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In this work we present an introduction to the theory of point processes in space and time with focus on space--time shot--noise Cox process. Further from theoretical point of view we study its simulation, space--time separability, kernel estimate of intensity function and non--parametric estimation of some summary statistics using edge corrections. For two ambit models and one space--time separable model we do numerical calculations using the presented theory and software Wolfram Mathematica 9.0. For these three models we do simulations, we select the best bandwidth for kernel estimate of the intensity function and we also calculate some theoretical summary statistics including the pair correlation function. Powered by TCPDF (www.tcpdf.org)

The charge and spin density correlations in a one dimensional electron gas (1DEG) confined in a semiconductor quantum wire structure at zero temperature are studied. The dielectric formulation of the many--body problem is employed and the longitudinal dielectric function, local-field correction, static structure factor, pair correlation function, ground state energy, compressibility, spin-dependent effective interaction potentials, paramagnon dispersion and static spin response function of the 1DEG are computed within the self-consistent field approximations of Singwi et al., known as the STLS and SSTL. The results are compared with those of other groups, and those obtained for two-dimensional electron gas systems whenever it is possible. It is observed that the SSTL satisfies the compressibility sum rule better than the STLS. Calculating the ground state energy of the 1DEG in unpolarized and fully polarized states, it is shown that both STLS and SSTL predict a Bloch transition for 1DEG systems at low electron densities. Finally, the coupled plasmon-phonon modes in semiconductor quantum wires are calculated within the Fermi and Luttinger liquid theories. The coupling of electrons to bulk longitudinal optical phonons without dispersion and to acoustic phonons via deformation potential with a linear dispersion are considered. Using the dielectric formalism, a unified picture of the collective coupled plasmon-phonon modes is presented. Considerable differences between the predictions of the Fermi and Luttinger liquid approaches at large wave vector values, which may be observed experimentally, are found.

L'objectif de la thèse était d'étudier la mobilité de traceurs particulaires dans des milieuxcomplexes par microscopie confocale à balayage laser (CLSM) combinée avec le suivi demultiple particules (MPT) et le recouvrement de fluorescence après photoblanchiment (FRAP).Tout d'abord, nous avons étudié la diffusion de particules dans les gels formés par des protéinesglobulaires. Dans ce but, des gels avec structures variés ont été préparés en faisant varier lesconcentrations en protéine et en sel. La structure a été caractérisée par l'analyse des imagesobtenues par CLSM en termes de fonction de corrélation de paires. La mobilité de particulesavec une large gamme de tailles (2nm - 1 micron) a été étudiée à la fois dans des gels homogèneset hétérogènes et reliée à la structure du gel.Deuxièmement, nous avons étudié des émulsions eau dans eau préparées en mélangeant dessolutions aqueuses de PEO et de dextran. Il a été montré que lorsque des particules colloïdalessont ajoutées, elles sont emprisonnées à l'interface eau-eau, car elles réduisent la tensioninterfaciale. La structure et le déplacement des particules à l'interface ont été déterminés parCLSM combinée avec MPT. / The objective of the thesis was to investigate the mobility of tracer particles in complex media byConfocal Laser Scanning Microscopy (CLSM) combined with multiple particle tracking (MPT)and fluorescence recovery after photobleaching (FRAP).First, we investigated the diffusion of tracer particles in gels formed by globular proteins. Gelswith a variety of structures were prepared by varying the protein and salt concentrations. Thestructure was characterized by analysis of the CLSM images in terms of the pair correlationfunction. The mobility of particles with a broad range of sizes (2nm - 1μm) was investigatedboth in homogeneous and heterogeneous gels and related to the gel structure.Second, we studied water-in-water-emulsions prepared by mixing aqueous solutions of PEO anddextran. It is shown that when colloidal particles are added they become trapped at the waterwaterinterface because they reduce the interfacial tension. The structure and the displacement ofthe particles at the interface were determined using CLSM combined with MPT.