Towards large scale microwave treatment of ores: Part 1 – Basis of design, construction and commissioning

Despite over thirty years of work, microwave pre-treatment processes for beneficiation of ores have not progressed much further than laboratory testing. In this paper we present a scaleable pilot-scale system for the microwave treatment of ores capable of operating at throughputs of up to 150tph. This has been achieved by confining the electric field produced from two 100kW generators operating at 896MHz in a gravity fed vertical flow system using circular choking structures yielding power densities of at least 6x108 W/m3 in the heated mineral phases. Measured S11 scattering parameters for a quartzite ore (-3.69±0.4dB) in the as-built applicator correlated well with the simulation (-3.25dB), thereby validating our design approach. We then show that by fully integrating the applicator with a materials handling system based on the concept of mass flow, we achieve a reliable, continuous process. The system was used to treat a range of porphyry copper ores

Towards large scale microwave treatment of ores: Part 2 - Metallurgical testing

A pilot scale microwave treatment system capable of treating 10-150t/h of material at 10-200kW was designed, constructed and commissioned in order to understand the engineering challenges of microwave-induced fracture of ores at scale and generate large metallurgical test samples of material treated at approximately 0.3-3kWh/t. It was demonstrated that exposing more of the ore to a region of high power density by improving treatment homogeneity with two single mode applicators in series yielded equivalent or better metallurgical performance with up to half the power and one third the energy requirement of that used with a single applicator. Comminution testing indicated that A*b values may be reduced by up to 7-14% and that the Bond Ball Mill Work Index may be reduced by up to 3-9% depending on the ore type under investigation. Liberation analysis of the microwave-treated ore indicated that equivalent liberation may be achievable for a grind size approximately 40-70µm coarser than untreated ore, which is in agreement with laboratory scale investigations reported in the literature at similar or higher doses. Flow sheet simulations further indicated that reduced ore competency following microwave treatment could potentially yield up to a 9% reduction in specific comminution energy (ECS) at a nominal plant grind of P₈₀190µm, or up to 24% reduction at a grind of P₈₀290µm, for a microwave energy input of 0.7-1.3kWh/t. Throughput could also be increased by up to approximately 30% depending on grind size, ore type and equipment constraints. To date, approximately 900t of material has been processed through the pilot plant, approximately 300t of which was under microwave power. Metallurgical testing has demonstrated that comminution and liberation benefits are achievable at doses lower than that previously reported in the literature, which allow high throughputs to be sustained with low installed power requirements providing a pathway to further scale-up of microwave treatment of ores

Towards a Simple Model of Compressible Alfvenic Turbulence

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted.Comment: 6 pages, one figure, REVTeX; this version to be published in PRE. For related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.htm

Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field

The effect of a homogeneous magnetic field on surface-tension-driven B\'{e}nard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.Comment: 26 pages, 9 figure

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Understanding microwave induced sorting of porphyry copper ores

Global demand for minerals and metals is increasing. It has been established that the impact of mining and mineral processing operations must be reduced to sustainably meet the demands of a low grade future. Successful incorporation of ore sorting in flow sheets has the potential to improve energy efficiency by rejecting non-economic material before grinding. Microwave heating combined with infra-red temperature measurement has been shown to distinguish low and high grade ore fragments from each other. In this work, experimentally validated 2-D finite difference models of a theoretical two phase ore, representing typical fragment textures and grades, are constructed. Microwave heating is applied at economically viable energy inputs and the resultant surface thermal profiles analysed up to 2 minutes after microwave heating. It is shown that the size and location of grains can dramatically alter surface temperature rise at short thermal measurement delay times and that the range of temperatures increases with increasing fragment grade. For the first time, it is suggested that increasing the delay time between microwave heating and thermal measurement can reduce the variation seen for fragments of the same grade but different textures, improving overall differentiation between high and low grade fragments

Flow of foam through a convergent channel

International audienceWe study experimentally the flow of a foam confined as a bubble monolayer between two plates through a convergent channel. We quantify the velocity, the distribution and orientation of plastic events, and the elastic stress, using image analysis. We use two different soap solutions: a sodium dodecyl sulfate (SDS) solution, with a negligible wall friction between the bubbles and the confining plates, and a mixture containing a fatty acid, giving a large wall friction. We show that for SDS solutions, the velocity profile obeys a self-similar form which results from the superposition of plastic events, and the elastic deformation is uniform. For the other solution, the velocity field differs and the elastic deformation increases towards the exit of the channel. We discuss and quantify the role of wall friction on the velocity profile, the elastic deformation, and the rate of plastic events

Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds

Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation Ad:H->\GL_R(S) of the stabilizer H. This article studies the superizations of M_0, i.e. its extensions to a homogeneous supermanifold M=G/H whose sheaf of superfunctions is isomorphic to Lambda(S^*(M_0)). Here G is the Lie supergroup associated with a certain extension of the Lie algebra of symmetry g_0 to an algebra of supersymmetry g=g_0+g_1=g_0+S via the Kostant-Koszul construction. Each algebra of supersymmetry naturally determines a flat connection nabla^{S} in the spin bundle S(M_0). Killing vectors together with generalized Killing spinors (i.e. nabla^{S}-parallel spinors) are interpreted as the values of appropriate geometric symmetries of M, namely even and odd Killing fields. An explicit formula for the Killing representation of the algebra of supersymmetry is obtained, generalizing some results of Koszul. The generalized spin connection nabla^{S} defines a superconnection on M, via the super-version of a theorem of Wang.Comment: 50 page

Development and Validation of a Tokamak Skin Effect Transformer model

A control oriented, lumped parameter model for the tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non linear interaction of the plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with Random Binary Signals (RBS) have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated in Ohmic conditions between 200kA and 300kA with 30ms rise time, several times faster than its time constant L/R\approx200ms. The model explains the most salient features of the plasma current transients without requiring detailed or explicit information about resistivity profiles. This proves that lumped parameter modeling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least in Ohmic conditions without external heating and current drive sources