A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

A mathematical model of concentrate solids content for the wet drum magnetic separator

Low concentrate density from wet drum magnetic separators in dense medium circuits can cause operating difficulties due to inability to obtain the required circulating medium density and, indirectly, high medium solids losses. The literature is almost silent on the processes controlling concentrate density. However, the common name for the region through which concentrate is discharged-the squeeze pan gap-implies that some extrusion process is thought to be at work. There is no model of magnetics recovery in a wet drum magnetic separator, which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was done using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 turn diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in this work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. It is proposed, based both on the experimental observations of the present work and on observations reported in the literature, that the process controlling magnetic separator concentrate density is one of drainage. Such a process should be able to be defined by an initial moisture, a drainage rate and a drainage time, the latter being defined by the volumetric flowrate and the volume within the drainage zone. The magnetics can be characterised by an experimentally derived ultimate drainage moisture. A model based on these concepts and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to be a good fit to data over concentrate solids content values from 40% solids to 80% solids and for both magnetite and ferrosilicon feeds. (C) 2003 Elsevier Science B.V. All rights reserved.

A mathematical model of recovery of dense medium magnetics in the wet drum magnetic separator

Loss of magnetic medium solids from dense medium circuits is a substantial contributor to operating cost. Much of this loss is by way of wet drum magnetic separator effluent. A model of the separator would be useful for process design, optimisation and control. A review of the literature established that although various rules of thumb exist, largely based on empirical or anecdotal evidence, there is no model of magnetics recovery in a wet drum magnetic separator which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was therefore carried out using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 mm diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in the work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. Observations carried out as an adjunct to this work, as well as magnetic theory, suggests that the capture of magnetic particles in the wet drum magnetic separator is by a flocculation process. Such a process should be defined by a flocculation rate and a flocculation time; the latter being defined by the volumetric flowrate and the volume within the separation zone. A model based on this concept and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to provide a satisfactory fit to the data over three orders of magnitude of magnetics loss. (C) 2003 Elsevier Science BY. All rights reserved.

A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones-a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

Determination of Cole parameters in multiple frequency bioelectrical impedance analysis using only the measurement of impedances

Conventional bioimpedance spectrometers measure resistance and reactance over a range of frequencies and, by application of a mathematical model for an equivalent circuit (the Cole model), estimate resistance at zero and infinite frequencies. Fitting of the experimental data to the model is accomplished by iterative, nonlinear curve fitting. An alternative fitting method is described that uses only the magnitude of the measured impedances at four selected frequencies. The two methods showed excellent agreement when compared using data obtained both from measurements of equivalent circuits and of humans. These results suggest that operational equivalence to a technically complex, frequency-scanning, phase-sensitive BIS analyser could be achieved from a simple four-frequency, impedance-only analyser.

Mathematical Morphology: Star/Galaxy Differentiation & Galaxy Morphology Classication

We present an application of Mathematical Morphology (MM) for the classification of astronomical objects, both for star/galaxy differentiation and galaxy morphology classification. We demonstrate that, for CCD images, 99.3 +/- 3.8% of galaxies can be separated from stars using MM, with 19.4 +/- 7.9% of the stars being misclassified. We demonstrate that, for photographic plate images, the number of galaxies correctly separated from the stars can be increased using our MM diffraction spike tool, which allows 51.0 +/- 6.0% of the high-brightness galaxies that are inseparable in current techniques to be correctly classified, with only 1.4 +/- 0.5% of the high-brightness stars contaminating the population. We demonstrate that elliptical (E) and late-type spiral (Sc-Sd) galaxies can be classified using MM with an accuracy of 91.4 +/- 7.8%. It is a method involving fewer 'free parameters' than current techniques, especially automated machine learning algorithms. The limitation of MM galaxy morphology classification based on seeing and distance is also presented. We examine various star/galaxy differentiation and galaxy morphology classification techniques commonly used today, and show that our MM techniques compare very favourably.

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

A mathematical model of HIV transmission in NSW prisons

A mathematical model was developed to estimate HIV incidence in NSW prisons. Data included: duration of imprisonment; number of inmates using each needle; lower and higher number of shared injections per IDU per week; proportion of IDUs using bleach; efficacy of bleach; HIV prevalence and probability of infection. HIV prevalence in IDUs in prison was estimated to have risen from 0.8 to 5.7% (12.2%) over 180 weeks when using lower (and higher) values for frequency of shared injections. The estimated minimum (and maximum) number of IDU inmates infected with HIV in NSW prisons was 38 (and 152) in 1993 according to the model. These figures require confirmation by seroincidence studies. (C) 1998 Published by Elsevier Science Ireland Ltd. All rights reserved.

The relationship between plasma lactate parameters, W-peak and 1-h cycling performance in women

Purpose: The relationship between six descriptors of lactate increase, peak (V) over dot O-2,W-peak, and 1-h cycling performance were compared in 24 trained, female cyclists (peak (V) over dot O-2 = 48.11 +/- 6.32 mL . kg(-1) . min(-1)). Methods: The six descriptors of lactate increase were: 1) lactate threshold (LT; the power output at which plasma lactate concentration begins to increase above the resting level during an incremental exercise test), 2) LT1 (the power output at which plasma lactate increases by 1 mM or more), 3) LTD (the lactate threshold calculated by the D-max method), 4) LTMOD (the lactate threshold calculated by a modified D-max method), 5) L4 (the power output at which plasma lactate reaches a concentration of 4 mmol-L-1), and 6) LTLOG (the power output at which plasma lactate concentration begins to increase when the log([La-]) is plotted against the log (power output)). Subjects first completed a peak (V) over dot O-2 test on a cycle ergometer. Finger-tip capillary blood was sampled within 30 s of the end of each 3-min stage for analysis of plasma lactate. Endurance performance was assessed 7 d later using a 1-h cycle test (OHT) in which subjects were directed to achieve the highest possible average power output. Results: The mean power output (W) for the OHT (+/- SD) was 183.01 +/- 18.88, and for each lactate variable was: LT (138.54 +/- 46.61), LT1 (179.17 +/- 27.25), LTLOG (143.97 +/- 45.74), L4 (198.09 +/- 33.84), LTD (178.79 +/- 24.07), LTMOD (212.28 +/- 31.75). Average power output during the OHT was more strongly correlated with all plasma lactate parameters (0.61 < r < 0.84) and W-peak (r = 0.81) than with peak (V) over dot O-2 (r = 0.55). The six lactate parameters were strongly correlated with each other (0.54 < r < 0.91) and of the six lactate parameters, LTD correlated best with endurance performance (r = 0.84). Conclusions: It was concluded that plasma lactate parameters and W-peak provide better indices of endurance performance than peak (V) over dot O-2 and that, of the six descriptors of lactate increase measured in this study, LTD is most strongly related to 1-h cycling performance in trained, female cyclists.

Theory of modulational instability in Bragg gratings with quadratic nonlinearity

Modulational instability in optical Bragg gratings with a quadratic nonlinearity is studied. The electric field in such structures consists of forward and backward propagating components at the fundamental frequency and its second harmonic. Analytic continuous wave (CW) solutions are obtained, and the intricate complexity of their stability, due to the large number of equations and number of free parameters, is revealed. The stability boundaries are rich in structures and often cannot be described by a simple relationship. In most cases, the CW solutions are unstable. However, stable regions are found in the nonlinear Schrodinger equation limit, and also when the grating strength for the second harmonic is stronger than that of the first harmonic. Stable CW solutions usually require a low intensity. The analysis is confirmed by directly simulating the governing equations. The stable regions found have possible applications in second-harmonic generation and dark solitons, while the unstable regions maybe useful in the generation of ultrafast pulse trains at relatively low intensities. [S1063-651X(99)03005-6].

Decoherence and fidelity in ion traps with fluctuating trap parameters

We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (wobbling) of the ion relative to the center of the trap, and fluctuations of the spring constant, which an due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived. [S1050-2947(99)06005-9].