Detection of unstable periodic orbits in mineralising geological systems.

Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particularly acute. We propose an innovative approach to mineral exploration and orebody characterisation, based on the analysis of geological core data as a spatial dynamical system, using the mathematical tools of dynamical system analysis. This approach is highly relevant for orogenic gold deposits, which-in contrast to systems formed at chemical equilibrium-exhibit many features of nonlinear dynamical systems, including episodic fluctuations on various length and time scales. Feedback relationships between thermo-chemical and deformation processes produce recurrent fluid temperatures and pressures and the deposition of vein-filling minerals such as pyrite and gold. We therefore relax the typical assumption of chemical equilibrium and analyse the underlying processes as aseismic, non-adiabatic, and inherent to a hydrothermal, nonlinear dynamical open-flow chemical reactor. These processes are approximated using the Gray-Scott model of reaction-diffusion as a complex toy system, which captures some of the features of the underlying mineralisation processes, including the spatiotemporal Turing patterns of unsteady chemical reactions. By use of this analysis, we demonstrate the capability of recurrence plots, recurrence power spectra, and recurrence time probabilities to detect underlying unstable periodic orbits as one sign of deterministic dynamics and their robustness for the analysis of data contaminated by noise. Recurrence plot based quantification is then applied to three mineral concentrations in the core data from the Sunrise Dam gold deposit in the Yilgarn region of Western Australia. Using a moving window, we reveal the episodic recurring low-dimensional dynamic structures and the period doubling route to instability with depth, embedded in and originating from higher-dimensional processes of the complex mineralisation system.

Effects of domain shapes on the morphological evolution of nonaqueous-phase-liquid dissolution fronts in fluid-saturated porous media.

The main purpose of this paper is to investigate the effects of different domain shapes in general and trapezoidal domain shape in particular on the morphological evolution of nonaqueous phase liquid (NAPL) dissolution fronts in two-dimensional fluid-saturated porous media. After the governing equations of NAPL dissolution problems are briefly described, the numerical procedure consisting of a combination of the finite element and finite difference methods is used to solve these equations. The related numerical simulation results have demonstrated that: (1) domain shapes have a significant effect on both the propagating speed and the morphological evolution pattern of a NAPL dissolution front in the fluid-saturated porous medium; (2) an increase in the divergent angle of a trapezoidal domain can lead to a decrease in the propagating speed of the NAPL dissolution front; (3) the morphological evolution pattern of the NAPL dissolution front in a rectangular domain is remarkably different from that in a trapezoidal domain of a large divergent angle; (4) for a rectangular domain, the simplified dispersion model, which is commonly used in the theoretical analysis and numerical simulation, is valid for solving NAPL dissolution instability problems in fluid-saturated porous media; and (5) compared with diverging flow (when the trapezoidal domain is inclined outward), converging flow (when the trapezoidal domain is inclined inward) can enhance the growth of NAPL fingers, indicating that pump-and-treat systems by extracting contaminated groundwater might enhance NAPL dissolution fingering and lead to less uniform dissolution fronts.

Scalar dispersion in a periodically reoriented potential flow: acceleration via Lagrangian chaos.

Although potential flows are irrotational, Lagrangian chaos can occur when these are unsteady, with rapid global mixing observed upon flow parameter optimization. What is unknown is whether Lagrangian chaos in potential flows results in accelerated scalar dispersion, to what magnitude, how robustly, and via what mechanisms. We consider scalar dispersion in a model unsteady potential flow, the Lagrangian topology of which is well understood. The asymptotic scalar dispersion rate q and corresponding scalar distribution (strange eigenmode) are calculated over the flow parameter space Q for Peclét numbers Pe=10{1}-10{4}. The richness of solutions over Q increases with Pe, with pattern mode locking, symmetry breaking transitions to chaos and fractally distributed maxima observed. Such behavior suggests detailed global resolution of Q is necessary for robust optimization, however localization of local optima to bifurcations between periodic and subharmonic eigenmodes suggests novel efficient means of optimization. Acceleration rates of 150 fold at Pe=10{4} are observed; significantly greater than corresponding values for chaotic Stokes flows, suggesting significant scope for dispersion acceleration in potential flows in general.

On oscillating flows in randomly heterogeneous porous media.

The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, near-critical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties.

Lagrangian topology of a periodically reoriented potential flow: symmetry, optimization, and mixing.

Scalar transport in closed potential flows is investigated for the specific case of a periodically reoriented dipole flow. Despite the irrotational nature of the flow, the periodic reorientations effectively create heteroclinic and/or homoclinic points arising from the joining of stable and unstable manifolds. For scalar advection, Lagrangian chaos can be achieved with breakdown of the regular Hamiltonian structure, which is governed by symmetry conditions imposed by the dipole flow. Instability envelopes associated with period-doubling bifurcations of fixed points govern which regions of the flow control parameter space admit global chaos. These regions are further refined via calculation of Lyapunov exponents. These results suggest significant scalar transport enhancement is possible within potential flows, given appropriate programming of stirring protocols.

Newtonian dislocation creep in quartzites: implications for the rheology of the lower crust.

Mechanical and microstructural evidence indicates that a natural and a synthetic quartzite deformed by Newtonian dislocation (Harper-Dorn) creep at temperatures higher than 1073 K and stresses lower than 300 megapascals. The observation of this creep in these materials suggests that the lower crust may flow like a Newtonian viscous fluid by a dislocation mechanism at stresses much smaller than those previously postulated.