Cette thèse traite essentiellement des liens qui peuvent exister entreles groupes de rang de Morley fini et les groupes algébriques linéaires. Eneffet, nous y établissons quelques propriétés algébriques aux K-groupes ;d'ailleurs une étude de linéarité sur ces groupes est dressée et permeten particulier d'obtenir une généralisation du théorème de Levi sur ladécomposition des groupes algébriques. Ensuite, nous étudions dans ununivers de rang de Morley fini, une action définissable de SL2(K) surun groupe abélien SL2(K)-minimal V où K est un corps définissable decaractéristique positive p > 0. À cet effet, nous montrons que le rang deMorley rk(V ) de V est pair et multiple de rk(K). Enfin, nous analysonssous quelles conditions, étant donné G un groupe algébrique sur un corpsalgébriquement clos de caractéristique non nulle, le quotient G=Z(G) estdéfinissablement linéaire.Par ailleurs, nous montrons sous certaines hypothèses le groupe desautomorphismes définissables d'un K*-groupe simple est interprétable. / This thesis essentially focuses on relationships that may exist betweengroups of finite Morley rank and linear algebraic groups. Indeed, weestablish some algebraic properties to K-groups; while a linearity studyon these groups is drawn and allows in particular to obtain an analogueto Levi decomposition theorem of algebraic groups. Next, in a univers offinite Morley rank, we study a definable action of SL2(K) on an abeliangroup V such as V is SL2(K)-minimal, where K is an definable field ofnonzero characteristic. For that purpose, we show that Morley rank ofV denoted rk(V ) is even and multiple of rk(K). Finally, we analyze theconditions under which, given an algebraic group G over an algebraicallyfield of nonzero characteristic, the quotient G=Z(G) is definably linear.Besides, we show under certain assymptions that the group of definable automorphism of a simple K*-group is interpretable.

Sediment, an integral part of rivers and watersheds, is eroded from, stored in, and transported through various watershed components. Rivers often receive sediment in the form of episodic, discrete pulses from a variety of natural and anthropogenic processes, this sediment can be transported downstream along the bed or suspended in the water column. Most sediment measurements are focused on the component suspended in the water column. Recent advances in data collection techniques have substantially increased both the resolution and spatial scale of data on suspended sediment dynamics, which is helpful in linking small, site-scale measurements of transport processes in the field with large-scale modeling efforts. Part of this research evaluates the accuracy of the latest laser diffraction instrument for suspended-sediment measurement in rivers, LISST-SL2 for measuring suspended sediment concentration (SSC), particle size distribution (PSD), and velocity by comparing to concurrent physical samples analyzed in a lab for SSC and PSD, and velocity measured using an acoustic Doppler current profiler (ADCP) at 11 sites in Washington and Virginia during 2018-2020. Another part of this work employs a 1-D river network, bed material transport model to investigate the magnitude, timing, and persistence of downstream changes due to the introduction of sediment pulses in a linear river network. We specifically focus on comparing bed responses between mixed and uniform grain size sediment pulses. Then the model capability is utilized to explore the control of hydrograph structure on debris flow sediment transport through a more complex river network at different time horizons. Another part of this work investigates the effect of differences in spatial distribution of debris flow sediment input to the network by analyzing corresponding tributary and mainstem characteristics. Based on an extensive dataset, our results highlight the need for a correction of the raw LISST-SL2 measurements to improve the estimation of effective density and particle size distribution with the help of a physical sample. Simulation results from the river network model show that bed response is primarily influenced by the sediment-pulse grain size and distribution. Intermediate mixed-size pulses are likely to have the largest downstream impact because finer sizes translate quickly and coarser sizes (median bed gravel size and larger) disperse slowly. Furthermore, a mixed-size pulse, with a smaller median grain size than the bed, increases bed mobility more than a uniform-size pulse. While investigating the hydrologic control on debris flow simulation, this study finds that differences between transport by a 30-year daily hydrograph and simplified hydrographs were greatest in the first few years, but errors decreased to around 10% after 10 years. Our simulation results highlight that the sequence of flows (initial high/low flow) is less important for transport of finer sediment. We show that such network-scale modeling can quantitatively identify geomorphically significant network characteristics for efficient transport from tributaries to the mainstem, and eventually to the outlet. Results suggest that watershed area and slope characteristics are important to predict aggradation hotspots in a network. However, to predict aggradation and fluvial geomorphic responses to variations in sediment supply from river network characteristics more confidently, more widespread (in several other river networks) model applications with field validation would be useful. This work has important implications for river management, as it allows us to better predict geomorphically significant tributaries and potential impact on downstream locations, which are important for river biodiversity. Model results lead the way to use of simplified flow hydrographs for different timescales, which is crucial in large-scale modeling as it is often restricted by computational capacity. Finally, given the ability for reliable quantification of a high-resolution time-series of different suspended-sediment characteristics, in-stream laser diffraction offers great potential to advance our understanding of suspended-sediment transport. / Doctor of Philosophy / Rivers receive sediment from different natural and human sources, and water moves this sediment in various ways. These ways include along the bottom of the stream or suspended in the water. Quantifying suspended sediment in streams is an important step to estimate the threat to riverine environments as suspended sediments not only carry chemicals and pollutants, but also interact with the river bottom to affect the characteristics of streams. Measurement of suspended-sediment concentration and particle-size is critical for many engineering, ecological, and river-structure issues, but obtaining an accurate measurement of sediment quantity in a river is challenging. The recent advancement of a laser diffraction instrument allows us to obtain frequent measurements of suspended-sediment concentration and particle size by volume. We applied the most recent such instrument at 11 sites in Washington and Virginia during 2018-2020, along with concurrent water samples to measure suspended-sediment concentration and particle size by mass in a laboratory. Our analysis suggests that at least one supporting physical mass measurement be obtained to improve the estimation from laser measurement. Beside this site-scale measurement, we apply a large-scale river network model to estimate how sediment moves along the bed of rivers at large spatial extents. We simulate how this added sediment results in downstream changes in the amount of sediment in the river channel. We compare observed changes in the elevation of the stream bottom and sediment accumulation rates in a downstream lake to model results. Then we investigate the magnitude, timing, and persistence of downstream changes due to the introduction of added sediment by comparing the changes against a baseline condition (without the added sediment). We find that the added sediment that is half as large as on the river bottom and with a range of sizes are likely to affect the largest downstream changes because smaller sizes move quickly and larger sizes move slowly. Furthermore, added sediment that is smaller than on the river bottom and with a range of sizes help more sediment on the river bottom move than if that sediment addition all had the same particle size. We also employ this model to explore the effect of flow variation and river characteristics on sediment movement. Comparing between a 30-year flow record and simplified flow records, we show that results from simplified flow records vary initially, but errors decrease after 10 years. That is, both flow records result in similar sediment movement in the long-term. In terms of aggradation from added sediment, results show that the characteristics of elevation change of the river bottom play a vital role along with the contributing landscape area. This work has important implications for river management, as it not only allows us to accurately measure suspended sediment with an advanced instrument, but also better understand how rivers and aquatic habitat are affected by variations in added sediment.

Dans cette thèse on s'attache à étudier les crochets de Rankin-Cohen et les déformations correspondantes selon de différents points de vue. On présente d'un côté une nouvelle interprétation des déformations de Rankin-Cohen via la théorie de "Quantification par Deformations de Fedosov(en collaboration avec P. Bieliavsky et X. Tang). On parvient notamment à redémontrer un théorème de Connes-Moscovici sur la déformation formelle des algèbres sous l'action d'une algèbre de Hopf H1 munie d'une structure projective. De l'autre cote on donne dans Chapitre III une interprétation détaillée des crochets de Rankin-Cohen via la théorie de représentations unitaires de SL2(R) et en utilisant cette interprétation on étudie certaines propriétés des produits déformés, notamment l'unicité des produits construits par Cohen-Manin-Zagier et une propriété de séparation du produit d'Eholzer. Dans le dernier chapitre on donne une démonstration élémentaire de l'identité combinatoire qui est cruciale pour démontrer l'associativité dans l'approche de la question de déformations par Cohen-Manin-Zagier, Eholzer, et Connes-Moscovici.