Les travaux présentés concernent l'étude analytique et numérique de différents modèles cinétiques appliqués à plusieurs domaines, plus particulièrement : aux neurosciences computationelles et à la volcanologie. Les points communs à ces sujets de recherche sont : - l'utilisation des équations aux dérivées partielles pour l'écriture des modèles mathématiques en partant d'une description microscopique du phénomène, - leur résolution numérique par des schémas déterministes, - une importante interaction avec les collègues bio et géo-physiciens. Les travaux effectuées en collaboration avec les collègues de géophysique (ISTO, Orléans), proposent une description statistique de l'évolution d'une population de bulles de gaz dans un fluide très visqueux. Cette modélisation souligne l'importance de la prise en compte de la coalescence de bulles et ouvre la voie à plusieurs axes de recherche en mathématique et en volcanologie. Les résultats obtenus en neurosciences computationelles sont basés sur des travaux récents concernant les systèmes d'équations stochastiques lents-rapides. Ils permettent de réduire un problème bidimensionnel, nécessitant des moyens de calcul importants, à un modèle unidimensionnel dont la solution d'équilibre est explicite.

The use of process capability indices in the industry is traditionally based on the assumptions that a sample from a process are observations on independently, identically and normally distributed random variables, IIN. However, all three assumptions are open to discussion and in this thesis, the estimation of the indices is studied when the assumption of independence is not fulfilled. In five reports, the indices Cpk and Cpm are studied, and instead of random samples, samples are regarded as observations on a time series. In the first four reports, each index is studied for either an AR(1) or an MA(1) process and the fifth report, both indices are studied for a general ARMA(p,q) process. In all reports, alternatives to Cpk and Cpm are suggested as well as point and interval estimators for the suggested indices. The accuracy of interval estimators are evaluated through large Monte Carlo simulations and the difference between empirical coverage rates and nominal confidence limits are calculated. It was found in all reports that a dependency among observations has a great impact on the coverage rates. The coverage rate difference depends on both the size of the autocorrelation and the type of time series model and for the original Cpk and Cpm the difference can be large. With the suggested alternative indices, however, the differences are always reduced and unless the autocorrelations are close to ±1, the sizes of differences are of little consequence.

Decision making with the help of graphs has been applied for a long time. Previous to the introduction of computerized solutions, graphs and complementary pictures were hand drawn. With the introduction of computers came the colored and dynamic “animations” called simulations which are used today. The focal company of this study, Ångpanneföreningen AB, has during an extensive period of time constructed simulations of complex systems which they have used in order to satisfy specific needs of their customers in different areas. Depending on the complexity of the product and the needs it is ought to fulfill, the exchange of it will have a direct impact on the interactions carried out between the buying and selling parties in various ways. A question that this thesis looked to answer was how the utilization of simulations affects Ångpanneföreningen AB’s relationship with its customers. The purpose of this study is to describe how the use of a simulation program may affect the relation between two parties in a business relationship. A case study approach based on focused and semi-structural interviews has been used for this study.The effects of the use of simulations on a business relationship, in terms of benefits perceived, depend on the purpose set for the software. This meaning that it depends on whether the results and benefits are of such kind that they are possible to measure. However, if measurable, then the awareness of perceived benefits contributes to a stronger relationship since trust is likely to follow from met expectations. The simulation software offered by ÅF has the characteristics of both a product and a service with a highly technological nature. When dealing with simulations holding such attributes, a high level of exchanges is likely to be involved. Furthermore, interdependencies between two parties in a business relationship tend to develop as both the exchanges due to, and the complexities of, the simulation are of a high level, meaning that exchanges are needed in both directions.

This paper examines the pricing of barrier options using Monte Carlo Simulations. MATLAB based software is developed to estimate the price of the option using Monte Carlo simulation. We consider a generalized barrier option of knock out type, but we let the domain take the shape of a rectangular box. We investigate the price of this kind of barrier options. We investigate how the box is placed and what effect it will have on the price of the option. We compare the number of trajectories that are needed in order to achieve the same accuracy between this box barrier option and an ordinary option.

In order to simulate both physically and visually realistic soft tissuedeformations, the Finite Element Method (FEM) is the mostpopular choice in the literature. However it is non-trivial to modelcomplex behaviour of soft tissue with sufficient refresh rates, especiallyfor haptic force feedback which requires an update rate ofthe order of 1 kHz. In this study the use of asynchronous regions isproposed to speed up the solution of FEM equations in real-time. Inthis way it is possible to solve the local neighborhood of the contactwith high refresh rates, while evaluating the more distant regions atlower frequencies, saving computational power to model complexbehaviour within the contact area. Solution of the different regionsusing different methods is also possible. To attain maximum efficiencythe size of the regions can be changed, in real-time, in responseto the size of the deformation.

Energy calibration of CdTe detectors is usually done using known reference sources disregarding the exact amount of charge that is collected in the pixels. However, to compare detector and detector model the quantity of charge collected is needed. We characterize the charge collection in a CdTe detector comparing test pulses, measured data and an improved TCAD simulation model [1]. The 1 mm thick detector is bump-bonded to a TIMEPIX chip and operating in Time-over-Threshold (ToT) mode. The resistivity in the simulation was adjusted to match the detector properties setting a deep intrinsic donor level [2]. This way it is possible to adjust properties like trap concentration, electron/hole lifetime and mobility in the simulation characterizing the detector close to measured data cite [3].

Numerical simulations of Mach shock reflections have shown that the Mach stem can bifurcate as a result of the slip line jetting forward. Numerical simulations were conducted in this study which determined that these bifurcations occur when the Mach number is high, the ramp angle is high, and specific heat ratio is low. It was clarified that the bifurcation is a result of a sufficiently large velocity difference across the slip line which drives the jet. This bifurcation phenomenon has also been observed after triple point collisions in detonation simulations. A triple point reflection was modelled as an inert shock reflecting off a wedge, and the accuracy of the model at early times after reflection indicates that bifurcations in detonations are a result of the shock reflection process. Further investigations revealed that bifurcations likely contribute to the irregular structure observed in certain detonations.

In the last few decades, an increasing number of physicists specialized in soft matter, including polymers, have turned their attention to biologically relevant materials. The properties of various molecules and fibres, such as DNA, RNA, proteins, and filaments of all sorts, are studied to better understand their behaviours and functions. Self-assembled biological membranes, or lipid bilayers, are also the focus of much attention as many life processes depend on these. Small lipid bilayers vesicles dubbed liposomes are also frequently used in the pharmaceutical and cosmetic industries. In this thesis, work is presented on both the elastic properties of polymers and the response of lipid bilayer vesicles to extrusion in narrow-channels. These two areas of research may seem disconnected but they both concern deformed soft materials. The thesis contains four articles: the first presenting a fundamental study of the entropic elasticity of circular chains; the second, a simple universal description of the effect of sequence on the elasticity of linear polymers such as DNA; the third, a model of the symmetric thermophoretic stretch of a nano-confined polymer; the fourth, a model that predicts the final sizes of vesicles obtained by pressure extrusion. These articles are preceded by an extensive introduction that covers all of the essential concepts and theories necessary to understand the work that has been done.

Hot microelectrodes are very small electrodes (usually 1 100 µm in diameter), which have a surface temperature much higher than the temperature in the bulk solution. In this work, the heating is achieved by applying an alternating potential of very high frequency (100 MHz 2 GHz) and of high amplitude (up to 2.8 Vrms) to the microelectrode. As a result, very fast (on the order of milliseconds) changes in the temperature of the electrolyte solution surrounding the electrode can be achieved. Due to the size of the heated microelectrodes, the hot zone in solution is small. Therefore, the solution can be easily overheated and temperatures above the boiling point can be reached.<p> The purpose of this research was to investigate and understand the phenomena occurring at ac polarized microelectrodes and to propose new applications of these electrodes. Using both steady-state and fast-scan (10 V/s) cyclic voltammetry measurements, mass transport of redox species has been studied at ac heated microelectrodes. It has been established that the convection at hot-disk microelectrodes is driven primarily by the electrothermal flow of an electrolyte solution. In addition, other effects such as ac dielectrophoresis and Soret (nonisothermal) diffusion are also observed. Numerical simulations have been employed to predict the distribution of temperature in the hot zone, the direction and magnitude of the electrothermal force and the solution flow rate, as well as the voltammetric response of hot-disk microelectrodes. The results of the simulations agree well with the experimental observations. Theoretical findings of this PhD work are very important for the understanding of the fundamentals of high temperature electrochemistry, particularly mass transport. The proposed explanation of the convection mechanism is most likely applicable not only to ac polarized microelectrodes, but also to the microwave heated microelectrodes, since the only difference between these two heating methods is in the way of delivering electrical energy (wired vs. wireless). The results of the studies of Soret diffusion indicate that it contributes significantly to mass transfer of redox species at hot microelectrodes. Taking into account that the magnitude of the Soret effect has been considered negligible by other electrochemists, the results obtained in this work prove the opposite and show that Soret diffusion affects both the faradaic current and the half-wave potential of the redox reaction. Therefore, the Soret effect can not be ignored if working with hot microelectrodes.<p> Hot microelectrodes can have a number of interesting applications. The results of the initial investigations indicate that these electrodes can be successfully used in the arrangement for Scanning Electrochemical Microscopy (such a novel technique is termed Hot-Tip SECM). In addition, the observed dielectrophoretic and electrothermal convection effects can enhance the performance of the electrochemical sensors based on hot microelectrodes. This can lead to the improvement of the detection limits of many biologically important analytes, such as proteins, bacteria and viruses.

Cytochrome c oxidase couples the reduction of dioxygen to proton pumping against an electrochemical gradient. The D-channel provides the principal uptake pathway for protons. A water chain is thought to mediate the relay of protons through the D-channel, but it is interrupted at N139 in all crystallographic structures. Here, free energy simulations are used to examine the proton uptake pathway in the wild type and in single-point mutants N139V and N139A, where reduction and pumping is compromised. A general approach for the calculation of water occupancy in protein cavities is presented and demonstrates that combining efficient sampling algorithms with long simulation times is required to achieve statistical convergence of equilibrium properties in the protein interior. The relative population of conformational and hydration states of the D-channel is characterized. Results shed light onto the role of N139 in the mechanism of proton uptake and clarify the physical basis for inactive phenotypes.