Computational modeling of the properties of TiO2 nanoparticles

In this study we discuss the electronic, structural, and optical properties of titanium dioxide nanoparticles, and also the properties of Ni(II) diimine dithiolato complexes as dyes in dye-sensitized TiO2 based solar cells. The abovementioned properties have been modeled by using computational codes based on the density functional theory. The results achieved show slight evidence on the structure-dependent band gap broadening, and clear blue-shifts in absorption spectra and refractive index functions of ultra-small TiO2 particles. It is also shown that these properties are strongly dependent on the shape of the nanoparticles. Regarding the Ni(II) diimine dithiolato complexes as dyes in dye-sensitized TiO2 based solar cells, it is shown that based on the experimental electrochemical investigation and DFT studies all studied diimine derivatives could serve as potential candidates for the light harvesting, but the e ciencies of the dyes studied are not very promising.

Computational modeling of stented coronary arteries

The application of computational fluid dynamics (CFD) and finite element analysis (FEA) has been growing rapidly in the various fields of science and technology. One of the areas of interest is in biomedical engineering. The altered hemodynamics inside the blood vessels plays a key role in the development of the arterial disease called atherosclerosis, which is the major cause of human death worldwide. Atherosclerosis is often treated with the stenting procedure to restore the normal blood flow. A stent is a tubular, flexible structure, usually made of metals, which is driven and expanded in the blocked arteries. Despite the success rate of the stenting procedure, it is often associated with the restenosis (re-narrowing of the artery) process. The presence of non-biological device in the artery causes inflammation or re-growth of atherosclerotic lesions in the treated vessels. Several factors including the design of stents, type of stent expansion, expansion pressure, morphology and composition of vessel wall influence the restenosis process. Therefore, the role of computational studies is crucial in the investigation and optimisation of the factors that influence post-stenting complications. This thesis focuses on the stent-vessel wall interactions followed by the blood flow in the post-stenting stage of stenosed human coronary artery. Hemodynamic and mechanical stresses were analysed in three separate stent-plaque-artery models. Plaque was modeled as a multi-layer (fibrous cap (FC), necrotic core (NC), and fibrosis (F)) and the arterial wall as a single layer domain. CFD/FEA simulations were performed using commercial software packages in several models mimicking the various stages and morphologies of atherosclerosis. The tissue prolapse (TP) of stented vessel wall, the distribution of von Mises stress (VMS) inside various layers of vessel wall, and the wall shear stress (WSS) along the luminal surface of the deformed vessel wall were measured and evaluated. The results revealed the role of the stenosis size, thickness of each layer of atherosclerotic wall, thickness of stent strut, pressure applied for stenosis expansion, and the flow condition in the distribution of stresses. The thicknesses of FC, and NC and the total thickness of plaque are critical in controlling the stresses inside the tissue. A small change in morphology of artery wall can significantly affect the distribution of stresses. In particular, FC is the most sensitive layer to TP and stresses, which could determine plaque’s vulnerability to rupture. The WSS is highly influenced by the deflection of artery, which in turn is dependent on the structural composition of arterial wall layers. Together with the stenosis size, their roles could play a decisive role in controlling the low values of WSS (<0.5 Pa) prone to restenosis. Moreover, the time dependent flow altered the percentage of luminal area with WSS values less than 0.5 Pa at different time instants. The non- Newtonian viscosity model of the blood properties significantly affects the prediction of WSS magnitude. The outcomes of this investigation will help to better understand the roles of the individual layers of atherosclerotic vessels and their risk to provoke restenosis at the post-stenting stage. As a consequence, the implementation of such an approach to assess the post-stented stresses will assist the engineers and clinicians in optimizing the stenting techniques to minimize the occurrence of restenosis.

Application of Computational Fluid Dynamics in Modeling Blood Flow in Human Thoracic Aorta

The aim of this study was to simulate blood flow in thoracic human aorta and understand the role of flow dynamics in the initialization and localization of atherosclerotic plaque in human thoracic aorta. The blood flow dynamics in idealized and realistic models of human thoracic aorta were numerically simulated in three idealized and two realistic thoracic aorta models. The idealized models of thoracic aorta were reconstructed with measurements available from literature, and the realistic models of thoracic aorta were constructed by image processing Computed Tomographic (CT) images. The CT images were made available by South Karelia Central Hospital in Lappeenranta. The reconstruction of thoracic aorta consisted of operations, such as contrast adjustment, image segmentations, and 3D surface rendering. Additional design operations were performed to make the aorta model compatible for the numerical method based computer code. The image processing and design operations were performed with specialized medical image processing software. Pulsatile pressure and velocity boundary conditions were deployed as inlet boundary conditions. The blood flow was assumed homogeneous and incompressible. The blood was assumed to be a Newtonian fluid. The simulations with idealized models of thoracic aorta were carried out with Finite Element Method based computer code, while the simulations with realistic models of thoracic aorta were carried out with Finite Volume Method based computer code. Simulations were carried out for four cardiac cycles. The distribution of flow, pressure and Wall Shear Stress (WSS) observed during the fourth cardiac cycle were extensively analyzed. The aim of carrying out the simulations with idealized model was to get an estimate of flow dynamics in a realistic aorta model. The motive behind the choice of three aorta models with distinct features was to understand the dependence of flow dynamics on aorta anatomy. Highly disturbed and nonuniform distribution of velocity and WSS was observed in aortic arch, near brachiocephalic, left common artery, and left subclavian artery. On the other hand, the WSS profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The comparison of instantaneous WSS profiles revealed that the model with straight branching arteries had relatively lower WSS compared to that in the aorta model with curved branches. In addition to this, significant differences were observed in the spatial and temporal profiles of WSS, flow, and pressure. The study with idealized model was extended to study blood flow in thoracic aorta under the effects of hypertension and hypotension. One of the idealized aorta models was modified along with the boundary conditions to mimic the thoracic aorta under the effects of hypertension and hypotension. The results of simulations with realistic models extracted from CT scans demonstrated more realistic flow dynamics than that in the idealized models. During systole, the velocity in ascending aorta was skewed towards the outer wall of aortic arch. The flow develops secondary flow patterns as it moves downstream towards aortic arch. Unlike idealized models, the distribution of flow was nonplanar and heavily guided by the artery anatomy. Flow cavitation was observed in the aorta model which was imaged giving longer branches. This could not be properly observed in the model with imaging containing a shorter length for aortic branches. The flow circulation was also observed in the inner wall of the aortic arch. However, during the diastole, the flow profiles were almost flat and regular due the acceleration of flow at the inlet. The flow profiles were weakly turbulent during the flow reversal. The complex flow patterns caused a non-uniform distribution of WSS. High WSS was distributed at the junction of branches and aortic arch. Low WSS was distributed at the proximal part of the junction, while intermedium WSS was distributed in the distal part of the junction. The pulsatile nature of the inflow caused oscillating WSS at the branch entry region and inner curvature of aortic arch. Based on the WSS distribution in the realistic model, one of the aorta models was altered to induce artificial atherosclerotic plaque at the branch entry region and inner curvature of aortic arch. Atherosclerotic plaque causing 50% blockage of lumen was introduced in brachiocephalic artery, common carotid artery, left subclavian artery, and aortic arch. The aim of this part of the study was first to study the effect of stenosis on flow and WSS distribution, understand the effect of shape of atherosclerotic plaque on flow and WSS distribution, and finally to investigate the effect of lumen blockage severity on flow and WSS distributions. The results revealed that the distribution of WSS is significantly affected by plaque with mere 50% stenosis. The asymmetric shape of stenosis causes higher WSS in branching arteries than in the cases with symmetric plaque. The flow dynamics within thoracic aorta models has been extensively studied and reported here. The effects of pressure and arterial anatomy on the flow dynamic were investigated. The distribution of complex flow and WSS is correlated with the localization of atherosclerosis. With the available results we can conclude that the thoracic aorta, with complex anatomy is the most vulnerable artery for the localization and development of atherosclerosis. The flow dynamics and arterial anatomy play a role in the localization of atherosclerosis. The patient specific image based models can be used to diagnose the locations in the aorta vulnerable to the development of arterial diseases such as atherosclerosis.

Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

Computational and Experimental Investigation of the Grooved Roll in Paper Machine Environment

In the paper machine, it is not a desired feature for the boundary layer flows in the fabric and the roll surfaces to travel into the closing nips, creating overpressure. In this thesis, the aerodynamic behavior of the grooved roll and smooth rolls is compared in order to understand the nip flow phenomena, which is the main reason why vacuum and grooved roll constructions are designed. A common method to remove the boundary layer flow from the closing nip is to use the vacuum roll construction. The downside of the use of vacuum rolls is high operational costs due to pressure losses in the vacuum roll shell. The deep grooved roll has the same goal, to create a pressure difference over the paper web and keep the paper attached to the roll or fabric surface in the drying pocket of the paper machine. A literature review revealed that the aerodynamic functionality of the grooved roll is not very well known. In this thesis, the aerodynamic functionality of the grooved roll in interaction with a permeable or impermeable wall is studied by varying the groove properties. Computational fluid dynamics simulations are utilized as the research tool. The simulations have been performed with commercial fluid dynamics software, ANSYS Fluent. Simulation results made with 3- and 2-dimensional fluid dynamics models are compared to laboratory scale measurements. The measurements have been made with a grooved roll simulator designed for the research. The variables in the comparison are the paper or fabric wrap angle, surface velocities, groove geometry and wall permeability. Present-day computational and modeling resources limit grooved roll fluid dynamics simulations in the paper machine scale. Based on the analysis of the aerodynamic functionality of the grooved roll, a grooved roll simulation tool is proposed. The smooth roll simulations show that the closing nip pressure does not depend on the length of boundary layer development. The surface velocity increase affects the pressure distribution in the closing and opening nips. The 3D grooved roll model reveals the aerodynamic functionality of the grooved roll. With the optimal groove size it is possible to avoid closing nip overpressure and keep the web attached to the fabric surface in the area of the wrap angle. The groove flow friction and minor losses play a different role when the wrap angle is changed. The proposed 2D grooved roll simulation tool is able to replicate the grooved aerodynamic behavior with reasonable accuracy. A small wrap angle predicts the pressure distribution correctly with the chosen approach for calculating the groove friction losses. With a large wrap angle, the groove friction loss shows too large pressure gradients, and the way of calculating the air flow friction losses in the groove has to be reconsidered. The aerodynamic functionality of the grooved roll is based on minor and viscous losses in the closing and opening nips as well as in the grooves. The proposed 2D grooved roll model is a simplification in order to reduce computational and modeling efforts. The simulation tool makes it possible to simulate complex paper machine constructions in the paper machine scale. In order to use the grooved roll as a replacement for the vacuum roll, the grooved roll properties have to be considered on the basis of the web handling application.

First principles modeling of metallic alloys and alloy surfaces

By alloying metals with other materials, one can modify the metal’s characteristics or compose an alloy which has certain desired characteristics that no pure metal has. The field is vast and complex, and phenomena that govern the behaviour of alloys are numerous. Theories cannot penetrate such complexity, and the scope of experiments is also limited. This is why the relatively new field of ab initio computational methods has much to give to this field. With these methods, one can extend the understanding given by theories, predict how some systems might behave, and be able to obtain information that is not there to see in physical experiments. This thesis pursues to contribute to the collective knowledge of this field in the light of two cases. The first part examines the oxidation of Ag/Cu, namely, the adsorption dynamics and oxygen induced segregation of the surface. Our results demonstrate that the presence of Ag on the Cu(100) surface layer strongly inhibits dissociative adsorption. Our results also confirmed that surface reconstruction does happen, as experiments predicted. Our studies indicate that 0.25 ML of oxygen is enough for Ag to diffuse towards the bulk, under the copper oxide layer. The other part elucidates the complex interplay of various energy and entropy contributions to the phase stability of paramagnetic duplex steel alloys. We were able to produce a phase stability map from first principles, and it agrees with experiments rather well. Our results also show that entropy contributions play a very important role on defining the phase stability. This is, to the author’s knowledge, the first ab initio study upon this subject.

Modeling of fireside deposit formation in two industrial furnaces

Fireside deposits can be found in many types of utility and industrial furnaces. The deposits in furnaces are problematic because they can reduce heat transfer, block gas paths and cause corrosion. To tackle these problems, it is vital to estimate the influence of deposits on heat transfer, to minimize deposit formation and to optimize deposit removal. It is beneficial to have a good understanding of the mechanisms of fireside deposit formation. Numerical modeling is a powerful tool for investigating the heat transfer in furnaces, and it can provide valuable information for understanding the mechanisms of deposit formation. In addition, a sub-model of deposit formation is generally an essential part of a comprehensive furnace model. This work investigates two specific processes of fireside deposit formation in two industrial furnaces. The first process is the slagging wall found in furnaces with molten deposits running on the wall. A slagging wall model is developed to take into account the two-layer structure of the deposits. With the slagging wall model, the thickness and the surface temperature of the molten deposit layer can be calculated. The slagging wall model is used to predict the surface temperature and the heat transfer to a specific section of a super-heater tube panel with the boundary condition obtained from a Kraft recovery furnace model. The slagging wall model is also incorporated into the computational fluid dynamics (CFD)-based Kraft recovery furnace model and applied on the lower furnace walls. The implementation of the slagging wall model includes a grid simplification scheme. The wall surface temperature calculated with the slagging wall model is used as the heat transfer boundary condition. Simulation of a Kraft recovery furnace is performed, and it is compared with two other cases and measurements. In the two other cases, a uniform wall surface temperature and a wall surface temperature calculated with a char bed burning model are used as the heat transfer boundary conditions. In this particular furnace, the wall surface temperatures from the three cases are similar and are in the correct range of the measurements. Nevertheless, the wall surface temperature profiles with the slagging wall model and the char bed burning model are different because the deposits are represented differently in the two models. In addition, the slagging wall model is proven to be computationally efficient. The second process is deposit formation due to thermophoresis of fine particles to the heat transfer surface. This process is considered in the simulation of a heat recovery boiler of the flash smelting process. In order to determine if the small dust particles stay on the wall, a criterion based on the analysis of forces acting on the particle is applied. Time-dependent simulation of deposit formation in the heat recovery boiler is carried out and the influence of deposits on heat transfer is investigated. The locations prone to deposit formation are also identified in the heat recovery boiler. Modeling of the two processes in the two industrial furnaces enhances the overall understanding of the processes. The sub-models developed in this work can be applied in other similar deposit formation processes with carefully-defined boundary conditions.

Computational studies for the design of process equipment with complex geometries

This study combines several projects related to the flows in vessels with complex shapes representing different chemical apparata. Three major cases were studied. The first one is a two-phase plate reactor with a complex structure of intersecting micro channels engraved on one plate which is covered by another plain plate. The second case is a tubular microreactor, consisting of two subcases. The first subcase is a multi-channel two-component commercial micromixer (slit interdigital) used to mix two liquid reagents before they enter the reactor. The second subcase is a micro-tube, where the distribution of the heat generated by the reaction was studied. The third case is a conventionally packed column. However, flow, reactions or mass transfer were not modeled. Instead, the research focused on how to describe mathematically the realistic geometry of the column packing, which is rather random and can not be created using conventional computeraided design or engineering (CAD/CAE) methods. Several modeling approaches were used to describe the performance of the processes in the considered vessels. Computational fluid dynamics (CFD) was used to describe the details of the flow in the plate microreactor and micromixer. A space-averaged mass transfer model based on Fick’s law was used to describe the exchange of the species through the gas-liquid interface in the microreactor. This model utilized data, namely the values of the interfacial area, obtained by the corresponding CFD model. A common heat transfer model was used to find the heat distribution in the micro-tube. To generate the column packing, an additional multibody dynamic model was implemented. Auxiliary simulation was carried out to determine the position and orientation of every packing element in the column. This data was then exported into a CAD system to generate desirable geometry, which could further be used for CFD simulations. The results demonstrated that the CFD model of the microreactor could predict the flow pattern well enough and agreed with experiments. The mass transfer model allowed to estimate the mass transfer coefficient. Modeling for the second case showed that the flow in the micromixer and the heat transfer in the tube could be excluded from the larger model which describes the chemical kinetics in the reactor. Results of the third case demonstrated that the auxiliary simulation could successfully generate complex random packing not only for the column but also for other similar cases.

Modeling of Liquid-Solid Flow in Industrial Scale

In the present work, liquid-solid flow in industrial scale is modeled using the commercial software of Computational Fluid Dynamics (CFD) ANSYS Fluent 14.5. In literature, there are few studies on liquid-solid flow in industrial scale, but any information about the particular case with modified geometry cannot be found. The aim of this thesis is to describe the strengths and weaknesses of the multiphase models, when a large-scale application is studied within liquid-solid flow, including the boundary-layer characteristics. The results indicate that the selection of the most appropriate multiphase model depends on the flow regime. Thus, careful estimations of the flow regime are recommended to be done before modeling. The computational tool is developed for this purpose during this thesis. The homogeneous multiphase model is valid only for homogeneous suspension, the discrete phase model (DPM) is recommended for homogeneous and heterogeneous suspension where pipe Froude number is greater than 1.0, while the mixture and Eulerian models are able to predict also flow regimes, where pipe Froude number is smaller than 1.0 and particles tend to settle. With increasing material density ratio and decreasing pipe Froude number, the Eulerian model gives the most accurate results, because it does not include simplifications in Navier-Stokes equations like the other models. In addition, the results indicate that the potential location of erosion in the pipe depends on material density ratio. Possible sedimentation of particles can cause erosion and increase pressure drop as well. In the pipe bend, especially secondary flows, perpendicular to the main flow, affect the location of erosion.

CFD modeling of dispersion water feed in wastewater cleaning application

Fluid particle breakup and coalescence are important phenomena in a number of industrial flow systems. This study deals with a gas-liquid bubbly flow in one wastewater cleaning application. Three-dimensional geometric model of a dispersion water system was created in ANSYS CFD meshing software. Then, numerical study of the system was carried out by means of unsteady simulations performed in ANSYS FLUENT CFD software. Single-phase water flow case was setup to calculate the entire flow field using the RNG k-epsilon turbulence model based on the Reynolds-averaged Navier-Stokes (RANS) equations. Bubbly flow case was based on a computational fluid dynamics - population balance model (CFD-PBM) coupled approach. Bubble breakup and coalescence were considered to determine the evolution of the bubble size distribution. Obtained results are considered as steps toward optimization of the cleaning process and will be analyzed in order to make the process more efficient.

Simulating the dynamics of silver market using computational market dynamics

Traditional econometric approaches in modeling the dynamics of equity and commodity markets, have, made great progress in the past decades. However, they assume rationality among the economic agents and and do not capture the dynamics that produce extreme events (black swans), due to deviation from the rationality assumption. The purpose of this study is to simulate the dynamics of silver markets by using the novel computational market dynamics approach. To this end, the daily data from the period of 1st March 2000 to 1st March 2013 of closing prices of spot silver prices has been simulated with the Jabłonska-Capasso-Morale(JCM) model. The Maximum Likelihood approach has been employed to calibrate the acquired data with JCM. Statistical analysis of the simulated series with respect to the actual one has been conducted to evaluate model performance. The model captures the animal spirits dynamics present in the data under evaluation well.

Computational models for and from biology : simple gene assembly and reaction systems

The advancement of science and technology makes it clear that no single perspective is any longer sufficient to describe the true nature of any phenomenon. That is why the interdisciplinary research is gaining more attention overtime. An excellent example of this type of research is natural computing which stands on the borderline between biology and computer science. The contribution of research done in natural computing is twofold: on one hand, it sheds light into how nature works and how it processes information and, on the other hand, it provides some guidelines on how to design bio-inspired technologies. The first direction in this thesis focuses on a nature-inspired process called gene assembly in ciliates. The second one studies reaction systems, as a modeling framework with its rationale built upon the biochemical interactions happening within a cell. The process of gene assembly in ciliates has attracted a lot of attention as a research topic in the past 15 years. Two main modelling frameworks have been initially proposed in the end of 1990s to capture ciliates’ gene assembly process, namely the intermolecular model and the intramolecular model. They were followed by other model proposals such as templatebased assembly and DNA rearrangement pathways recombination models. In this thesis we are interested in a variation of the intramolecular model called simple gene assembly model, which focuses on the simplest possible folds in the assembly process. We propose a new framework called directed overlap-inclusion (DOI) graphs to overcome the limitations that previously introduced models faced in capturing all the combinatorial details of the simple gene assembly process. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs. We also introduce DOI graph-based rewriting rules that capture all the operations of the simple gene assembly model and prove that they are equivalent to the string-based formalization of the model. Reaction systems (RS) is another nature-inspired modeling framework that is studied in this thesis. Reaction systems’ rationale is based upon two main regulation mechanisms, facilitation and inhibition, which control the interactions between biochemical reactions. Reaction systems is a complementary modeling framework to traditional quantitative frameworks, focusing on explicit cause-effect relationships between reactions. The explicit formulation of facilitation and inhibition mechanisms behind reactions, as well as the focus on interactions between reactions (rather than dynamics of concentrations) makes their applicability potentially wide and useful beyond biological case studies. In this thesis, we construct a reaction system model corresponding to the heat shock response mechanism based on a novel concept of dominance graph that captures the competition on resources in the ODE model. We also introduce for RS various concepts inspired by biology, e.g., mass conservation, steady state, periodicity, etc., to do model checking of the reaction systems based models. We prove that the complexity of the decision problems related to these properties varies from P to NP- and coNP-complete to PSPACE-complete. We further focus on the mass conservation relation in an RS and introduce the conservation dependency graph to capture the relation between the species and also propose an algorithm to list the conserved sets of a given reaction system.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

A conspectus on estimating function theory and its applicability to recurrent modeling issues in forest biometry

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Modeling Forest Growth with Management Data: A Matrix Approach for the Italian Alps

Summary