Intergranular diffusion rates from the analysis of garnet surfaces: implications for metamorphic equilibration

Novel approaches to garnet analysis have been used to assess rates of intergranular diffusion between different matrix phases and garnet porphyroblasts in a regionally metamorphosed staurolite-mica-schist from the Barrovian-type area in Scotland. X-ray maps and chemical traverses of planar porphyroblast surfaces reveal chemical heterogeneity of the garnet grain boundary linked to the nature of the adjacent matrix phase. The garnet preserves evidence of low temperature retrograde exchange with matrix minerals and diffusion profiles documenting cation movement along the garnet boundaries. Garnet–quartz and garnet–plagioclase boundaries preserve evidence of sluggish Mg, Mn and Fe diffusion at comparable rates to volume diffusion in garnet, whereas diffusion along garnet–biotite interfaces is much more effective. Evidence of particularly slow Al transport, probably coupled to Fe3+ exchange, is locally preserved on garnet surfaces adjacent to Fe-oxide phases. The Ca distribution on the garnet surface shows the most complex behaviour, with long-wavelength heterogeneities apparently unrelated to the matrix grain boundaries. This implies that the Ca content of garnet is controlled by local availability and is thought likely to reflect disequilibrium established during garnet growth. Geochemical anomalies on the garnet surfaces are also linked to the location of triple junctions between the porphyroblasts and the matrix phases, and imply enhanced transport along these channels. The slow rates of intergranular diffusion and the characteristics of different boundary types may explain many features associated with the prograde growth of garnet porphyroblasts. Thus, minerals such as quartz, Fe-oxides and plagioclase whose boundaries with garnet are characterized by slow intergranular diffusion rates appear to be preferentially trapped as inclusions within porphyroblasts. As such grain boundary diffusion rates may be a significant kinetic impediment to metamorphic equilibrium and garnet may struggle to maintain chemical and textural equilibrium during growth in pelites

A tale of two airfoils: resolvent-based modelling of an oscillator vs. an amplifier from an experimental mean

The flows around a NACA 0018 airfoil at a Reynolds number of 10250 and angles of attack of alpha = 0 (A0) and alpha = 10 (A10) are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity profiles are data-assimilated so that they are solutions of the incompressible Reynolds-averaged Navier-Stokes equations forced by Reynolds stress terms which are derived from experimental data. Spectral proper orthogonal decompositions (SPOD) of the velocity fluctuations and nonlinear forcing find low-rank behaviour at the shedding frequency and its higher harmonics for the A0 case. In the A10 case, low-rank behaviour is observed for the velocity fluctuations in two bands of frequencies. Resolvent analysis of the data-assimilated means identifies low-rank behaviour only in the vicinity of the shedding frequency for A0 and none of its harmonics. The resolvent operator for the A10 case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by SPOD. It is also shown that the second linear mechanism, corresponding to the Kelvin-Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as a mean flow due to the fact that experimental data are missing near the leading edge. The A0 case is classified as an oscillator where the flow is organised around an intrinsic instability while the A10 case behaves like an amplifier whose forcing is unstructured. For both cases, resolvent modes resemble those from SPOD when the operator is low-rank. To model the higher harmonics where this is not the case, we add parasitic resolvent modes, as opposed to classical resolvent modes which are the most amplified, by approximating the nonlinear forcing from limited triadic interactions of known resolvent modes.Comment: 32 pages, 23 figure

Influence of a local change of depth on the behavior of bouncing oil drops

The work of Couder \textit{et al} (see also Bush \textit{et al}) inspired consideration of the impact of a submerged obstacle, providing a local change of depth, on the behavior of oil drops in the bouncing regime. In the linked videos, we recreate some of their results for a drop bouncing on a uniform depth bath of the same liquid undergoing vertical oscillations just below the conditions for Faraday instability, and show a range of new behaviors associated with change of depth. This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion of the 66th Annual Meeting of the APS Division of Fluid Dynamics.Comment: High and low resolutions videos included as ancillary file

A Series of Electro-Magnetic Investigations: I. On a Gyro Magnetic Effect; II. On Diffusion in Flames; III. On an Induction Coil Interrupter; and IV. On the Electrical Conductivity of Hot Solutions

A Gray-Ross magnetometer was used to obtain I-H curves for a steel rod under normal conditions and under the influence of arotating magnetic field to find whether the effect of the latter would he to help in the process of producing longitudinal magnetisation of the rod. The rotation of a bar-magnet in a plane at right angles to the axis of the specimen, and near to the magnetising solenoid, was used to supply this field, which was therefore not very strong and decreased towards the end of the specimen distant from the rotating magnet. When the I-H curves for a given range, and under the different conditions, were compared, the curve obtained for either direction of rotation of the magnet differed but slightly from the curve for normal conditions. Sometimes it seemed that the rotating field helped, but in other experiments the opposite was indicated, and in other sets no difference was distinguishable, so it was concluded that a rotating magnetic field of the order used has no distinct effect on the longitudinal magnetisation of a specimen lying in the direction of the axis of rotation

On non-normality and classification of amplification mechanisms in stability and resolvent analysis

We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how non-normality from mean shear distributes perturbation energy in different velocity components of the forcing and response modes. The inverse of their inner product, which is unity for a purely normal mechanism, is proposed as a measure to quantify non-normality. In flows where there is downstream spatial dependence of the base/mean, mean flow advection separates the spatial support of forcing and response modes which impacts the inner product. Success of mean stability analysis depends on the normality of amplification. If the amplification is normal, the resolvent operator written in its dyadic representation reveals that the adjoint and forward stability modes are proportional to the forcing and response resolvent modes. If the amplification is non-normal, then resolvent analysis is required to understand the origin of observed flow structures. Eigenspectra and pseudospectra are used to characterize these phenomena. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The first deals mainly with normal mechanisms and quantification of non-normality using the inverse inner product of the leading forcing and response modes agrees well with the product of the resolvent norm and distance between the imaginary axis and least stable eigenvalue. In turbulent channel flow, structures result from both normal and non-normal mechanisms. Mean shear is exploited most efficiently by stationary disturbances while bounds on the pseudospectra illustrate how non-normality is responsible for the most amplified disturbances at spatial wavenumbers and temporal frequencies corresponding to well-known turbulent structures

Determinants of Capital Flight in the East African Community

The region has lost an immense amount of capital that has led to sluggish regional integration in terms of capital formation and productive capabilities. Albeit most of these countries are in the ranking list of the huge volumes of capital flight, East Africa has never been considered as a sub-region in the capital-related studies. Cognizant of this, this paper intends to contribute to this body of knowledge by filling a noticeable gap. This paper examined the determinant of capital flight from East African Community countries that include Kenya, Tanzania, Uganda, Rwanda, and Burundi using panel data for the years 1988 to 2018 using the real gross domestic product, interest rate differential, external debt, corruption index, and exchange rate as explanatory variables. Secondary data obtained from EAC member countries National Bureau of Statistics. Levin-Lin-Chu panel unit root test was carried out and capital flight and Exchange rate found to be stationary at level. The fixed effect regression results showed that corruption, external debt, and the exchange rate had a positive and statistically significant effect on capital flight while real GDP had a negative and statistically significant effect on capital flight. Thus, policymakers should endeavor to achieve a broad investor base for its domestic and foreign obligations, with due regard to cost and risk, and should treat investors equally. In addition, there is a need to harmonize the judiciary and the executives in EAC to facilitate the fight against corruption which is a major concern for a capital flight. Keywords: Capital flight, External debt, Exchange rate, GDP, Corruption, EAC DOI: 10.7176/JESD/12-10-01 Publication date:May 31st 2021