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Geological materials are often seen as the antithesis of soft; rocks are hard. However, during the formation of minerals and rocks, all the systems we shall discuss, indeed geological materials in general, pass through a stage where they are soft. This occurs either because they are at a high temperature -- igneous or metamorphic rock -- or because they are at a lower temperature but in the presence of water -- sedimentary rock. For this reason it is useful to introduce soft-matter concepts into the geological domain. There is a universality in the diverse instances of geological patterns that may be appreciated by looking at the common aspect in their formation of having passed through a stage as soft matter.

The history of the discovery of nuclear fission and how science fiction had anticipated it.

The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate a refined description of the particle interaction that includes an ad hoc design of the inside of the system constituents, and use temperature as a control parameter. We show that all these features can emerge from a minimal athermal two-dimensional model where particles interact isotropically by a double-well potential, which includes an excluded volume and a maximum coordination number. The rich variety of structural patterns shown by this simple geometrical model apply to a wide range of real systems including water, silicon, and different amorphous materials., Comment: 6 pages, 5 figures

Mysterious craters, with anomalously high concentrations of methane, have formed in the Yamal and Taymyr peninsulas of Siberia since 2014. While thawing permafrost owing to climate warming promotes methane releases, it is unknown how such release might be associated with explosion and crater formation. A significant volume of surface ice-melt water can migrate downward driven by osmotic pressure associated with a cryopeg, a lens of salty water below. Overpressure reached at depth may lead to the cracking of the soil and subsequent decomposition of methane hydrates, with implications for the climate., Comment: Published version

We demonstrate that nature has produced a close-packed helical twisted filamentous material in the biomineralization of the mollusc. In liquid crystals, twist-bend nematics have been predicted and observed. We present and analyse evidence that the helical biomineral microstructure of mollusc shells may be formed from such a liquid-crystal precursor.

Could nature be harnessing quantum mechanics in cilia to optimize the sensitivity of the mechanism of left-right symmetry breaking during development in vertebrates? I evaluate whether mechanosensing -- i.e., the detection of a left-right asymmetric signal through mechanical stimulation of sensory cilia, as opposed to biochemical signalling -- might be functioning in the embryonic left-right organizer of the vertebrate bodyplan through quantum mechanics. I conclude that there is a possible role for quantum biology in mechanosensing in cilia. The system may not be limited by classical thermal noise, but instead by quantum noise, with an amplification process providing active cooling., Comment: Published version

We investigate the dynamics of spheroids immersed in the journal bearing flow subject to a contractible non-reciprocal loop. We show how geometric phases appear not only in the position, but also in the orientation of such particles. We show how control and targeting can be carried out on spheroidal particles in the flow., Comment: 7 pages, 5 figures. Submitted to Physical Review Fluids

2019 is the bicentenary of George Gabriel Stokes, who in 1851 described the drag - Stokes drag - on a body moving immersed in a fluid, and 2020 is the centenary of Christopher Robin Milne, for whom the game of poohsticks was invented; his father A. A. Milne's "The House at Pooh Corner", in which it was first described in print, appeared in 1928. So this is an apt moment to review the state of the art of the fluid mechanics of a solid body in a complex fluid flow, and one floating at the interface between two fluids in motion. Poohsticks pertains to the latter category, when the two fluids are water and air., Comment: Review article, part of a Philosophical Transactions theme issue 'Stokes at 200'

Gioseffo Zarlino reintroduced the Pythagorean paradigm into Renaissance musical theory. In a similar fashion, Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Isaac Newton reinvigorated Pythagorean ideas in celestial mechanics; Kepler and Newton explicitly invoked musical principles. Today, the theory of dynamical systems allows us to describe very different applications of physics, from the orbits of asteroids in the Solar System to the pitch of complex sounds. Our aim in this text is to review the overarching aims of our research in this field over the past quarter of a century. We demonstrate with a combination of dynamical systems theory and music theory the thread running from Pythagoras to Zarlino that allowed the latter to construct musical scales using the ideas of proportion known to the former, and we discuss how the modern theory of dynamical systems, with the study of resonances in nonlinear systems, returns to Pythagorean ideas of a Musica Universalis.

If you throw a needle or stick at random onto a floor ruled with parallel lines, such as the cracks between floorboards or tiles, from the proportion of times that the stick lands crossing a crack you can estimate $\pi$; can we get $e$ as well? Yes, we can. All of these aspects have been discussed before, but I haven't seen them discussed in this way: that one can estimate both $\pi$ and $e$ with the same Buffon's needle experiment.

Gas and vapour explosions have been involved in industrial accidents since the beginnings of industry. A century ago, at 11:55 am on Friday 24th September 1920, the petroleum barge Warwick exploded in London's docklands and seven men were killed. Understanding what happened when it blew up as it was being refurbished, and how to prevent similar explosions, involves fluid mechanics and thermodynamics plus chemistry. I recount the 1920 accident as an example, together with the history of thermo-kinetic explosions prior to 1920 and up to the present day, and I review the history and the actual state of the science of explosion and the roles of fluid mechanics, thermodynamics, and chemistry in that science. The science of explosions has been aware of its societal implications from the beginning, but, despite advances in health and safety over the past century, is there still work to do?

Condensed matter is thermodynamically unstable in a vacuum. That is what thermodynamics tells us through the relation showing that condensed matter at temperatures above absolute zero always has non-zero vapour pressure. This instability implies that at low temperatures energy must not be distributed equally among atoms in the crystal lattice but must be concentrated. In dynamical systems such concentrations of energy in localized excitations are well known in the form of discrete breathers, solitons, and related nonlinear phenomena. It follows that to satisfy thermodynamics such localized excitations must exist in systems of condensed matter at arbitrarily low temperature and as such the nonlinear dynamics of condensed matter is crucial for its thermodynamics., Comment: Part of a Philosophical Transactions theme issue 'Stokes at 200'

Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18$\times$ 20, $\ldots$, 18$\times$ 20$^n$. We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written in different ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems.

Brinicles are self-assembling tubular ice membrane structures, centimeters to meters in length, found beneath sea ice in the polar regions of Earth. We discuss how the properties of brinicles make them of possible importance for chemistry in cold environments-including that of life's emergence-and we consider their formation in icy ocean world. We argue that the non-ice composition of the ice on Europa and Enceladus will vary spatially due to thermodynamic and mechanical properties that serve to separate and fractionate brines and solid materials. The specifics of the composition and dynamics of both the ice and the ocean in these worlds remain poorly constrained. We demonstrate through calculations using FREZCHEM that sulfate likely fractionates out of accreting ice in Europa and Enceladus, and thus that an exogenous origin of sulfate observed on Europa's surface need not preclude additional endogenous sulfate in Europa's ocean. We suggest that, like hydrothermal vents on Earth, brinicles in icy ocean worlds constitute ideal places where ecosystems of organisms might be found.

High speeds have been measured at seep and mud-volcano sites expelling methane-rich fluids from the seabed. Thermal or solute-driven convection alone cannot explain such high velocities in low-permeability sediments. Here, we demonstrate that in addition to buoyancy, osmotic effects generated by the adsorption of methane onto the sediments can create large overpressures, capable of recirculating seawater from the seafloor to depth in the sediment layer, then expelling it upwards at rates of up to a few hundreds of metres per year. In the presence of global warming, such deep recirculation of seawater can accelerate the melting of methane hydrates at depth from timescales of millennia to just decades, and can drastically increase the rate of release of methane into the hydrosphere and perhaps the atmosphere.

In order to model ion transport across protocell membranes in Hadean hydrothermal vents, we consider both theoretically and experimentally the planar growth of a precipitate membrane formed at the interface between two parallel fluid streams in a two-dimensional microfluidic reactor. The growth rate of the precipitate is found to be proportional to the square root of time, which is characteristic of diffusive transport. However, the dependence of the growth rate on the concentrations of hydroxide and metal ions is approximately linear and quadratic, respectively. We show that such a difference in ionic transport dynamics arises from the enhanced transport of metal ions across a thin gel layer present at the surface of the precipitate. The fluctuations in transverse velocity in this wavy porous gel layer allow an enhanced transport of the cation, so that the effective diffusivity is about an order of magnitude higher than that expected from molecular diffusion alone. Our theoretical predictions are in excellent agreement with our laboratory measurements of the growth of a manganese hydroxide membrane in a microfluidic channel, and this enhanced transport is thought to have been needed to account for the bioenergetics of the first single-celled organisms.

August M\"obius discovered his eponymous strip --- also found almost contemporaneously by Johann Listing --- in 1858, so a pre-1858 M\"obius band would be an interesting object. It turns out there were lots of them.

Cuttlebone, the sophisticated buoyancy device of cuttlefish, is made of extensive superposed chambers that have a complex internal arrangement of calcified pillars and organic membranes. It has not been clear how this structure is assembled. We find that the membranes result from a myriad of minor membranes initially filling the whole chamber, made of nanofibres evenly oriented within each membrane and slightly rotated with respect to those of adjacent membranes, producing a helical arrangement. We propose that the organism secretes a chitin-protein complex, which self-organizes layer-by-layer as a cholesteric liquid crystal, whereas the pillars are made by viscous fingering. The liquid crystallization mechanism permits us to homologize the elements of the cuttlebone with those of other coleoids and with the nacreous septa and the shells of nautiloids. These results challenge our view of this ultra-light natural material possessing desirable mechanical, structural and biological properties, suggesting that two self-organizing physical principles suffice to understand its formation.

Chemical gardens are mineral aggregates that grow in three dimensions with plant-like forms and share properties with self-assembled structures like nano-scale tubes, brinicles or chimneys at hydrothermal vents. The analysis of their shapes remains a challenge, as their growth is influenced by osmosis, buoyancy and reaction-diffusion processes. Here we show that chemical gardens grown by injection of one reactant into the other in confined conditions feature a wealth of new patterns including spirals, flowers, and filaments. The confinement decreases the influence of buoyancy, reduces the spatial degrees of freedom and allows analysis of the patterns by tools classically used to analyze two-dimensional patterns. Injection moreover allows the study in controlled conditions of the effects of variable concentrations on the selected morphology. We illustrate these innovative aspects by characterizing quantitatively, with a simple geometrical model, a new class of self-similar logarithmic spirals observed in a large zone of the parameter space.

We establish that the nonlinear dynamics of collisions between particles favors the charging of a insulating, friable, self-replicating granular material that undergoes nucleation, growth, and fission processes; we demonstrate with a minimal dynamical model that secondary nucleation produces a positive feedback in an electrification mechanism that leads to runaway charging. We discuss ice as an example of such a self-replicating granular material: We confirm with laboratory experiments in which we grow ice from the vapor phase in situ within an environmental scanning electron microscope that charging causes fast-growing and easily breakable palm-like structures to form, which when broken off may form secondary nuclei. We propose that thunderstorms, both terrestrial and on other planets, and lightning in the solar nebula are instances of such runaway charging arising from this nonlinear dynamics in self-replicating granular matter.

We derive from kinetic theory, fluid mechanics, and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely-used semi-empirical relations of Kedem and Katchalsky (1958), which have hitherto been validated experimentally but not theoretically. The above linearity between the fluxes and the driving forces breaks down for concentrated or non-ideal mixtures, for which our equations go beyond the Kedem-Katchalsky formulation. We show that the heretofore empirical solute permeability coefficient reflects the momentum transfer between the solute molecules that are rejected at a pore entrance and the solvent molecules entering the pore space; it can be related to the inefficiency of a Maxwellian demi-demon.}

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows., Comment: Review article; 72 pages, 55 figures

Pearls, the most flawless and highly prized of them, are perhaps the most perfectly spherical macroscopic bodies in the biological world. How are they so round? Why are other pearls solids of revolution (off-round, drop, ringed), and yet others have no symmetry (baroque)? We find that with a spherical pearl the growth fronts of nacre are spirals and target patterns distributed across its surface, and this is true for a baroque pearl, too, but that in pearls with rotational symmetry spirals and target patterns are found only in the vicinity of the poles; elsewhere the growth fronts are arrayed in ratchet fashion around the equator. We demonstrate that pearl rotation is a self-organized phenomenon caused and sustained by physical forces from the growth fronts, and that rotating pearls are a - perhaps unique - example of a natural ratchet.

Brinicles are hollow tubes of ice from centimetres to metres in length that form under floating sea ice in the polar oceans when dense, cold brine drains downwards from sea ice into sea water close to its freezing point. When this extremely cold brine leaves the ice it freezes the water it comes into contact with; a hollow tube of ice --- a brinicle --- growing downwards around the plume of descending brine. We show that brinicles can be understood as a form of the self-assembled tubular precipitation structures termed chemical gardens, plant-like structures formed on placing together a soluble metal salt, often in the form of a seed crystal, and an aqueous solution of one of many anions, often silicate. On one hand, in the case of classical chemical gardens, an osmotic pressure difference across a semipermeable precipitation membrane that filters solutions by rejecting the solute leads to an inflow of water and to its rupture. The internal solution, generally being lighter than the external solution, flows up through the break, and as it does so a tube grows upwards by precipitation around the jet of internal solution. Such chemical-garden tubes can grow to many centimetres in length. In the case of brinicles, on the other hand, in floating sea ice we have porous ice in a mushy layer that filters out water, by freezing it, and allows concentrated brine through. Again there is an osmotic pressure difference leading to a continuing ingress of sea water in a siphon pump mechanism that is sustained as long as the ice continues to freeze. Since the brine that is pumped out is denser than the sea water, and descends rather rises, a brinicle is a downwards growing tube of ice; an inverse chemical garden.

Although the polymorphism of calcium carbonate is well known, and its polymorphs-calcite, aragonite, and vaterite-have been highly studied in the context of biomineralization, polyamorphism is a much more recently discovered phenomenon, and the existence of more than one amorphous phase of calcium carbonate in biominerals has only very recently been understood. Here we summarize what is known about polyamorphism in calcium carbonate as well as what is under- stood about the role of amorphous calcium carbonate in biominerals. We show that consideration of the amorphous forms of calcium carbonate within the physical notion of polyamorphism leads to new insights when it comes to the mechanisms by which polymorphic structures can evolve in the first place. This not only has implications for our understanding of biomineralization, but also of the means by which crystallization may be controlled in medical, pharmaceutical, and industrial contexts.