On the problem of large-scale magnetic field generation in rotating compressible convection

Mean-field dynamo theory suggests that turbulent convection in a rotating layer of electrically-conducting fluid produces a significant alpha-effect, which is one of the key ingredients in any mean-field dynamo model. Provided that this alpha-effect operates more efficiently than (turbulent) magnetic diffusion, such a system should be capable of sustaining a large-scale dynamo. However, in the Boussinesq model that was considered by Cattaneo&Hughes (2006) the dynamo produced small-scale, intermittent magnetic fields with no significant large-scale component. In this paper, we consider the compressible analogue of the rotating convective layer that was considered by Cattaneo&Hughes (2006). Varying the horizontal scale of the computational domain, we investigate the dependence of the dynamo upon the rotation rate. Our simulations indicate that these turbulent compressible flows can drive a small-scale dynamo but, even when the layer is rotating very rapidly (with a mid-layer Taylor number of Ta=10^8), we find no evidence for the generation of a significant large-scale component of the magnetic field on a dynamical timescale. Like Cattaneo&Hughes(2006), we measure a negligible (time-averaged) alpha-effect when a uniform horizontal magnetic field is imposed across the computational domain. Although the total horizontal magnetic flux is a conserved quantity in these simulations, the (depth-dependent) horizontally-averaged magnetic field always exhibits strong fluctuations. If these fluctuations are artificially suppressed within the code, we measure a significant mean electromotive force that is comparable to that found in related calculations in which the alpha-effect is measured using the test-field method, even though we observe no large-scale dynamo action.Comment: 25 pages, 10 figures, to appear in J. Fluid Mec

Antiferromagnetic spin-coupling between MnII and amminium radical cation ligands: models for coordination polymer magnets

One and two electron oxidation of the manganese(II) complex [L2Mn(hfac)2] {L = 4'',4'''-di-tert-butyl-2',2'',2'''trimethoxy-{4-(4'-diphenylaminophenyl)pyridine} were studied by ultra violet/ visible/ near infra red spectroscopy, cyclic voltammetry and magnetometry. A one-electron oxidation converts the triarylamine ligand to its radical cation and gives a complex in which the antiferromagnetic coupling between the spin on the ligand and that on the metal J/kb is -1.5 K. In a dilute frozen matrix and at low temperature this behaves as an S = 2 system. A two electron oxidation gives [L2Mn(hfac)2]2.+ which at low enough temperatures behaves as an S = 3/2 system but the spin-coupling between the metal and the ligand is weaker (J/kb = -0.3 K). The weakness of these spin-couplings mean that MnII/amminium radical cation complexes are not promising systems on which to base coordination polymer magnets. The equivalent copper(II) complex [L2Cu(hfac)2] was also investigated but this decomposes when an attempt is made to oxidise the ligand to its amminium radical cation

Mesogranulation and small-scale dynamo action in the quiet Sun

Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying the aspect ratio and the Reynolds number). In purely hydrodynamic convection, we find that mesogranulation is a robust feature of this system provided that the domain is wide enough to accommodate these large-scale motions. The mesogranular peak in the kinetic energy spectrum is more pronounced in the higher Reynolds number simulations. We investigate the dynamo properties of this system in both the kinematic and the nonlinear regimes and we find that the dynamo is always more efficient in larger domains, when mesogranulation is present. Furthermore, we use a filtering technique in Fourier space to demonstrate that it is indeed the larger scales of motion that are primarily responsible for driving the dynamo. In the nonlinear regime, the magnetic field distribution compares very favourably to observations, both in terms of the spatial distribution and the measured field strengths.Comment: 12 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Nanoindentation of bone: Comparison of specimens tested in liquid and embedded in polymethylmethacrylate

Elastic modulus of bone was investigated by nanoindentation using common methods of sample preparation, data collection, and analysis, and compared to dynamic mechanical analysis (DMA: three-point bending) for the same samples. Nanoindentation (Berkovich, 5 μm and 21 μm radii spherical indenters) and DMA were performed on eight wet and dehydrated (100% ethanol), machined equine cortical bone beams. Samples were embedded in polymethylmethacrylate (PMMA) and mechanical tests repeated. Indentation direction was transverse to the bone long axis while DMA tested longitudinally, giving approximately 12% greater modulus in DMA. For wet samples, nanoindentation with spherical indenters revealed a low modulus surface layer. Estimates of the volume of material contributing to elastic modulus measurement showed that the surface layer influences the measured modulus at low loads. Consistent results were obtained for embedded tissue regardless of indenter geometry, provided appropriate methods and analysis were used. Modulus increased for nanoindentation (21 μm radius indenter) from 11.7 GPa ± 1.7 to 15.0 GPa ± 2.2 to 19.4 GPa ± 2.1, for wet, dehydrated in ethanol, and embedded conditions, respectively. The large increases in elastic modulus caused by replacing water with ethanol and ethanol with PMMA demonstrate that the role of water in fine pore space and its interaction with collagen strongly influence the mechanical behavior of the tissue

Asymptotic Solutions for Mean-Field Slab Dynamos

We discuss asymptotic solutions of the kinematic $\alpha\omega$-dynamo in a thin disc (slab). Focusing upon the strong dynamo regime, in which the dynamo number $D$ satisfies $|D|\gg1$, we resolve uncertainties in the earlier treatments and conclude that some of the simplifications that have been made in previous studies are questionable. Comparing numerical solutions with asymptotic results obtained for $|D|\gg1$ and $|D|\ll1$ we find that the asymptotic solutions give a reasonably accurate description of the dynamo even far beyond their formal ranges of applicability. Indeed, our results suggest a simple analytical expression for the growth rate of the mean magnetic field that remains accurate in the range $-200< D< -10$ (which is appropriate for dynamos in spiral galaxies and accretion discs). Finally, we analyse the role of various terms in the dynamo equations to clarify the fine details of the dynamo process.Comment: "This is an Author's Original Manuscript of an article submitted for consideration in Geophysical and Astrophysical Fluid Dynamics [copyright Taylor & Francis]; Geophysical and Astrophysical Fluid Dynamics is available online at http://www.tandfonline.com/gafd