Quantitative risk assessment of groundwater quality utilizing GIS technology and coupled groundwater models

The thesis presents a two-dimensional Risk Assessment Method (RAM) where the assessment of risk to the groundwater resources incorporates both the quantification of the probability of the occurrence of contaminant source terms, as well as the assessment of the resultant impacts. The approach emphasizes the need for a greater dependency on the potential pollution sources, rather than the traditional approach where assessment is based mainly on the intrinsic geo-hydrologic parameters. The risk is calculated using Monte Carlo simulation methods whereby random pollution events were generated to the same distribution as historically occurring events or a priori potential probability distribution. Integrated mathematical models then simulate contaminant concentrations at the predefined monitoring points within the aquifer. The spatial and temporal distributions of the concentrations were calculated from repeated realisations, and the number of times when a user defined concentration magnitude was exceeded is quantified as a risk. The method was setup by integrating MODFLOW-2000, MT3DMS and a FORTRAN coded risk model, and automated, using a DOS batch processing file. GIS software was employed in producing the input files and for the presentation of the results. The functionalities of the method, as well as its sensitivities to the model grid sizes, contaminant loading rates, length of stress periods, and the historical frequencies of occurrence of pollution events were evaluated using hypothetical scenarios and a case study. Chloride-related pollution sources were compiled and used as indicative potential contaminant sources for the case study. At any active model cell, if a random generated number is less than the probability of pollution occurrence, then the risk model will generate synthetic contaminant source term as an input into the transport model. The results of the applications of the method are presented in the form of tables, graphs and spatial maps. Varying the model grid sizes indicates no significant effects on the simulated groundwater head. The simulated frequency of daily occurrence of pollution incidents is also independent of the model dimensions. However, the simulated total contaminant mass generated within the aquifer, and the associated volumetric numerical error appear to increase with the increasing grid sizes. Also, the migration of contaminant plume advances faster with the coarse grid sizes as compared to the finer grid sizes. The number of daily contaminant source terms generated and consequently the total mass of contaminant within the aquifer increases in a non linear proportion to the increasing frequency of occurrence of pollution events. The risk of pollution from a number of sources all occurring by chance together was evaluated, and quantitatively presented as risk maps. This capability to combine the risk to a groundwater feature from numerous potential sources of pollution proved to be a great asset to the method, and a large benefit over the contemporary risk and vulnerability methods.

Integrated component scheduling models for chip shooter machines

This paper focuses on minimizing printed circuit board (PCB) assembly time for a chipshootermachine, which has a movable feeder carrier holding components, a movable X–Y table carrying a PCB, and a rotary turret with multiple assembly heads. The assembly time of the machine depends on two inter-related optimization problems: the component sequencing problem and the feeder arrangement problem. Nevertheless, they were often regarded as two individual problems and solved separately. This paper proposes two complete mathematical models for the integrated problem of the machine. The models are verified by two commercial packages. Finally, a hybrid genetic algorithm previously developed by the authors is presented to solve the model. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total assembly time.

Feasibility studies of an on-line identification technique

This thesis is concerned with the study of a non-sequential identification technique, so that it may be applied to the identification of process plant mathematical models from process measurements with the greatest degree of accuracy and reliability. In order to study the accuracy of the technique under differing conditions, simple mathematical models were set up on a parallel hybrid. computer and these models identified from input/output measurements by a small on-line digital computer. Initially, the simulated models were identified on-line. However, this method of operation was found not suitable for a thorough study of the technique due to equipment limitations. Further analysis was carried out in a large off-line computer using data generated by the small on-line computer. Hence identification was not strictly on-line. Results of the work have shovm that the identification technique may be successfully applied in practice. An optimum sampling period is suggested, together with noise level limitations for maximum accuracy. A description of a double-effect evaporator is included in this thesis. It is proposed that the next stage in the work will be the identification of a mathematical model of this evaporator using the teclmique described.

Mechanisms of convective drying in thick beds of solids

The literature on heat and mass transfer mechanisms in the convective drying of thick beds of solids has been critically reviewed. Related mathematical models of heat transfer are also considered. Experimental and theoretical studies were made of the temperature distribution within beds, and of drying rates, with various materials undergoing convective drying. The experimental work covered thick beds of hygroscopic and non-hygroscopic materials (glass beads of different diameters, polystyrene pellets, activated alumina and wood powder) at air temperatures of 54°C to 84°C. Tests were carried out in a laboratory drying apparatus comprising a wind tunnel through which the air, of controlled temperature and humidity, was passed over a sample suspended from a balance. Thermocouples were inserted at different depths within the sample bed. The temperature distribution profiles for both hygroscopic and non-hygroscopic beds exhibited a clear difference between the temperatures at the surface and bottom during the constant rate period. An effective method was introduced for predicting the critical moisture content. During the falling rate the profiles showed the existence of a receding evaporation plane; this divided the system into a hotter dry zone in the upper section and a wet zone near the bottom. A graphical procedure was established to predict accurately the position of the receding evaporation front at any time. A new mathematical model, based on the receding evaporation front phenomenon, was proposed to predict temperature distributions throughout a bed during drying. Good agreement was obtained when the model was validated by comparing its predictions with experimental data. The model was also able to predict the duration of each drying stage. In experiments using sample trays of different diameters, the drying rate was found to increase with a decrease in the effective length of the bed surface. During the constant rate period with trays of a small effective length, i.e. less than 0.08 m, an 'inversion' in temperature distribution occurred in the bed; the bottom temperature increased and became greater than that of the surface. Experimental measurements were verified in several ways to ensure this phenomenon was real. Theoretical explanations are given for both the effective length and temperature inversion phenomena.

A Mathematical Apparatus for Domain Ontology Simulation. Logical Relationship Systems

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers

For metal and metal halide vapor lasers excited by high frequency pulsed discharge, the thermal effect mainly caused by the radial temperature distribution is of considerable importance for stable laser operation and improvement of laser output characteristics. A short survey of the obtained analytical and numerical-analytical mathematical models of the temperature profile in a high-powered He-SrBr2 laser is presented. The models are described by the steady-state heat conduction equation with mixed type nonlinear boundary conditions for the arbitrary form of the volume power density. A complete model of radial heat flow between the two tubes is established for precise calculating the inner wall temperature. The models are applied for simulating temperature profiles for newly designed laser. The author’s software prototype LasSim is used for carrying out the mathematical models and simulations.

Mathematical modelling of integrin-like receptors systems

Nel presente lavoro, ho studiato e trovato le soluzioni esatte di un modello matematico applicato ai recettori cellulari della famiglia delle integrine. Nel modello le integrine sono considerate come un sistema a due livelli, attivo e non attivo. Quando le integrine si trovano nello stato inattivo possono diffondere nella membrana, mentre quando si trovano nello stato attivo risultano cristallizzate nella membrana, incapaci di diffondere. La variazione di concentrazione nella superficie cellulare di una sostanza chiamata attivatore dà luogo all’attivazione delle integrine. Inoltre, questi eterodimeri possono legare una molecola inibitrice con funzioni di controllo e regolazione, che chiameremo v, la quale, legandosi al recettore, fa aumentare la produzione della sostanza attizzatrice, che chiameremo u. In questo modo si innesca un meccanismo di retroazione positiva. L’inibitore v regola il meccanismo di produzione di u, ed assume, pertanto, il ruolo di modulatore. Infatti, grazie a questo sistema di fine regolazione il meccanismo di feedback positivo è in grado di autolimitarsi. Si costruisce poi un modello di equazioni differenziali partendo dalle semplici reazioni chimiche coinvolte. Una volta che il sistema di equazioni è impostato, si possono desumere le soluzioni per le concentrazioni dell’inibitore e dell’attivatore per un caso particolare dei parametri. Infine, si può eseguire un test per vedere cosa predice il modello in termini di integrine. Per farlo, ho utilizzato un’attivazione del tipo funzione gradino e l’ho inserita nel sistema, valutando la dinamica dei recettori. Si ottiene in questo modo un risultato in accordo con le previsioni: le integrine legate si trovano soprattutto ai limiti della zona attivata, mentre le integrine libere vengono a mancare nella zona attivata.

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.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.