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Στην εργασία γίνεται μελέτη του προβλήματος μεταφοράς και διάχυσης σε μια και δυο διαστάσεις με αναλυτικό και αριθμητικό τρόπο για ρύπους βιομηχανικής μονάδας. / We study in the paper the advection/ diffusion problem in one and two dimension. We use analytical and arithmetical solutions to solve the air pollution problem.

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

Ce travail de thèse porte sur la modélisation et la caractérisation des transferts de chaleur et de masse dans les parois multicouches des bâtiments à ossature bois. Un code instationnaire permettant de simuler les transferts de chaleur et de masse dans une lame d'air en géométrie bidimensionnelle, qui est un élément de la paroi multicouches, a été développé et validé. Les validations numériques en régimes transitoire et stationnaire ont porté sur la totalité des modes de transfert (conduction, écoulement en convection naturelle et forcée, rayonnement entre surfaces, transfert massique et condensation surfacique). Ensuite, ce code intégrant la présence d'une lame d'air dans la paroi a été couplé au code Transpore développé au LERFOB. Ce dernier traite rigoureusement les transferts dans les matériaux solides hygroscopiques. Pour la validation expérimentale du code complet couplé, une cellule expérimentale a été construite et instrumentée pour étudier le comportement hygrothermique des parois étudiées. Cette cellule, régulée thermiquement et hygroscopiquement en température et en humidité relative, a été mise en place au CRITT BOIS d'Epinal. Des comparaisons entre les résultats expérimentaux et numériques sont également présentées et discutées. De nombreuses campagnes de caractérisation thermique sur divers matériaux (isolants à base de fibres de bois, bois massifs, ...) ont également été menées. L'influence de la température et de l'humidité sur la conductivité thermique et la chaleur spécifique a été largement analysée / This thesis focuses on modeling and characterization of heat and mass transfer in a wooden building envelope. A code which simulates unsteady heat and mass in an air layer in two-dimensional geometry, which is part of the multi-layer wall, was developed and validated. Numerical validations that include all transfer modes were achieved for unsteady and steady states regimes (conduction, convection, surface-to-surface radiation, mass transfer and surface condensation). Then, the code developed for the air layer at the LEMTA was coupled to the code Transpore used at the LERFOB. The latter one deals with the transfer in hygroscopic solid materials. For the experimental validation of the fully coupled code, an experimental cell was constructed and instrumented to study the hygrothermal behavior of the studied walls. This cell which is thermally and hygroscopicly controlled was set up at the CRITT BOIS. Comparisons between the experimental and numerical results are presented and discussed. Besides, several experiments of thermal characterization of various materials (insulators containing wood fibers, solid wood ...) were also conducted. The influence of temperature and moisture on thermal conductivity and specific heat was largely investigated