abstract: Current models of pain coping typically focus on how pain contributes to poor physical and psychological functioning. Researchers have argued that this focus on the negative consequences is too narrow and does not account for times when individuals are able to maintain meaningful functioning despite their pain. Thus, the current study sought to investigate the day-to-day processes that both help and hinder recovery from pain and persistence towards daily goals. Specifically, the present study tested: a) a two-factor model of risk and resilience “factors” that capture key processes across affective, cognitive and social dimensions of functioning, and b) whether the relation between morning pain and end-of-day physical disability is mediated by increases in these afternoon risk and resilience factors. Within-day study measures were collected for 21 days via an automated phone system from 220 participants with Fibromyalgia. The results of multi-level confirmatory factor analysis indicated that, consistent with prediction, risk and resilience do constitute two factors. Findings from multilevel structural equation models also showed resilience factor mediated the link between late morning increases in pain and end-of-day disability, in line with hypotheses. Although the vulnerability factor as a whole did not mediate the within-day link between pain and disability, pain-catastrophizing individually did serve as a significant mediator of this relation. This study was the first to empirically test a within-day latent factor model of resilience and vulnerability and the first to capture the multidimensional nature of the pain experience by examining mechanisms across affective, cognitive and social domains of functioning. The findings of the current study suggest that in addition to studying the processes by which pain has a negative influence on the lives of pain sufferers, our understanding of the pain adaptation process can be further improved by concurrently examining mechanisms that motivate individuals to overcome the urge to avoid pain and to function meaningfully despite it. / Dissertation/Thesis / Doctoral Dissertation Psychology 2018

Cette thèse est consacrée à l’étude théorique et numérique de plusieurs équations aux dérivées partielles non linéaires qui apparaissent dans la modélisation de la séparation de phase et des micro-systèmes électro-mécaniques (MSEM). Dans la première partie, nous étudions des modèles d’ordre élevé en séparation de phase pour lesquels nous obtenons le caractère bien posé et la dissipativité, ainsi que l’existence de l’attracteur global et, dans certains cas, des simulations numériques. De manière plus précise, nous considérons dans cette première partie des modèles de type Allen-Cahn et Cahn-Hilliard d’ordre élevé avec un potentiel régulier et des modèles de type Allen-Cahn d’ordre élevé avec un potentiel logarithmique. En outre, nous étudions des modèles anisotropes d’ordre élevé et des généralisations d’ordre élevé de l’équation de Cahn-Hilliard avec des applications en biologie, traitement d’images, etc. Nous étudions également la relaxation hyperbolique d’équations de Cahn-Hilliard anisotropes d’ordre élevé. Dans la seconde partie, nous proposons des schémas semi-discrets semi-implicites et implicites et totalement discrétisés afin de résoudre l’équation aux dérivées partielles non linéaire décrivant à la fois les effets élastiques et électrostatiques de condensateurs MSEM. Nous faisons une analyse théorique de ces schémas et de la convergence sous certaines conditions. De plus, plusieurs simulations numériques illustrent et appuient les résultats théoriques. / This thesis is devoted to the theoretical and numerical study of several nonlinear partial differential equations, which occur in the mathematical modeling of phase separation and micro-electromechanical system (MEMS). In the first part, we study higher-order phase separation models for which we obtain well-posedness and dissipativity results, together with the existence of global attractors and, in certain cases, numerical simulations. More precisely, we consider in this first part higher-order Allen-Cahn and Cahn-Hilliard equations with a regular potential and higher-order Allen-Cahn equation with a logarithmic potential. Moreover, we study higher-order anisotropic models and higher-order generalized Cahn-Hilliard equations, which have applications in biology, image processing, etc. We also consider the hyperbolic relaxation of higher-order anisotropic Cahn-Hilliard equations. In the second part, we develop semi-implicit and implicit semi-discrete, as well as fully discrete, schemes for solving the nonlinear partial differential equation, which describes both the elastic and electrostatic effects in an idealized MEMS capacitor. We analyze theoretically the stability of these schemes and the convergence under certain assumptions. Furthermore, several numerical simulations illustrate and support the theoretical results.