables leading to the FitzHugh–Nagumo equations.
Systems with a discrete set of mesostates and their canonical description in equilibrium are introduced. Observing trajectories in equilibrium yields the thermodynamic potentials of these mesostates. Time-scale separation allows one to describe the dynamics using a Markovian master equation. The ratio of transition rates is constrained by the free energy difference of the corresponding mesostates. First for relaxation and then for time-dependent driving, work, heat, and internal energy are identified along individual trajectories. Entropy production along such a trajectory is shown to contain three contributions given by the dissipated heat and the change in internal entropy and in stochastic entropy. The distributions of these thermodynamic quantities obey various exact fluctuation relations. For entropy production, the relation to the arrow of time and a putative identification within a Hamiltonian dynamics is discussed.
The interaction between the dynamics of a flame front and the acoustic field within a combustion chamber represents an aerothermochemical problem with the potential to generate hazardous instabilities, which limit burner performance by constraining design and operational parameters. The experimental configuration described here involves a laminar premixed flame burning in an open–closed slender tube, which can also be studied through simplified modelling. The constructive coupling of the chamber acoustic modes with the flame front can be affected via strategic placement of porous plugs, which serve to dissipate thermoacoustic instabilities. These plugs are lattice-based, 3-D-printed using low-force stereolithography, allowing for complex geometries and optimal material properties. A series of porous plugs was tested, with variations in their porous density and location, in order to assess the effects of these variables on viscous dissipation and acoustic eigenmode variation. Pressure transducers and high-speed cameras are used to measure oscillations of a stoichiometric methane–air flame ignited at the tube’s open end. The findings indicate that the porous medium is effective in dissipating both pressure amplitude and flame-front oscillations, contingent on the position of the plug. Specifically, the theoretical fluid mechanics model is developed to calculate frequency shifts and energy dissipation as a function of plug properties and positioning. The theoretical predictions show a high degree of agreement with the experimental results, thereby indicating the potential of the model for the design of dissipators of this nature and highlighting the first-order interactions of acoustics, viscous flow in porous media and heat transfer processes.
We investigate the dynamics of a cavitation bubble near rigid surfaces decorated with a single gas-entrapping hole to understand the competition between the attraction of the rigid and the repulsion of the free boundary. The dynamics of laser-induced bubbles near this gas-entrapping hole is studied as a function of the stand-off distance and diameter of the hole. Two kinds of toroidal collapses are observed that are the result of the collision of a wide microjet with the bubble wall. The bubble centroid displacement and the strength of the microjet are compared with the anisotropy parameter $\zeta$, which is derived from a Kelvin impulse analysis. We find that the non-dimensional displacement $\delta$ scales with $\zeta$.
The fate of deformable buoyancy-driven bubbles rising near a vertical wall under highly inertial conditions is investigated numerically. In the absence of path instability, simulations reveal that, when the Galilei number, $Ga$, which represents the buoyancy-to-viscous force ratio, exceeds a critical value, bubbles escape from the near-wall region after one to two bounces, while at smaller $Ga$ they perform periodic bounces without escaping. The escape mechanism is rooted in the vigorous rotational flow that forms around a bubble during its bounce at high enough $Ga$, resulting in a Magnus-like repulsive force capable of driving it away from the wall. Path instability takes place with bubbles whose Bond number, the buoyancy-to-capillary force ratio, exceeds a critical $Ga$-dependent value. Such bubbles may or may not escape from the wall region, depending on the competition between the classical repulsive wake–wall interaction mechanism and a specific wall-ward trapping mechanism. The latter results from the reduction of the bubble oblateness caused by the abrupt drop of the rise speed when the bubble–wall gap becomes very thin. Owing to this transient shape variation, bubbles exhibiting zigzagging motions with a large enough amplitude experience larger transverse drag and virtual mass forces when departing from the wall than when returning to it. With moderately oblate bubbles, i.e. in an intermediate Bond number range, this effect is large enough to counteract the repulsive interaction force, forcing such bubbles to perform a periodic zigzagging-like motion at a constant distance from the wall.
This paper introduces a novel ray-tracing methodology for various gradient-index materials, particularly plasmas. The proposed approach utilizes adaptive-step Runge–Kutta integration to compute ray trajectories while incorporating an innovative rasterization step for ray energy deposition. By removing the requirement for rays to terminate at cell interfaces – a limitation inherent in earlier cell-confined approaches – the numerical formulation of ray motion becomes independent of specific domain geometries. This facilitates a unified and concise tracing method compatible with all commonly used curvilinear coordinate systems in laser–plasma simulations, which were previously unsupported or prohibitively complex under cell-confined frameworks. Numerical experiments demonstrate the algorithm’s stability and versatility in capturing diverse ray physics across reduced-dimensional planar, cylindrical and spherical coordinate systems. We anticipate that the rasterization-based approach will pave the way for the development of a generalized ray-tracing toolkit applicable to a broad range of fluid simulations and synthetic optical diagnostics.
The dynamics of ice basal melting in seawater is one of the key factors in understanding and modelling the ice–seawater interaction in the polar oceans. In this work we study the basal melting of solid ice in seawater, and focus on the interaction between the melting process and the double diffusive convection developed in the seawater layer. Different temperatures and salinity differences are systematically simulated, and two different flow regimes are identified. For a relatively weak salinity difference, the convection layer occupies most of the liquid layer and grows in height as the ice melts. When the salinity difference is strong enough, the convection layer shrinks with time and a stably stratified layer grows between the ice layer and convection layer. When the dynamics is dominated by the convection layer, the global heat and salinity transfer rates follow a power-law scaling. Theoretical models are developed for the local mean salinity at the ice–water interface and the melting rates, and the critical density ratio corresponding to the transition between the two regimes, which all agree with the numerical results. Density inversion happens consistently adjacent to the ice–seawater interface, which has a profound influence on the ice surface shape. All these findings provide useful insights into the detailed dynamics of ice basal melting in oceans.
Many hypersonic flows of interest feature high free-stream stagnation enthalpies, which lead to high flow-field temperatures and thermochemical non-equilibrium (TCNE) effects, such as finite-rate chemistry and vibrational excitation. However, very few studies have considered receptivity for high-enthalpy flows. In this paper, we investigate the receptivity of a high-enthalpy Mach 5 straight-cone boundary layer to slow and fast acoustic free-stream waves using direct numerical simulation alongside linear stability theory and the linear parabolised stability equations. In addition, we investigate the TCNE effect on receptivity by comparing results between the TCNE gas model and a thermochemically frozen gas model. The dominant instability mechanism for this flow configuration is found to be Mack’s second mode, with the unstable mode being the fast mode. Second-mode receptivity coefficients are obtained for a number of frequencies. For free-stream slow acoustic waves, these receptivity coefficients are found to generally increase with frequency. For a small subset of the considered frequency range, the receptivity coefficients corresponding to free-stream fast acoustic waves are found to be several times larger than for free-stream slow acoustic waves. The TCNE effects are found to lead to higher peak $N$-factors while also reducing second-mode receptivity coefficients, indicating that TCNE effects have competing impacts on receptivity versus stability for the considered frequencies.