Continuous property measurement techniques and physics based mathematical model for frost growth control

The development of a new set of frost property measurement techniques to be used in the control of frost growth and defrosting processes in refrigeration systems was investigated. Holographic interferometry and infrared thermometry were used to measure the temperature of the frost-air interface, while a beam element load sensor was used to obtain the weight of a deposited frost layer. The proposed measurement techniques were tested for the cases of natural and forced convection, and the characteristic charts were obtained for a set of operational conditions. ^ An improvement of existing frost growth mathematical models was also investigated. The early stage of frost nucleation was commonly not considered in these models and instead an initial value of layer thickness and porosity was regularly assumed. A nucleation model to obtain the droplet diameter and surface porosity at the end of the early frosting period was developed. The drop-wise early condensation in a cold flat plate under natural convection to a hot (room temperature) and humid air was modeled. A nucleation rate was found, and the relation of heat to mass transfer (Lewis number) was obtained. It was found that the Lewis number was much smaller than unity, which is the standard value usually assumed for most frosting numerical models. The nucleation model was validated against available experimental data for the early nucleation and full growth stages of the frosting process. ^ The combination of frost top temperature and weight variation signals can now be used to control the defrosting timing and the developed early nucleation model can now be used to simulate the entire process of frost growth in any surface material. ^

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.

A Parameter Estimation and Identifiability Analysis Methodology Applied to a Street Canyon Air Pollution Model

Mathematical models are increasingly used in environmental science thus increasing the importance of uncertainty and sensitivity analyses. In the present study, an iterative parameter estimation and identifiability analysis methodology is applied to an atmospheric model – the Operational Street Pollution Model (OSPMr). To assess the predictive validity of the model, the data is split into an estimation and a prediction data set using two data splitting approaches and data preparation techniques (clustering and outlier detection) are analysed. The sensitivity analysis, being part of the identifiability analysis, showed that some model parameters were significantly more sensitive than others. The application of the determined optimal parameter values was shown to succesfully equilibrate the model biases among the individual streets and species. It was as well shown that the frequentist approach applied for the uncertainty calculations underestimated the parameter uncertainties. The model parameter uncertainty was qualitatively assessed to be significant, and reduction strategies were identified.

The use of mathematical modelling in fire safety engineering

Fire is a form of uncontrolled combustion which generates heat, smoke, toxic and irritant gases. All of these products are harmful to man and account for the heavy annual cost of 800 lives and £1,000,000,000 worth of property damage in Britain alone. The new discipline of Fire Safety Engineering has developed as a means of reducing these unacceptable losses. One of the main tools of Fire Safety Engineering is the mathematical model and over the past 15 years a number of mathematical models have emerged to cater for the needs of this discipline. Part of the difficulty faced by the Fire Safety Engineer is the selection of the most appropriate modelling tool to use for the job. To make an informed choice it is essential to have a good understanding of the various modelling approaches, their capabilities and limitations. In this paper some of the fundamental modelling tools used to predict fire and evacuation are investigated as are the issues associated with their use and recent developments in modelling technology.

Impact populationnel de la vaccination contre les virus du papillome humain : revue systématique et synthèse des prédictions de 16 modèles mathématiques dynamiques

Introduction: En 2015, 65 pays avaient des programmes de vaccination contre les VPH. La modélisation mathématique a joué un rôle crucial dans leur implantation. Objectifs: Nous avons réalisé une revue systématique et analysé les prédictions de modèles mathématiques de l’efficacité populationnelle de la vaccination sur la prévalence des VPH-16/18/6/11 chez les femmes et les hommes, afin d’évaluer la robustesse/variabilité des prédictions concernant l’immunité de groupe, le bénéfice ajouté par la vaccination des garçons et l’élimination potentielle des VPH-16/18/6/11. Méthodes: Nous avons cherché dans Medline/Embase afin d’identifier les modèles dynamiques simulant l’impact populationnel de la vaccination sur les infections par les VPH-16/18/6/11 chez les femmes et les hommes. Les équipes participantes ont réalisé des prédictions pour 19 simulations standardisées. Nous avons calculé la réduction relative de la prévalence (RRprev) 70 ans après l’introduction de la vaccination. Les résultats présentés correspondent à la médiane(10ème;90èmeperccentiles) des prédictions. Les cibles de la vaccination étaient les filles seulement ou les filles & garçons. Résultats: 16/19 équipes éligibles ont transmis leurs prédictions. Lorsque 40% des filles sont vaccinées, la RRprev du VPH-16 est 53%(46%;68%) chez les femmes et 36%(28%;61%) chez les hommes. Lorsque 80% des filles sont vaccinées, la RRprev est 93%(90%;100%) chez les femmes et 83%(75%;100%) chez les hommes. Vacciner aussi les garçons augmente la RRprev de 18%(13%;32%) chez les femmes et 35%(27%;39%) chez les hommes à 40% de couverture, et 7%(0%;10%) et 16%(1%;25%) à 80% de couverture. Les RRprev étaient plus élevées pour les VPH-18/6/11 (vs. VPH-16). Si 80% des filles & garçons sont vaccinés, les VPH-16/18/6/11 pourraient être éliminés. Interprétation: Même si les modèles diffèrent entre eux, les prédictions s’accordent sur: 1)immunité de groupe élevée même à basse couverture, 2)RRprev supérieures pour les VPH-18/6/11 (vs. VPH-16), 3)augmenter la couverture chez les filles a un meilleur impact qu’ajouter les garçons, 4)vacciner 80% des filles & garçons pourraient éliminer les VPH-16/18/6/11.

Modeling of burden distribution in the blast furnace

The blast furnace is the main ironmaking production unit in the world which converts iron ore with coke and hot blast into liquid iron, hot metal, which is used for steelmaking. The furnace acts as a counter-current reactor charged with layers of raw material of very different gas permeability. The arrangement of these layers, or burden distribution, is the most important factor influencing the gas flow conditions inside the furnace, which dictate the efficiency of the heat transfer and reduction processes. For proper control the furnace operators should know the overall conditions in the furnace and be able to predict how control actions affect the state of the furnace. However, due to high temperatures and pressure, hostile atmosphere and mechanical wear it is very difficult to measure internal variables. Instead, the operators have to rely extensively on measurements obtained at the boundaries of the furnace and make their decisions on the basis of heuristic rules and results from mathematical models. It is particularly difficult to understand the distribution of the burden materials because of the complex behavior of the particulate materials during charging. The aim of this doctoral thesis is to clarify some aspects of burden distribution and to develop tools that can aid the decision-making process in the control of the burden and gas distribution in the blast furnace. A relatively simple mathematical model was created for simulation of the distribution of the burden material with a bell-less top charging system. The model developed is fast and it can therefore be used by the operators to gain understanding of the formation of layers for different charging programs. The results were verified by findings from charging experiments using a small-scale charging rig at the laboratory. A basic gas flow model was developed which utilized the results of the burden distribution model to estimate the gas permeability of the upper part of the blast furnace. This combined formulation for gas and burden distribution made it possible to implement a search for the best combination of charging parameters to achieve a target gas temperature distribution. As this mathematical task is discontinuous and non-differentiable, a genetic algorithm was applied to solve the optimization problem. It was demonstrated that the method was able to evolve optimal charging programs that fulfilled the target conditions. Even though the burden distribution model provides information about the layer structure, it neglects some effects which influence the results, such as mixed layer formation and coke collapse. A more accurate numerical method for studying particle mechanics, the Discrete Element Method (DEM), was used to study some aspects of the charging process more closely. Model charging programs were simulated using DEM and compared with the results from small-scale experiments. The mixed layer was defined and the voidage of mixed layers was estimated. The mixed layer was found to have about 12% less voidage than layers of the individual burden components. Finally, a model for predicting the extent of coke collapse when heavier pellets are charged over a layer of lighter coke particles was formulated based on slope stability theory, and was used to update the coke layer distribution after charging in the mathematical model. In designing this revision, results from DEM simulations and charging experiments for some charging programs were used. The findings from the coke collapse analysis can be used to design charging programs with more stable coke layers.

Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Scheduling of track inspection and maintenance activities in railroad networks

The U.S. railroad companies spend billions of dollars every year on railroad track maintenance in order to ensure safety and operational efficiency of their railroad networks. Besides maintenance costs, other costs such as train accident costs, train and shipment delay costs and rolling stock maintenance costs are also closely related to track maintenance activities. Optimizing the track maintenance process on the extensive railroad networks is a very complex problem with major cost implications. Currently, the decision making process for track maintenance planning is largely manual and primarily relies on the knowledge and judgment of experts. There is considerable potential to improve the process by using operations research techniques to develop solutions to the optimization problems on track maintenance. In this dissertation study, we propose a range of mathematical models and solution algorithms for three network-level scheduling problems on track maintenance: track inspection scheduling problem (TISP), production team scheduling problem (PTSP) and job-to-project clustering problem (JTPCP). TISP involves a set of inspection teams which travel over the railroad network to identify track defects. It is a large-scale routing and scheduling problem where thousands of tasks are to be scheduled subject to many difficult side constraints such as periodicity constraints and discrete working time constraints. A vehicle routing problem formulation was proposed for TISP, and a customized heuristic algorithm was developed to solve the model. The algorithm iteratively applies a constructive heuristic and a local search algorithm in an incremental scheduling horizon framework. The proposed model and algorithm have been adopted by a Class I railroad in its decision making process. Real-world case studies show the proposed approach outperforms the manual approach in short-term scheduling and can be used to conduct long-term what-if analyses to yield managerial insights. PTSP schedules capital track maintenance projects, which are the largest track maintenance activities and account for the majority of railroad capital spending. A time-space network model was proposed to formulate PTSP. More than ten types of side constraints were considered in the model, including very complex constraints such as mutual exclusion constraints and consecution constraints. A multiple neighborhood search algorithm, including a decomposition and restriction search and a block-interchange search, was developed to solve the model. Various performance enhancement techniques, such as data reduction, augmented cost function and subproblem prioritization, were developed to improve the algorithm. The proposed approach has been adopted by a Class I railroad for two years. Our numerical results show the model solutions are able to satisfy all hard constraints and most soft constraints. Compared with the existing manual procedure, the proposed approach is able to bring significant cost savings and operational efficiency improvement. JTPCP is an intermediate problem between TISP and PTSP. It focuses on clustering thousands of capital track maintenance jobs (based on the defects identified in track inspection) into projects so that the projects can be scheduled in PTSP. A vehicle routing problem based model and a multiple-step heuristic algorithm were developed to solve this problem. Various side constraints such as mutual exclusion constraints and rounding constraints were considered. The proposed approach has been applied in practice and has shown good performance in both solution quality and efficiency.

The study of the impact of demand controlled ventilation in energy consumption of offices in Portuguese commercial buildings

Indoor Air 2016 - The 14th International Conference of Indoor Air Quality and Climate

Quantificação do ião cálcio nas uvas e vinhos brancos por espectroscopia de infravermelho

Com o objetivo de diminuir a incidência das leveduras encapsulas em alginato se aglomerarem na segunda fermentação em garrafa e reduzir custos associados à sua eliminação, pretendeu-se utilizar a metodologia NIR para determinar a quantidade de cálcio no vinho. Foram quantificados outros minerais para avaliar hipotéticos antagonismos iónicos. Observou-se também que este controlo de qualidade poderá ser efetuado no mosto. Atualmente este controlo é realizado por metodologias de análise de referência bastante morosas como EAA. Contudo a metodologia NIR demonstrou ser uma boa alternativa no controlo dos parâ-metros de qualidade na produção de vinho espumante, permitindo a diminuição do tempo de análise e de resíduos. No desenvolvimento dos modelos matemáticos para a calibração do NIR utilizaram-se 79 vinhos brancos e 60 amostras de mosto. Foram desenvolvidos 11 modelos de calibração onde o coeficiente de correlação foi, em aproximadamente 58% dos casos, maior que 0,99; ABSTRACT: In order to reduce the incidence of alginate beads aggregation during the second fermentation in the bottle and to reduce costs associated with their disposal, it was used the NIR technology to quantify calcium content in the wine. Other minerals were also quantified in order to evaluate possible ionic antagonisms. Quality control is usually done in the base wine but it can also be evaluated in the must. Currently this control was carried out by reference analysis methodologies generally rather slow as AAS. However NIR proved to be a good alternative technique in the control of quality parameters of wine production, allowing the reduction of the analysis time and waste. In order to develop mathematical models for the calibration of NIR it was used 79 white wine samples and 60 must samples. Eleven calibration models have been developed, where the correlation coeffi-cient was, in approximately 58% of cases, greater than 0,99.

Modelling and studies of the spectral response of some optoelectronic components

Solar radiation takes in today's world, an increasing importance. Different devices are used to carry out spectral and integrated measurements of solar radiation. Thus the sensors can be divided into the fallow types: Calorimetric, Thermomechanical, Thermoelectric and Photoelectric. The first three categories are based on components converting the radiation to temperature (or heat) and then into electrical quantity. On the other hand, the photoelectric sensors are based on semiconductor or optoelectronic elements that when irradiated change their impedance or generate a measurable electric signal. The response function of the sensor element depends not only on the intensity of the radiation but also on its wavelengths. The radiation sensors most widely used fit in the first categories, but thanks to the reduction in manufacturing costs and to the increased integration of electronic systems, the use of the photoelectric-type sensors became more interesting. In this work we present a study of the behavior of different optoelectronic sensor elements. It is intended to verify the static response of the elements to the incident radiation. We study the optoelectronic elements using mathematical models that best fit their response as a function of wavelength. As an input to the model, the solar radiation values are generated with a radiative transfer model. We present a modeling of the spectral response sensors of other types in order to compare the behavior of optoelectronic elements with other sensors currently in use.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

Data surveillance for infectious diseases: models, complex networks and machine learning

In this thesis, we investigate the role of applied physics in epidemiological surveillance through the application of mathematical models, network science and machine learning. The spread of a communicable disease depends on many biological, social, and health factors. The large masses of data available make it possible, on the one hand, to monitor the evolution and spread of pathogenic organisms; on the other hand, to study the behavior of people, their opinions and habits. Presented here are three lines of research in which an attempt was made to solve real epidemiological problems through data analysis and the use of statistical and mathematical models. In Chapter 1, we applied language-inspired Deep Learning models to transform influenza protein sequences into vectors encoding their information content. We then attempted to reconstruct the antigenic properties of different viral strains using regression models and to identify the mutations responsible for vaccine escape. In Chapter 2, we constructed a compartmental model to describe the spread of a bacterium within a hospital ward. The model was informed and validated on time series of clinical measurements, and a sensitivity analysis was used to assess the impact of different control measures. Finally (Chapter 3) we reconstructed the network of retweets among COVID-19 themed Twitter users in the early months of the SARS-CoV-2 pandemic. By means of community detection algorithms and centrality measures, we characterized users’ attention shifts in the network, showing that scientific communities, initially the most retweeted, lost influence over time to national political communities. In the Conclusion, we highlighted the importance of the work done in light of the main contemporary challenges for epidemiological surveillance. In particular, we present reflections on the importance of nowcasting and forecasting, the relationship between data and scientific research, and the need to unite the different scales of epidemiological surveillance.