Magma Flow Instabilities in a Volcanic Conduit: Implications for Long-Period Seismicity

Silicic volcanic eruptions are typically accompanied by repetitive Long-Period (LP) seismicity that originates from a small region of the upper conduit. These signals have the capability to advance eruption prediction, since they commonly precede a change in the eruption vigour. Shear bands forming along the conduit wall, where the shear stresses are highest, have been linked to providing the seismic trigger. However, existing computational models are unable to generate shear bands at the depths where the LP signals originate using simple magma strength models. Presented here is a model in which the magma strength is determined from a constitutive relationship dependent upon crystallinity and pressure. This results in a depth-dependent magma strength, analogous to planetary lithospheres. Hence, in shallow highly-crystalline regions a macroscopically discontinuous brittle type of deformation will prevail, whilst in deeper crystal-poor regions there will be a macroscopically continuous plastic deformation mechanism. This will result in a depth where the brittle-ductile transition occurs, and here shear bands disconnected from the free-surface may develop. We utilize the Finite Element Method and use axi-symmetric coordinates to model magma flow as a viscoplastic material, simulating quasi-static shear bands along the walls of a volcanic conduit. Model results constrained to the Soufrière Hills Volcano, Montserrat, show the generation of two types of shear bands: upper-conduit shear bands that form between the free-surface to a few 100 metres below it and discrete shear bands that form at the depths where LP seismicity is measured to occur corresponding to the brittle-ductile transition and the plastic shear region. It is beyond the limitation of the model to simulate a seismic event, although the modelled viscosity within the discrete shear bands suggests a failure and healing cycle time that supports the observed LP seismicity repeat times. However, due to the paucity of data and large parameter space available these results can only be considered to be qualitative rather than quantitative at this stage.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Concordance between dispersal and mitochondrial gene flow: isolation by distance in a tropical teleost, Lates calcarifer (Australian barramundi)

Patterns of population subdivision and the relationship between gene flow and geographical distance in the tropical estuarine fish Lares calcarifer (Centropomidae) were investigated using mtDNA control region sequences. Sixty-three putative haplotypes were resolved from a total of 270 individuals from nine localities within three geographical regions spanning the north Australian coastline. Despite a continuous estuarine distribution throughout the sampled range, no haplotypes were shared among regions. However, within regions, common haplotypes were often shared among localities. Both sequence-based (average Phi(ST)=0.328) and haplotype-based (average Phi(ST)=0.182) population subdivision analyses indicated strong geographical structuring. Depending on the method of calculation, geographical distance explained either 79 per cent (sequence-based) or 23 per cent (haplotype-based) of the variation in mitochondrial gene flow. Such relationships suggest that genetic differentiation of L. calcarifer has been generated via isolation-by-distance, possibly in a stepping-stone fashion. This pattern of genetic structure is concordant with expectations based on the life history of L. calcarifer and direct studies of its dispersal patterns. Mitochondrial DNA variation, although generally in agreement with patterns of allozyme variation, detected population subdivision at smaller spatial scales. Our analysis of mtDNA variation in L. calcarifer confirms that population genetic models can detect population structure of not only evolutionary significance but also of demographic significance. Further, it demonstrates the power of inferring such structure from hypervariable markers, which correspond to small effective population sizes.

Velocimetry and thermometry of supersonic flow around a cylindrical body

The supersonic flow around a cylindrical body has been studied using two optical techniques. For both sets of measurements, the cylinder was mounted from the side of the tunnel, allowing investigation of the bow shock region as well as in the wake. A new technique, laser-enhanced ionization flow tagging, was used for streamwise velocity determinations behind the body. From these measurements, it was found that the downstream velocity outside the wake was (1.90 +/- 0.06) km/s, whereas inside the wake the velocity was about 0-500 m/s in the upstream direction. Planar laser induced fluorescence of nitric oxide was employed for temperature determinations. It was established that the freestream temperature was (2120 +/- 100) K, decreasing to around (1550 +/- 400) K in the wake.

Peptidergic control of gastrointestinal blood flow in the estuarine crocodile, Crocodylus porosus

Peptidergic mechanisms influencing the resistance of the gastrointestinal vascular bed of the estuarine crocodile, Crocodylus porosus, were investigated. The gut was perfused in situ via the mesenteric and the celiac arteries, and the effects of different neuropeptides were tested using bolus injections. Effects on vascular resistance were recorded as changes in inflow pressures. Peptides found in sensory neurons [substance P, neurokinin A, and calcitonin gene-related peptide (CGRP)] all caused significant relaxation of the celiac vascular bed, as did vasoactive intestinal polypeptide (VIP), another well-known vasodilator. Except for VIP, the peptides also induced transitory gut contractions. Somatostatin and neuropeptide Y (NPY), which coexist in adrenergic neurons of the C. porosus, induced vasoconstriction in the celiac vascular bed without affecting the gut motility. Galanin caused vasoconstriction and occasionally activated the gut wall. To elucidate direct effects on individual vessels, the different peptides were tested on isolated ring preparations of the mesenteric and celiac arteries. Only CGRP and VIP relaxed the epinephrine-precontracted celiac artery, whereas the effects on the mesenteric artery were variable. Somatostatin and NPY did not affect the resting tonus of these vessels, but somatostatin potentiated the epinephrine-induced contraction of the celiac artery. Immunohistochemistry revealed the existence and localization of the above-mentioned peptides in nerve fibers innervating vessels of different sizes in the gut region. These data support the hypothesis of an important role for neuropeptides in the control of the vascular bed of the gastrointestinal tract in C. porosus.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Relative dispersions of intra-albumin transit times across rat and elasmobranch perfused livers, and implications for intra- and inter-species scaling of hepatic clearance using microsomal data

It is recognized that vascular dispersion in the liver is a determinant of high first-pass extraction of solutes by that organ. Such dispersion is also required for translation of in-vitro microsomal activity into in-vivo predictions of hepatic extraction for any solute. We therefore investigated the relative dispersion of albumin transit times (CV2) in the livers of adult and weanling rats and in elasmobranch livers. The mean and normalized variance of the hepatic transit time distribution of albumin was estimated using parametric non-linear regression (with a correction for catheter influence) after an impulse (bolus) input of labelled albumin into a single-pass liver perfusion. The mean +/- s.e. of CV2 for albumin determined in each of the liver groups were 0.85 +/- 0.20 (n = 12), 1.48 +/- 0.33 (n = 7) and 0.90 +/- 0.18 (n = 4) for the livers of adult and weanling rats and elasmobranch livers, respectively. These CV2 are comparable with that reported previously for the dog and suggest that the CV2 Of the liver is of a similar order of magnitude irrespective of the age and morphological development of the species. It might, therefore, be justified, in the absence of other information, to predict the hepatic clearances and availabilities of highly extracted solutes by scaling within and between species livers using hepatic elimination models such as the dispersion model with a CV2 of approximately unity.

Modeling the fluid-flow-induced stress and collapse in a dendritic network

An analytical approach to the stress development in the coherent dendritic network during solidification is proposed. Under the assumption that stresses are developed in the network as a result of the friction resisting shrinkage-induced interdendritic fluid flow, the model predicts the stresses in the solid. The calculations reflect the expected effects of postponed dendrite coherency, slower solidification conditions, and variations of eutectic volume fraction and shrinkage. Comparing the calculated stresses to the measured shear strength of equiaxed mushy zones shows that it is possible for the stresses to exceed the strength, thereby resulting in reorientation or collapse of the dendritic network.

Hypoxia stimulates cerebral blood flow in the estuarine crocodile (Crocodylus porosus)

The effect of N-2 respiration on cerebral blood flow (CBF) velocity on the dorsal surface of cerebellum was examined in the estuarine crocodile, Crocodylus porosus, using epi-illumination microscopy. Twelve minutes of N-2 respiration resulted in a 126% increase in CBF velocity. N-2 respiration had no effect on blood pressure, indicating an underlying cerebral vasodilation. In addition, heart rate increased significantly. Systemic injections of aminophylline and the NO synthase (NOS) inhibitor nitro-L-arginine (L-NA) did not affect the hypoxia induced increase in CBF. We conclude that C. porosus responds to hypoxia with adenosine and nitric oxide (NO) independent cerebral vasodilation, and that this is likely to be a mechanism protecting the brain from energy deficiency during prolonged dives. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.