Julyan H. E. Cartwright

Calcium Carbonate Polyamorphism and Its Role in Biomineralization: How Many Amorphous Calcium Carbonates Are There?

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 understood 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.

The dynamics of nacre self-assembly

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.

Ice structures, patterns, and processes: A view across the icefields

European Science Foundation workshop Euroice 2008 held in Granada, Spain from 1–4 October 2008; Spanish national project, Hielocris, financed by the Consejo Superior de Investigaciones Cientificas; funding from FWF, Austria (No. P23027); MINCINN, Spain (No. FIS2010-16455, No. PR2010-0012, and No. FIS2010-22322-528C02-02); and SNSF, Switzerland (No. 200021121857)

THE DYNAMICS OF RUNGE–KUTTA METHODS

The first step in investigating the dynamics of a continuous-time system described by an ordinary differential equation is to integrate to obtain trajectories. In this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, Runge–Kutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis.

Dynamics of a Small Neutrally Buoyant Sphere in a Fluid and Targeting in Hamiltonian Systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.

Mineral bridges in nacre

We confirm with high-resolution techniques the existence of mineral bridges between superposed nacre tablets. In the towered nacre of both gastropods and the cephalopod Nautilus there are large bridges aligned along the tower axes, corresponding to gaps (150-200nm) in the interlamellar membranes. Gaps are produced by the interaction of the nascent tablets with a surface membrane that covers the nacre compartment. In the terraced nacre of bivalves bridges associated with elongated gaps in the interlamellar membrane (>100nm) have mainly been found at or close to the edges of superposed parental tablets. To explain this placement, we hypothesize that the interlamellar membrane breaks due to differences in osmotic pressure across it when the interlamellar space below becomes reduced at an advanced stage of calcification. In no cases are the minor connections between superimposed tablets (<60nm), earlier reported to be mineral bridges, found to be such.

Chaotic advection in three-dimensional unsteady incompressible laminar flow

We discuss chaotic advection in three-dimensional unsteady incompressible laminar flow, and analyse in detail the most important novel advection phenomenon in these flows : the global dispersion of passive scalars in flows with two slow and one fast velocity components. We make a comprehensive study of the first model of an experimentally realizable flow to exhibit this resonance-induced dispersion : biaxial unsteady spherical Couette flow is a three-dimensional incompressible laminar flow with periodic time dependence derived analytically from the Navier-Stokes equations in the low-Reynolds-number limit.

From Chemical Gardens to Chemobrionics

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap.

Fuzzy Control of Chaos

In this chapter a Mamdani fuzzy model based fuzzy control technique is proposed to control chaotic systems, whose dynamics is complex and unknown, to the unstable periodic orbits (UPO). Some empirical tricks are introduced for building up a proper fuzzy rule base and designing a fuzzy controller. Finally, an example of fuzzy control of the Chua’s circuit is presented to illustrate the effectiveness of the proposed approach.

The key role of the surface membrane in why gastropod nacre grows in towers

The nacre of gastropod molluscs is intriguingly stacked in towers. It is covered by a surface membrane, which protects the growing nacre surface from damage when the animal withdraws into its shell. The surface membrane is supplied by vesicles that adhere to it on its mantle side and secretes interlamellar membranes from the nacre side. Nacre tablets rapidly grow in height and later expand sideways; the part of the tablet formed during this initial growth phase is here called the core. During initial growth, the tips of the cores remain permanently submerged within the surface membrane. The interlamellar membranes, which otherwise separate the nacre tablet lamellae, do not extend across cores, which are aligned in stacked tablets forming the tower axis, and thus towers of nacre tablets are continuous along the central axis. We hypothesize that in gastropod nacre growth core formation precedes that of the interlamellar membrane. Once the core is complete, a new interlamellar membrane, which covers the area of the tablet outside the core, detaches from the surface membrane. In this way, the tower-like growth of gastropod nacre becomes comprehensible.