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Stingless bees of the genus Tetragonula construct a brood comb with a spiral or a target pattern architecture in three dimensions. Crystals possess these same patterns on the molecular scale. Here, we show that the same excitable-medium dynamics governs both crystal nucleation and growth and comb construction in Tetragonula, so that a minimal coupled-map lattice model based on crystal growth explains how these bees produce the structures seen in their bee combs., J.H.E.C. and C.I.S.D. acknowledge the financial support of theSpanish MINCINN FIS2016-77692-C2-2-P and A.G.C., CGL2017-85118-P.

Weak bubble plumes carry liquid from the environment upwards and release it at multiple intermediate levels in the form of radial intrusive currents. In this study, laboratory experiments are performed to explore the spreading of turbulent axisymmetric bubble plumes in a liquid with linear density stratification. The thickness, volumetric flowrate and spreading rates of multiple radial intrusions of plume fluid were measured by tracking the movement of dye injected at the source of bubbles. The experimental results are compared with scaling predictions. Our findings suggest that the presence of multiple intrusions reduces their spreading rate, compared to that of a single intrusion. This work is of relevance to the spreading of methane plumes issuing from the seabed in the Arctic Ocean, above methane-hydrate deposits. The slower, multiple spreading favours the presence of methane-rich seawater close to the plume, which may reduce the dissolution of methane in the bubbles, and thus promote the direct transport of methane to the atmosphere. This article is part of the theme issue 'Stokes at 200 (part 2)'., Funding. J.M.B. acknowledges financial support from the Woolf Fisher Trust for his PhD study. J.H.E.C. acknowledges the financial support of the Spanish MINCINN project FIS2016-77692-C2-2-P. S.S.S.C. acknowledges the financial support of the UK Leverhulme Trust project RPG-2015-002.

We present the second half of the papers from the Stokes 200 symposium celebrating the bicentenary of George Gabriel Stokes. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

Mixing fluids often involves a periodic action, like stirring one's tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So how can fluid be mixed in such circumstances? The answer involves a geometric phase. Geometric phases are found everywhere in physics as anholonomies, where after a closed circuit in the parameters, some system variables do not return to their original values. We discuss the geometric phase in fluid mixing: geometric mixing. This article is part of the theme issue 'Stokes at 200 (part 2)'., Authors’ contributions. All authors designed research; J.A., E.G. and I.T. performed numerical simulations; N.P. and O.P. conducted theoretical analysis; J.H.E.C. and J.A. wrote the first version of the paper and all authors contributed to the final version. Competing interests. We declare we have no competing interests. Funding. We acknowledge the support from the Spanish Ministry of Economy and Competitiveness (AEI, FEDER EU) grant nos FIS2016-77692-C2-1-P (I.T., O.P. and J.A.), FIS2016-77692-C2-2-P (J.H.E.C.) and CTM-2017-83774-D (J.A.). J.A thanks the Govern de les Illes Balears for financial support through the Vicenç Mut subprogram partially funded by the European Social Fund.

Sir George Gabriel Stokes PRS was for 30 years an inimitable Secretary of the Royal Society and its President from 1885 to 1890. Two hundred years after his birth, Stokes is a towering figure in physics and applied mathematics; fluids, asymptotics, optics, acoustics among many other fields. At the Stokes 200 meeting, held at Pembroke College, Cambridge from 15–18th September 2019, an invited audience of about 100 discussed the state of the art in all the modern research fields that have sprung from his work in physics and mathematics, along with the history of how we have got from Stokes’ contributions to where we are now. This theme issue is based on work presented at the Stokes 200 meeting. In bringing together people whose work today is based upon Stokes’ own, we aim to emphasize his influence and legacy at 200 to the community as a whole. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

Concentration cycles are important for bonding of basic molecular building components at the emergence of life. We demonstrate that oscillations occur intrinsically in precipitation reactions when coupled with fluid mechanics in self-Assembled precipitate membranes, such as at submarine hydrothermal vents. We show that, moreover, the flow of ions across one pore in such a prebiotic membrane is larger than that across one ion channel in a modern biological cell membrane, suggesting that proto-biological processes could be sustained by osmotic flow in a less efficient prebiotic environment. Oscillations in nanoreactors at hydrothermal vents may be just right for these warm little pores to be the cradle of life., S.S.S.C. acknowledges the financial support of the UK Leverhulme Trust project RPG-2015-002. J.H.E.C. acknowledges the financial support of the Spanish MINECO project FIS2016-77692-C2-2PP. S.S.S.C. and J.H.E.C. acknowledge the European COST action CA17120.

The March 2019 meeting in Granada on which this theme issue is based was funded by the European COST Action CA17120.

Black smokers and Lost City-type springs are varieties of hydrothermal vents on the ocean floors that emit hot, acidic water and cool, alkaline water, respectively. While both produce precipitation structures as the issuing fluid encounters oceanic water, Lost City-type hydrothermal vents in particular have been implicated in the origin of life on the Earth. We present a parallel-velocity flow model for the radius and flow rate of a cylindrical jet of fluid that forms the template for the growth of a tube precipitated about itself and we compare the solution with previous laboratory experimental results from growth of silicate chemical gardens. We show that when the growth of the solid structure is determined by thermal diffusion, fluid flow is slow at the solid-liquid contact. However, in the case of chemical diffusive transport, the fluid jet effectively drags the liquid in the pores of the solid precipitate. These findings suggest a continuum in the diffusive growth rate of hydrothermal vent structures, where Lost City-type hydrothermal vents favour contact between the vent fluid and the external seawater. We explore the implications for the road to life., S.S.S.C. acknowledges the financial support of the UK Leverhulme Trust project RPG-2015-002. J.H.E.C. acknowledges the financial support of the Spanish project FIS2016-77692-C2-2-P.

11 pages, 4 figures.-- Published online 7 October 2009., We study the influence of competing microstructure symmetries on the emergence of different morphologies during the growth by vapour deposition of thin solid films. We perform extensive numerical simulations with a minimal model that includes different microstructures, as well as thermal surface diffusion, to compute the corresponding structure zone model (SZM) and analyse, with statistical physics techniques, the details of transitional morphologies at border zones. We show that the maximum coordination number of the underlying microstructure provides a classification of the statistics of the transitional morphologies at the border between zones I (porous structures) and II (columnar faceted structures) of the SZM., This work was undertaken with the financial support of the CSIC project Hielocris. T.S. also ackowledges project FIS2007-60327.

15 pages, 8 figures, We show how nacre and pearl construction in bivalve and gastropod molluscs can be understood in terms of successive processes of controlled self-assembly from the molecular- to the macro-scale. This dynamics involves the physics of the formation of both solid and liquid crystals and of membranes and fluids to produce a nanostructured hierarchically constructed biological composite of polysaccharides, proteins and mineral, whose mechanical properties far surpass those of its component parts., We thank José Gavira, Fernando Gervilla, Chris Previti, Ignacio Sainz and Ana Villacampa for interesting discussions, Juan de Dios Bueno for sample preparation, Stephen Hyde for procuring some useful references, Mitsuo Kakei for providing us with material from the late Hiroshi Nakahara and Luis Sánchez for obtaining some gastropod specimens. J.H.E.C. is supported by the Spanish Ministerio de Educación y Ciencia grant CTQ2004-04648, and A.G.C. is supported by the Spanish Ministerio de Educacio´n y Ciencia grant CGL2004-00802 and by Andalusian Research Group RMN190.

9 pages, 5 figures., We address with fluid-dynamical simulations using direct numerical techniques three important and fundamental questions with respect to fluid flow within the mouse node and left–right development. First, we consider the differences between what is experimentally observed when assessing cilium-induced fluid flow in the mouse node in vitro and what is to be expected in vivo. The distinction is that in vivo, the leftward fluid flow across the mouse node takes place within a closed system and is consequently confined, while this is no longer the case on removing the covering membrane and immersing the embryo in a fluid-filled volume to perform in vitro experiments. Although there is a central leftward flow in both instances, we elucidate some important distinctions about the closed in vivo situation. Second, we model the movement of the newly discovered nodal vesicular parcels (NVPs) across the node and demonstrate that the flow should indeed cause them to accumulate on the left side of the node, as required for symmetry breaking. Third, we discuss the rupture of NVPs. Based on the biophysical properties of these vesicles, we argue that the morphogens they contain are likely not delivered to the surrounding cells by their mechanical rupture either by the cilia or the flow, and rupture must instead be induced by an as yet undiscovered biochemical mechanism., The authors thank the anonymous referees for suggesting improvements which they have incorporated in the manuscript and Salvador Balle for valuable discussions. N.P. performed the simulations, while J.H.E.C., N.P. and I.T. wrote the paper. The ideas were developed by all four authors. J.H.E.C. acknowledges the financial support of the Spanish Ministerio de Ciencia y Tecnología grant CTQ2004-04648, O.P. acknowledges the financial support of CONOCE2 (FIS2004-00953) and HIELOCRIS (200530F0052) contracts and the Secretaria de Estado de Universidades e Investigacion del Ministerio de Educación y Ciencias for additional financial help.