In this Ph.D. thesis, we have carried out 2D numerical simulations to study the influence of dielectric surfaces on the propagation dynamics of plasma discharges at atmospheric pressure. First we have improved the computational efficiency of the discharge code used in this work in implementing parallelization techniques and more efficient numerical schemes. Second we have studied the dynamics of an air discharge at atmospheric pressure in a point-to-plane geometry with a dielectric layer on the cathode plane. Then, we have studied the influence of a dielectric layer obstacle in the inter-electrode gap. We have shown that depending on the characteristics of the dielectric layer and the amplitude and polarity of the applied voltage, a second discharge may reignite or not below the dielectric in the second air gap. The comparison of simulation results with experiments has shown that in a point-to-plane geometry with a sharp point and a high over-voltage, a single conical discharge structure is observed. A good agreement on the discharge diameter and propagation velocity has been obtained. With a dielectric obstacle in the gap, the simulated reignition dynamics is faster than in the experiments. To improve the agreement, we have studied the influence of several physico-chemical processes. Finally, we have studied the dynamics of discharges in dielectric tubes at atmospheric pressure. For a He -N2 mixture, we have put forward the importance of three body reactions. Last, the influence of the tube radius on the structure of discharges in He - N2 and air is discussed.

Pressure drawdown tests were conducted using Schlumberger’s Modular Formation Dynamics Tester™ (MDT) wireline tool in the Mallik methane hydrate (MH) reservoirs in February 2002 as well as in the Mount Elbert (Alaska) MH reservoirs in February 2007, while a production test was conducted applying a depressurization method in one of the Mallik MH reservoirs in April 2007. All of these tests aimed at measuring production and bottomhole pressure (BHP) responses by reducing BHP below the MH stability pressure to estimate reservoir properties such as permeability and MH dissociation radius. We attempted to analyze the results of these tests through history matching using the numerical simulator (MH21-HYDRES) coded especially for gas hydrate reservoirs. Although the magnitude of depressurization and the total duration spent for these tests were almost identical to each other, the simulation studies revealed that there existed significant differences in what could be inferred and could not be inferred from test results between a MDT test and a production test. The simulation studies mainly clarified that (1) the MDT tests were useful to estimate initial effective permeability in the presence of MH, (2) when BHP is reduced below the MH stability pressure at MDT tests, the pressure and temperature responses were significantly influenced by the wellbore storage erasing all the important data such as those indicating a radius of MH dissociation and effective permeability after partial MH dissociation, and (3) history matching of production tests tended to result in multiple solutions unless establishing steady flow conditions. This paper presents the results of history matching for the typical MDT and production tests conducted in Mallik and Alaska MH reservoirs. This paper also discusses the parameters reliably estimated through MDT and production tests, which should provide many suggestions on future designs and analyses of short-term tests for MH reservoirs.

A gas hydrate production test using the depressurization method was conducted in early April 2007 as part of the JOGMEC/NRCan/Aurora Mallik production research program. The results of the production test were analyzed using a numerical simulator (MH21-HYDRES) coded especially for gas hydrate reservoirs. This paper evaluates the test results based on analyses of production test data, numerical modeling and a series of history matching simulations. Methane gas and water was produced from a 12 m perforation interval within one of the major methane hydrate (MH) reservoirs at the Mallik MH field, by reducing the bottomhole pressure down to about 7 MPa. The measured gas production rate was far higher than that expected for a comparatively small pressure drawdown. However, irregular (on-off) pumping operations, probably related to excessive sand production, resulted in unstable fluid flow within the wellbore, which made the analysis of test performance extremely complicated. A numerical reservoir model was constructed as a series of grid blocks, including those mimicking the wellbore, to enable rigorous simulation of fluid flow patterns in the vicinity of the wellbore. The model was then tuned through history matching, not by simply adjusting reservoir parameters, but by introducing the concept that sand production might have dramatically increased the near-wellbore permeability. The good agreement between observed and simulated performances suggests the mechanism of MH dissociation/production during the test. The history matched reservoir model was employed to predict the second-year production test performance, in order to examine the gas production potential of the Mallik MH reservoir, and to provide insight into future exploration and development planning for MH reservoirs.

Polymer electrolyte membrane (PEM) fuel cells have increasingly become promising green energy sources for automobile and stationary cogeneration applications but its success in commercialization depends on performance optimization and manufacturing cost. The activation losses, expensive platinum catalyst, and water flooding phenomenon are the key factors currently hindering commercialization of PEM fuel cells. These factors are associated with the cathode catalyst layer (CCL), which is about ten micrometers thick. Given the small scale of this layer, it is extremely difficult to study transport phenomena inside the catalyst layer experimentally, either intrusively or non-intrusively. Therefore, mathematical and numerical models become the only means to provide insight on the physical phenomena occurring inside the CCL and to optimize the CCL designs before building a prototype for engineering application. In this thesis research, a comprehensive two-phase mathematical model for the CCL has been derived from the fundamental conservation equations using a volume-averaging method. The model also considers several water transport and physical processes that are involved in the CCL. The processes are: (a) electro-osmotic transport from the membrane to the CCL, (b) back-diffusion of water from the CCL to the membrane, (c) condensation and evaporation of water, and (d) removal of liquid water to the gas flow channel through the gas diffusion layer (GDL). A simple analytical model for the activation overpotential in the CCL has also been developed and an optimization study has been carried out using the analytical activation overpotential formulation. Further, the mathematical model has been simplified for the CCL and an analytical approach has been provided for the liquid water transport in the catalyst layer. The volume-averaged mathematical model of the CCL is finally implemented numerically along with an investigation how the physical structure of a catalyst layer affects fuel cell performance. Since the numerical model requires various effective transport properties, a set of mathematical expressions has been developed for estimating the effective transport properties in the CCL and GDL of a PEM fuel cell. The two-dimensional (2D) numerical model has been compared with the analytical model to validate the numerical results. Subsequently, using this validated model, 2D numerical studies have been carried out to investigate the effect of various physical and wetting properties of CCL and GDL on the performance of a PEM fuel cell. It has been observed that the wetting properties of a CCL control the flooding behavior, and hydrophilic characteristics of the CCL play a significant role on the cell performance. To investigate the effect of concentration variation in the flow channel, a three-dimensional numerical simulation is also presented.

In the nucleus of eukaryotic cells, DNA wraps around histone proteins to form nucleosomes, which in turn associate in a compact and dynamic fiber called chromatin. The physical properties of this fiber at different lengthscales, from the DNA double-helix to micrometer-sized chromosomes, are essential to the complex mechanisms of gene expression and its regulation. The present thesis is a contribution to the development of physical models, which are able to link different scales and to interpret and integrate data from a wide range of experimental and computational approaches. In the first part, we use Molecular Dynamics simulations of DNA oligomers to study doublehelical DNA at different temperatures. We estimate the sequence-dependent contribution of entropy to DNA elasticity, in relation with recent experiments on DNA persistence length. In the second part, we model the DNA-histone interactions within the nucleosome core particle,using DNA nanomechanics to extract a force field from a set of crystallographic nucleosome structures and Molecular Dynamics snapshots. In the third part, we consider the softer part of the nucleosome, the linker DNA between coreparticles which transiently associates with the histone H1 to form a "stem".We combine existing structural knowledge with experimental data at two different resolutions (DNA footprints and electro-micrographs) to develop a nanoscale model of the stem.

Since its introduction by Bloembergen in 1949, nuclear spin diffusion has been a topic of significant interest in magnetic resonance. Spin diffusion, which can be defined as the transfer of spin polarisation induced by the dipolar interaction, is a ubiquitous transport mechanism in solids. Experimental observations of spin diffusion contain structural information. However, the many-body nature of the problem makes it difficult to describe from first principles. The central goal of this thesis is to obtain a quantitative description of the spin diffusion phenomenon from first-principles, through the development of suitable models of the underlying many-body dynamics. To that end we first consider an extension of an existing approach that relies on a master equation to describe the polarisations, for the case of proton-driven carbon-13 spin diffusion (PDSD). Second, a novel approach is introduced for the simulation of the time evolution of selected observables for large strongly coupled nuclear spin systems, using low-order correlations in Liouville space (LCL). Following the introduction of this new simulation method, Liouville-space reduction in solids is analysed in more detail, in order to identify the conditions under which the LCL approximation is valid. Finally, using the LCL model, simulations of proton spin diffusion (PSD) and PDSD are performed, directly from crystal geometry and with no adjustable parameters, and are found to be in excellent agreement with experimental measurements for polycrystalline organic solids.

The first goal of this thesis is to develop and validate a modeling tool into which fundamental combustion chemistry and aerosol dynamics theory are implemented for investigating soot formation/oxidation in multi-dimensional laminar coflow diffusion flames taking into account soot polydispersity and fractal-like aggregate structure. The second goal is to use the tool to study soot aggregate formation/oxidation in experimentally studied laminar coflow diffusion flames to advance the understanding of soot aggregate formation/oxidation mechanism. The first part of the thesis deals with the large CPU time problem when detailed models are coupled together. Using the domain decomposition method, a high performance parallel flame code is successfully developed. An advanced sectional aerosol dynamics model which can model fractal-like aggregate structure is successfully implemented into the parallel flame code. The performance of the parallel code is demonstrated through its application to the modeling of soot formation/oxidation in a laminar coflow CH4/air diffusion flame. The parallel efficiency reaches as high as 83%. The second part of the thesis numerically explores soot aggregate formation in a laminar coflow C2H4/air diffusion flame using detailed PAH-based combustion chemistry and a PAH-based soot formation/oxidation model. Compared to the measured data, flame temperature, axial velocity, C2H2 and OH concentrations, soot volume fraction, the average diameter and the number density of primary particles are reasonably well predicted. However, it is very challenging to predict effectively the average degree of particle aggregation. To do so, particle-particle and fluid-particle interactions that may cause non-unitary soot coagulation efficiency need to be considered. The original coagulation model is enhanced in this thesis to accommodate soot coagulation efficiency. Different types of soot coagulation efficiency are numerically investigated. It is found that a simple adjustment of soot coagulation efficiency from 100% to 20% provides good predictions on soot aggregate structure as well as flame properties. In the third part of the thesis, the effects of oxidation-driven soot aggregate fragmentation on aggregate structure and soot oxidation rate are studied. Three fragmentation models with different fragmentation patterns are developed and implemented into the sectional aerosol dynamics model. The implementation of oxidation-driven aggregate fragmentation significantly improves the prediction of soot aggregate structure in the soot oxidation region.

The first goal of this thesis is to develop and validate a modeling tool into which fundamental combustion chemistry and aerosol dynamics theory are implemented for investigating soot formation/oxidation in multi-dimensional laminar coflow diffusion flames taking into account soot polydispersity and fractal-like aggregate structure. The second goal is to use the tool to study soot aggregate formation/oxidation in experimentally studied laminar coflow diffusion flames to advance the understanding of soot aggregate formation/oxidation mechanism. The first part of the thesis deals with the large CPU time problem when detailed models are coupled together. Using the domain decomposition method, a high performance parallel flame code is successfully developed. An advanced sectional aerosol dynamics model which can model fractal-like aggregate structure is successfully implemented into the parallel flame code. The performance of the parallel code is demonstrated through its application to the modeling of soot formation/oxidation in a laminar coflow CH4/air diffusion flame. The parallel efficiency reaches as high as 83%. The second part of the thesis numerically explores soot aggregate formation in a laminar coflow C2H4/air diffusion flame using detailed PAH-based combustion chemistry and a PAH-based soot formation/oxidation model. Compared to the measured data, flame temperature, axial velocity, C2H2 and OH concentrations, soot volume fraction, the average diameter and the number density of primary particles are reasonably well predicted. However, it is very challenging to predict effectively the average degree of particle aggregation. To do so, particle-particle and fluid-particle interactions that may cause non-unitary soot coagulation efficiency need to be considered. The original coagulation model is enhanced in this thesis to accommodate soot coagulation efficiency. Different types of soot coagulation efficiency are numerically investigated. It is found that a simple adjustment of soot coagulation efficiency from 100% to 20% provides good predictions on soot aggregate structure as well as flame properties. In the third part of the thesis, the effects of oxidation-driven soot aggregate fragmentation on aggregate structure and soot oxidation rate are studied. Three fragmentation models with different fragmentation patterns are developed and implemented into the sectional aerosol dynamics model. The implementation of oxidation-driven aggregate fragmentation significantly improves the prediction of soot aggregate structure in the soot oxidation region.

Šiame darbe apžvelgiama šiluminių reiškinių lazerio aktyvioje terpėje teorija, pristatomi temperatūros bei įtempių ir deformacijų pasiskirstymo aktyviojioje lazerio terpėje kompiuterinio modeliavimo metodika. Temperatūros ir įtempių skaičiavimai atlikti trims aktyviosios terpės konfigūracijoms – Nd:YVO4 plokštelės, dviejų Nd:YAG plokštelių, kaupinamų zigzagu ir plokščiojo kompozitinio keraminio YAG elemento. Ištirta kaupinimo galios, legiruoto sluoksnio storio, aušintuvo ir aktyvios terpės šiluminių parametrų įtaka temperatūros pasiskirstymui, įtempiams ir deformacijoms aktyviojoje terpėje. / Theory of thermal effects in laser active medium is observed in this work. The metodology of temperature, thermal strain and stresses distribution in laser active medium numerical simulation is presented. Modeling of temperature, strain and stress is done by three active medium configurations: Nd:YVO4 plate, thin Nd:YAG elements and composite YAG ceramic slab. The influence to temperature, stresses and strain distribution of pump power and doped layer thickness in laser active medium has been investigated.

Biojutikliai yra įrenginiai, skirti medžiagoms aptikti bei jų koncentracijoms matuoti. Siekiant sumažinti biojutiklių gamybos kaštus yra pasitelkiamas matematinis biojutikliuose vykstančių procesų modeliavimas. Disertacijoje nagrinėjami matematiniai ir kompiuteriniai biojutiklių modeliai, aprašantys biojutiklių, sudarytų iš kelių, skirtingas savybes turinčių dalių, veikimą. Nagrinėjami modeliai yra formuluojami vienmatėje bei dvimatėje erdvėse, aprašomi diferencialinėmis lygtimis dalinėmis išvestinėmis su netiesiniais nariais ir yra sprendžiami skaitiškai, naudojant baigtinių skirtumų metodą. Skaitiniai modeliai yra įgyvendinami kompiuterine programa. Disertacijoje pateikiamas originalus matematinis modelis biojutikliui su anglies nanovamzdelių elektrodu, nustatyti kriterijai, apibrėžiantys, kada biojutiklį su perforuota membrana galima modeliuoti vienmačiu modeliu. Darbe susisteminti elementai, naudojami biojutiklių modelių formulavimui, pagrindinį dėmesį skiriant biojutiklio struktūrinėms savybėms modeliuoti. Apibrėžta biojutiklių modelių aprašo kalba ir sukurta programinė įranga, leidžianti modeliuoti biojutiklių veikimą vienmačiais modeliais arba modeliais, formuluojamais stačiakampėje dvimatės erdvės srityje. Taikant sukurtą biojutiklių modeliavimo programinę įrangą, ištirtas biojutiklio su anglies nanovamzdelių elektrodu modelio adekvatumas ir struktūrinių bei geometrinių savybių įtaka biojutiklio elgsenai. / Biosensors are analytical devices mainly used to detect analytes and measure their concentrations. Mathematical modeling is widely used for optimizing and analyzing an operation of biosensors for reducing price of development of new biosensors. The object of this research is mathematical and computer models, describing an operation of biosensors, made of several parts with different properties. The dissertation covers models, formulated in one and two-dimensional spaces by partial differential equations with non-linear members, and solved numerically, using the method of finite differences. The numerical models are implemented by a computer program. An original mathematical model for a biosensor with a carbon nanotube electrode is presented in the dissertation. The conditions at which the one-dimensional mathematical model can be used instead of two-dimensional one for accurate prediction of the biosensor response are investigated. Elements, used to build models of biosensors with a complex structure, were systemized. The biosensor description language is proposed and the computer software, simulating an operation of biosensors in the one-dimensional space and a rectangular domain of the two-dimensional space, is developed. An adequateness of the model for the biosensor with the carbon nanotube electrode and the impact of structural and geometrical properties on a response of the biosensor were investigated, performing computer experiments using the developed software.