Conical spouted beds have been commonly used for drying suspensions, solutions and pasty materials. They can also be utilized in many other processes, such as catalytic partial oxidation of methane to synthesis gas, coating of tablets, coal gasification and liquefaction, pyrolysis of sawdust or mixtures of wood residues. The main objectives of this work include both the experimental research and mathematical modelling of the conical spouted bed hydrodynamics. For experimental research, pressure transducers and static pressure probes were applied to investigate the evolution of the internal spout and the local static pressure distribution; optical fibre probes were utilized to measure axial particle velocity profiles and voidage profiles; the step tracer injection technique using helium as the tracer and thermal conductivity cells as detectors was used to investigate the gas mixing behaviour inside a conical spouted bed. It was found that many factors might affect calibration of the effective distance of an optical fibre probe. Therefore, a new calibration setup was designed and assembled, and a comprehensive sensitivity analysis was conducted to calibrate the optical probes used in this study. For mathematical modelling, a stream-tube model based on the bed structure inside a conical spouted bed was proposed to simulate partial spouting states. By introducing an adjustable parameter, this model is capable of predicting the total pressure drop under different operating conditions, and estimating axial superficial gas velocity profiles and gauge pressure profiles. A mathematical model based on characteristics of conical spouted beds and the commercial software FLUENT was also developed and validated using measured experimental data. The proposed new CFD model can simulate both stable spouting and partial spouting states, with an adjustable solids-phase source term. At stable spouting states, simulation results agree very well with almost all experimental data, such as static pressure profiles, axial particle velocity profiles, voidage profiles etc. A comprehensive sensitivity analysis was also conducted to investigate the effect of all possible factors on simulation results, including the fluid inlet profile, solid bulk viscosity, frictional viscosity, restitution coefficient, exchange coefficient, and solid phase source term. The proposed new CFD model was also used successfully to simulate gas mixing behaviours inside a conical spouted bed, and simulate cylindrical packed beds as well as cylindrical fluidized beds in one code package.

Conical spouted beds have been commonly used for drying suspensions, solutions and pasty materials. They can also be utilized in many other processes, such as catalytic partial oxidation of methane to synthesis gas, coating of tablets, coal gasification and liquefaction, pyrolysis of sawdust or mixtures of wood residues. The main objectives of this work include both the experimental research and mathematical modelling of the conical spouted bed hydrodynamics. For experimental research, pressure transducers and static pressure probes were applied to investigate the evolution of the internal spout and the local static pressure distribution; optical fibre probes were utilized to measure axial particle velocity profiles and voidage profiles; the step tracer injection technique using helium as the tracer and thermal conductivity cells as detectors was used to investigate the gas mixing behaviour inside a conical spouted bed. It was found that many factors might affect calibration of the effective distance of an optical fibre probe. Therefore, a new calibration setup was designed and assembled, and a comprehensive sensitivity analysis was conducted to calibrate the optical probes used in this study. For mathematical modelling, a stream-tube model based on the bed structure inside a conical spouted bed was proposed to simulate partial spouting states. By introducing an adjustable parameter, this model is capable of predicting the total pressure drop under different operating conditions, and estimating axial superficial gas velocity profiles and gauge pressure profiles. A mathematical model based on characteristics of conical spouted beds and the commercial software FLUENT was also developed and validated using measured experimental data. The proposed new CFD model can simulate both stable spouting and partial spouting states, with an adjustable solids-phase source term. At stable spouting states, simulation results agree very well with almost all experimental data, such as static pressure profiles, axial particle velocity profiles, voidage profiles etc. A comprehensive sensitivity analysis was also conducted to investigate the effect of all possible factors on simulation results, including the fluid inlet profile, solid bulk viscosity, frictional viscosity, restitution coefficient, exchange coefficient, and solid phase source term. The proposed new CFD model was also used successfully to simulate gas mixing behaviours inside a conical spouted bed, and simulate cylindrical packed beds as well as cylindrical fluidized beds in one code package.

<p>Cellular dynamics arise from intricate interactions among diverse components, such as metabolites, RNAs, and proteins. An in-depth understanding of these interactions requires an integrated approach to the investigation of biological systems. This task can benefit from a combination of mathematical modeling and experimental validations, which is becoming increasingly indispensable for basic and applied biological research. </p> <p>Utilizing a combination of modeling and experimentation, we investigate mammalian cell cycle entry. We begin our investigation by making predictions with a mathematical model, which is constructed based on the current knowledge of biology. To test these predictions, we develop experimental platforms for validations, which in turn can be used to further refine the model. Such iteration of model predictions and experimental validations has allowed us to gain an in-depth understanding of the cell cycle entry dynamics. </p> <p>In this dissertation, we have focused on the Myc-Rb-E2F signaling pathway and its associated pathways, dysregulation of which is associated with virtually all cancers. Our analyses of these signaling pathways provide insights into three questions in biology: 1) regulation of the restriction point (R-point) in cell cycle entry, 2) regulation of the temporal dynamics in cell cycle entry, and 3) post-translational regulation of Myc by its upstream signaling pathways. The well-studied pathways can serve as a foundation for perturbations and tight control of cell cycle entry dynamics, which may be useful in developing cancer therapeutics. </p> <p>We conclude by demonstrating how a combination of mathematical modeling and experimental validations provide mechanistic insights into the regulatory networks in cell cycle entry.</p> / Dissertation

Mathematical modeling is a key component of various disciplines in science and engineering. A mathematical model which represents important behavior of a real system can be used as a substitute for the real process for many analysis and synthesis tasks. The performance of model based techniques, e.g. system analysis, computer simulation, controller design, sensor development, state filtering, product monitoring, and process optimization, is highly dependent on the quality of the model used. Therefore, it is very important to be able to develop an accurate model from available experimental data. Parameter estimation is usually formulated as an optimization problem where the parameter estimate is computed by minimizing the discrepancy between the model prediction and the experimental data. If a simple model and a large amount of data are available then the estimation problem is frequently well-posed and a small error in data fitting automatically results in an accurate model. However, this is not always the case. If the model is complex and only sparse and noisy data are available, then the estimation problem is often ill-conditioned and good data fitting does not ensure accurate model predictions. Many challenges that can often be neglected for estimation involving simple models need to be carefully considered for estimation problems involving complex models. To obtain a reliable and accurate estimate from sparse and noisy data, a set of techniques is developed by addressing the challenges encountered in estimation of complex models, including (1) model analysis and simplification which identifies the important sources of uncertainty and reduces the model complexity; (2) experimental design for collecting information-rich data by setting optimal experimental conditions; (3) regularization of estimation problem which solves the ill-conditioned large-scale optimization problem by reducing the number of parameters; (4) nonlinear estimation and filtering which fits the data by various estimation and filtering algorithms; (5) model verification by applying statistical hypothesis test to the prediction error. The developed methods are applied to different types of models ranging from models found in the process industries to biochemical networks, some of which are described by ordinary differential equations with dozens of state variables and more than a hundred parameters.

Modeling and inferential control studies are carried out on a reactive batch distillation system for the esterification reaction of ethanol with acetic acid to produce ethyl acetate. A dynamic model is developed based on a previous study done on a batch distillation column. The column is modified for a reactive system where Artificial Neural Network Estimator is used instead of Extended Kalman Filter for the estimation of compositions of polar compounds for control purposes. The results of the developed dynamic model of the column is verified theoretically with the results of a similar study. Also, in order to check the model experimentally, a lab scale column (40 cm height, 5 cm inner diameter with 8 trays) is used and it is found that experimental data is not in good agreement with the models&rsquo / . Therefore, the model developed is improved by using different rate expressions and thermodynamic models (fi-fi, combination of equations of state (EOS) and excess Gibbs free energy (EOS-Gex), gama-fi) with different equations of states (Peng Robinson (PR) / Peng Robinson - Stryjek-Vera (PRSV)), mixing rules (van der Waals / Huron Vidal (HV) / Huron Vidal Original (HVO) / Orbey Sandler Modification of HVO (HVOS)) and activity coefficient models (NRTL / Wilson / UNIQUAC). The gama-fi method with PR-EOS together with van der Waals mixing rule and NRTL activity coefficient model is selected as the best relationships which fits the experimental data. The thermodynamic models / EOS, mixing rules and activity coefficient models, all are found to have very crucial roles in modeling studies. A nonlinear optimization problem is also carried out to find the optimal operation of the distillation column for an optimal reflux ratio profile where the maximization of the capacity factor is selected as the objective function. In control studies, to operate the distillation system with the optimal reflux ratio profile, a control system is designed with an Artificial Neural Network (ANN) Estimator which is used to predict the product composition values of the system from temperature measurements. The network used is an Elman network with two hidden layers. The performance of the designed network is tested first in open-loop and then in closed-loop in a feedback inferential control algorithm. It is found that, the control of the product compositions with the help of an ANN estimator with error refinement can be done considering optimal reflux ratio profile.

Supercritical fluid extraction has been used to recover biomaterials from natural matrices. Mathematical modeling of the extraction is required for process design and scale up. Existing models in literature are correlative and dependent upon the experimental data. Construction of predictive models giving reliable results in the lack of experimental data is precious. The long term objective of this study was to construct a predictive mass transfer model, representing supercritical fluid extraction of biomaterials in packed beds by the method of volume averaging. In order to develop mass transfer equations in terms of volume averaged variables, velocity and velocity deviation fields, closure variables were solved for a specific case and the coefficients of volume averaged mass transfer equation for the specific case were computed using one and two-dimensional geometries via analytical and numerical solutions, respectively. Spectral Element method with Domain Decomposition technique, Preconditioned Conjugate Gradient algorithm and Uzawa method were used for the numerical solution. The coefficients of convective term with additional terms of volume averaged mass transfer equation were similar to superficial velocity. The coefficients of dispersion term were close to diffusivity of oil in supercritical carbon dioxide. The coefficients of interphase mass transfer term were overestimated in both geometries. Modifications in boundary conditions, change in geometry of particles and use of three-dimensional computations would improve the value of the coefficient of interphase mass transfer term.

The omnipresent tendency to &ldquo / live easy&rdquo / is a sign of our need for automatization. To enable for such a &ldquo / comfortable and safe&rdquo / world, the automatic systems have to be developed that satisfies the necessities of life. Biologically inspired robots, especially the humanoids, are thus the key, and research in this area focuses on the improvement of such systems. Lately, it has been shown by high dexterity examples that the humanoid robots achieved to a mature level even if there are still open issues to be improved, especially in the control and stability of the bipeds. The purpose of this thesis is to study biped locomotion in different floor conditions, such as stairs and obstacles / to improve the research done in this area / to contribute to the development of autonomous biped robots, dynamic modeling, gait planning, supervisory and guidence control, stability analysis of biped robots / and to implement new control algorithms for biped locomotion, especially by using optimization and high level intelligent control techniques. The locomotion aimed to be realized results from complex, high-dimensional, nonlinear and dynamically related interactions between the robot and its environment. The mathematical modeling of the physical system is realized based on a 5-link 7 DOF biped robot model walking on a 3D planar surface and the dynamic simulation is performed using MATLAB. In terms of control, several different methods applied, comparison and the performance of each method are given. The 3D dynamic simulation software is developed, which allows the user to operate the biped systems within a 3D virtual environment.

<p>This thesis work aimed to provide a better knowledge of inclusion behavior at the steel-slag interface. All results are based on mathematical modeling of liquid and solid inclusion separation to the slag. The model descriptions of the inclusion transfer are based on the equation of motion at the system. It is assumed that the inclusion transfer is governed by four forces acting on the inclusion as it has reached the steel-slag interface. These are the buoyancy force, the added mass force, the drag force and the rebound force. The models assume two cases of inclusion separation depending on the inclusion Reynolds number. In the case where Reynolds number is larger or equal to unity, Re≥1, a steel film is formed between the inclusion and the slag. This steel film must first be drained before the inclusion can separate to the slag. If Reynolds number, Re<1, then no steel film is formed and the inclusion will be in direct contact with the slag. The mathematical models also propose three types of inclusion behavior as the inclusion crosses the steel-slag interface. The inclusion can either, pass and separate to the slag, oscillate at the interface with the possibility of reentering the steel bath with the steel flow or it can remain at the interface not completely separated to the slag. A parameter study for 20 μm inclusions showed that the most important parameters controlling the inclusion behavior at the steel-slag interface are the slag viscosity and the interfacial tensions between the phases. For 100μm inclusions also the inclusion density affects the inclusion behavior. The models were applied to ladle and tundish conditions. Since the slags in the chosen industrial conditions have not been studied experimentally before, estimations of the important physical property parameters were made. Future measurements will therefore be needed in order to make predictions of inclusion transfer behavior at the steel-slag interface which are more relevant for the industry. The main conclusion is that useful plots can be made in order to illustrate the tendency for the inclusion transfer and how to manipulate the physical property parameters in order to increase the inclusion separation in ladles and tundishes.</p>

Growth rate of prostate cancer tumor is an important aspect of understanding the natural history of prostate cancer. Using real prostate cancer data from the SEER database with tumor size as a response variable, we have clustered the cancerous tumor sizes into age groups to enhance its analytical behavior. The rate of change of the response variable as a function of age is given for each cluster. Residual analysis attests to the quality of the analytical model and the subject estimates. In addition, we have identified the probability distribution that characterize the behavior of the response variable and proceeded with basic parametric analysis. There are several remarkable treatment options available for prostate cancer patients. In this present study, we have considered the three commonly used treatment for prostate cancer: radiation therapy, surgery, and combination of surgery and radiation therapy. The study uses data from the SEER database to evaluate and rank the effectiveness of these treatment options using survival analysis in conjunction with basic parametric analysis. The evaluation is based on the stage of the prostate cancer classification. Improvement in prostate cancer disease can be measured by improvement in its mortality. Also, mortality projection is crucial for policy makers and the financial stability of insurance business. Our research applies a parametric model proposed by Renshaw et al. (1996) to project the force of mortality for prostate cancer. The proposed modeling structure can pick up both age and year effects.

Det är allt vanligare inom tredjepartslogistik att kunder hyr en yta för lagring. För den uthyrande parten, i detta fall Delta Terminal, är arean den begränsande faktorn för hur stor yta som kan hyras ut. Idag använ-der sig Delta Terminal av beslutsunderlag i form av lokalernas area och erfarenhet vart gods ska placeras och har inget hjälpmedel för att beräkna vart och hur mycket gods som kan allokeras för att använda så liten yta som möjligt. Studiens syfte har därför varit att ta fram ett faktabaserat hjälpmedel som kan användas som beslutsunderlag. För att uppnå syftet har en matematisk modell utvecklats för att optimera hur gods kan placeras till olika lokaler för att använda så liten area som möjligt och även kunna simulera förändringar. Modellen testades genom att jämföra den maximala godsvolym som lagrades 2012 mot optimeringsmodellens lösning baserat på samma gods- och lokaldata. De vanligaste godstyperna hos Delta terminal var bulk, storsäck och pall och användes i modellen. För dessa så approximerades den förväntade area- och volymåtgång vilket också gav beslutsfattaren en förväntad volymkapacitet för respektive lokal och gods. Resultatet i den optime-rade lösningen visade att ett av godsen skulle kunna flyttas till en annan lokal vilket skulle innebära att ungefär 25 procent mindre area används jämfört med den area som godsets placering upptar idag. Dessutom innebar den optimerade lösningen att tre lokaler frigjordes. Resultatet från simulering av volymkapaciteten för respektive gods och lokal kan hjälpa till vid en beslutssituation om en viss godsvolym får plats i lokalen eller inte och kan därmed hjälpa till att anpassa lokalens kapaci-tet mot godsets volym. Modellen fungerar teoretiskt och skulle kunna implementeras som ett användbart verktyg för beslutsfattaren i frågor som rör optimering eller simulering av ytorna. Vid en implementering gäller det emellertid att modellen valideras och jämförs mot verkliga utfall. / An increasingly common part in third party logistics is that customers rent an area for storage. For the party that leases out the area, in this case Delta Terminal, the area is the limiting factor for the amount of how much can be let out to lease. Today Delta Terminal uses decision sup-port in the form of premises area and experience where goods should be placed and have no means to calculate where and how much goods that can be allocated to use as small space as possible. The purpose of this study was therefore to develop a data based tool that can be used as support in the decision process. To achieve the objective a mathematical model was developed to optimize how freight can be placed at different locations to use as small an area as possible and also be able to simulate changes. The model was tested by comparing the maximum amount of cargo during 2012 against optimization model solution based on the same freight and local data. The most common goods handled at Delta Terminal were bulk, big bags and EUR-pallets and were used in the optimization model. For those goods an approximation of the expected area and volume was made that gave the decision maker an expected volume capacity for each local and goods. The result showed with the optimized solution that one of the goods could be moved to another storage place which would release approximate 25 percent reduction in area compared to where the goods are placed today and also three of the local spaces were released. The result from simulation of the volume capacity of each goods and local can help in a decision situation if a given volume of goods will fit in the local space and thus help to adapt the local capacity against the goods volume. Theoretically the model works and could be implemented as a useful tool for decision-makers on issues related to optimization or simulation of surfaces. However, when implementing the optimization model it is important to validate and compare the model’s result against actual outcomes.