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.

A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

Mathematical modelling of patient risks in a hospital environment, using multiple regression analysis

The aim of this research work was primarily to examine the relevance of patient parameters, ward structures, procedures and practices, in respect of the potential hazards of wound cross-infection and nasal colonisation with multiple resistant strains of Staphylococcus aureus, which it is thought might provide a useful indication of a patient's general susceptibility to wound infection. Information from a large cross-sectional survey involving 12,000 patients from some 41 hospitals and 375 wards was collected over a five-year period from 1967-72, and its validity checked before any subsequent analysis was carried out. Many environmental factors and procedures which had previously been thought (but never conclusively proved) to have an influence on wound infection or nasal colonisation rates, were assessed, and subsequently dismissed as not being significant, provided that the standard of the current range of practices and procedures is maintained and not allowed to deteriorate. Retrospective analysis revealed that the probability of wound infection was influenced by the patient's age, duration of pre-operative hospitalisation, sex, type of wound, presence and type of drain, number of patients in ward, and other special risk factors, whilst nasal colonisation was found to be influenced by the patient's age, total duration of hospitalisation, sex, antibiotics, proportion of occupied beds in the ward, average distance between bed centres and special risk factors. A multi-variate regression analysis technique was used to develop statistical models, consisting of variable patient and environmental factors which were found to have a significant influence on the risks pertaining to wound infection and nasal colonisation. A relationship between wound infection and nasal colonisation was then established and this led to the development of a more advanced model for predicting wound infections, taking advantage of the additional knowledge of the patient's state of nasal colonisation prior to operation.

A mathematical model for the maneuvering simulation of a propelled SPAR vessel

To predict the maneuvering performance of a propelled SPAR vessel, a mathematical model was established as a path simulator. A system-based mathematical model was chosen as it offers advantages in cost and time over full Computational Fluid Dynamics (CFD) simulations. The model is intended to provide a means of optimizing the maneuvering performance of this new vessel type. In this study the hydrodynamic forces and control forces are investigated as individual components, combined in a vectorial setting, and transferred to a body-fixed basis. SPAR vessels are known to be very sensitive to large amplitude motions during maneuvers due to the relatively small hydrostatic restoring forces. Previous model tests of SPAR vessels have shown significant roll and pitch amplitudes, especially during course change maneuvers. Thus, a full 6 DOF equation of motion was employed in the current numerical model. The mathematical model employed in this study was a combination of the model introduced by the Maneuvering Modeling Group (MMG) and the Abkowitz (1964) model. The new model represents the forces applied to the ship hull, the propeller forces and the rudder forces independently, as proposed by the MMG, but uses a 6DOF equation of motion introduced by Abkowitz to describe the motion of a maneuvering ship. The mathematical model was used to simulate the trajectory and motions of the propelled SPAR vessel in 10˚/10˚, 20˚/20˚ and 30˚/30˚ standard zig-zag maneuvers, as well as turning circle tests at rudder angles of 20˚ and 30˚. The simulation results were used to determine the maneuverability parameters (e.g. advance, transfer and tactical diameter) of the vessel. The final model provides the means of predicting and assessing the performance of the vessel type and can be easily adapted to specific vessel configurations based on the generic SPAR-type vessel used in this study.

Parameter space of experimental chaotic circuits with high-precision control parameters

The authors thank Professor Iber^e Luiz Caldas for the suggestions and encouragement. The authors F.F.G.d.S., R.M.R., J.C.S., and H.A.A. acknowledge the Brazilian agency CNPq and state agencies FAPEMIG, FAPESP, and FAPESC, and M.S.B. also acknowledges the EPSRC Grant Ref. No. EP/I032606/1.

Basin stability approach for quantifying responses of multistable systems with parameters mismatch

Acknowledgement This work is funded by the National Science Center Poland based on the decision number DEC-2015/16/T/ST8/00516. PB is supported by the Foundation for Polish Science (FNP).

Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Who is in charge? An L2 Discourse Intonation Study on Four Prosodic Parameters to Exert the Pragmatic Function of Dominance and Control in the Context of L2 Non-specialist Public Speaking

This paper reports the findings from a study of the learning of English intonation by Spanish speakers within the discourse mode of L2 oral presentation. The purpose of this experiment is, firstly, to compare four prosodic parameters before and after an L2 discourse intonation training programme and, secondly, to confirm whether subjects, after the aforementioned L2 discourse intonation training, are able to match the form of these four prosodic parameters to the discourse-pragmatic function of dominance and control. The study designed the instructions and tasks to create the oral and written corpora and Brazil’s Pronunciation for Advanced Learners of English was adapted for the pedagogical aims of the present study. The learners’ pre- and post-tasks were acoustically analysed and a pre / post- questionnaire design was applied to interpret the acoustic analysis. Results indicate most of the subjects acquired a wider choice of the four prosodic parameters partly due to the prosodically-annotated transcripts that were developed throughout the L2 discourse intonation course. Conversely, qualitative and quantitative data reveal most subjects failed to match the forms to their appropriate pragmatic functions to express dominance and control in an L2 oral presentation.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data points for 11 binary mixtures of ILs were collected from literature to establish this model. All the binary data consist of 128 training data points used for the optimization of binary interaction parameters and 838 test data points used for the comparison of the pure evaluated values. The relative average absolute deviation (RAAD) for training and test is 2.9% and 3.9%, respectively.

Residence Time Distribution (Rtd) Associated with Statistical Weighted Moments to Fit Mathematical Models Using In Industrial Systems Diagnosis

This work presents a computational, called MOMENTS, code developed to be used in process control to determine a characteristic transfer function to industrial units when radiotracer techniques were been applied to study the unit´s performance. The methodology is based on the measuring the residence time distribution function (RTD) and calculate the first and second temporal moments of the tracer data obtained by two scintillators detectors NaI positioned to register a complete tracer movement inside the unit. Non linear regression technique has been used to fit various mathematical models and a statistical test was used to select the best result to the transfer function. Using the code MOMENTS, twelve different models can be used to fit a curve and calculate technical parameters to the unit.

Hydrometallurgical process modeling using advanced mathematical tools

Hydrometallurgical process modeling is the main objective of this Master’s thesis work. Three different leaching processes namely, high pressure pyrite oxidation, direct oxidation zinc concentrate (sphalerite) leaching and gold chloride leaching using rotating disc electrode (RDE) are modeled and simulated using gPROMS process simulation program in order to evaluate its model building capabilities. The leaching mechanism in each case is described in terms of a shrinking core model. The mathematical modeling carried out included process model development based on available literature, estimation of reaction kinetic parameters and assessment of the model reliability by checking the goodness fit and checking the cross correlation between the estimated parameters through the use of correlation matrices. The estimated parameter values in each case were compared with those obtained using the Modest simulation program. Further, based on the estimated reaction kinetic parameters, reactor simulation and modeling for direct oxidation zinc concentrate (sphalerite) leaching is carried out in Aspen Plus V8.6. The zinc leaching autoclave is based on Cominco reactor configuration and is modeled as a series of continuous stirred reactors (CSTRs). The sphalerite conversion is calculated and a sensitivity analysis is carried out so to determine the optimum reactor operation temperature and optimum oxygen mass flow rate. In this way, the implementation of reaction kinetic models into the process flowsheet simulation environment has been demonstrated.