Analysis of Self-Organization

The dissertation is devoted to the study of problems in calculus of variation, free boundary problems and gradient flows with respect to the Wasserstein metric. More concretely, we consider the problem of characterizing the regularity of minimizers to a certain interaction energy. Minimizers of the interaction energy have a somewhat surprising relationship with solutions to obstacle problems. Here we prove and exploit this relationship to obtain novel regularity results. Another problem we tackle is describing the asymptotic behavior of the Cahn-Hilliard equation with degenerate mobility. By framing the Cahn-Hilliard equation with degenerate mobility as a gradient flow in Wasserstein metric, in one space dimension, we prove its convergence to a degenerate parabolic equation under the framework recently developed by Sandier-Serfaty.

TESTING THE JOINT ROLES OF CAREER DECISION SELF-EFFICACY AND PERSONALITY TRAITS IN THE PREDICTION OF CAREER INDECISION

Career decision-making self-efficacy and the Big Five traits of neuroticism, extraversion, and conscientiousness were examined as predictors of career indecision in a sample of 181 undergraduates. Participants completed an online survey. I predicted that the Big Five traits and career decision-making self-efficacy would (a) interrelate moderately and (b) each relate significantly and moderately to career indecision. In addition, I predicted that career decision-making self-efficacy would partially mediate the relationships between the Big Five traits and career indecision, while the Big Five traits were predicted to moderate the relationship between career decision-making self-efficacy and career indecision. Finally, I predicted that career decision-making self-efficacy would account for a greater amount of unique variance in career indecision than the Big Five traits. All predicted correlations were significant. Career decision-making self-efficacy fully mediated the relationship of Extraversion to career indecision and partially mediated the relationships of Neuroticism and Conscientiousness to career indecision. Conscientiousness was found to moderate the relationship of career decision-making self-efficacy to career indecision such that the negative relation between self-efficacy and career indecision was stronger in the presence of high conscientiousness. This study builds upon existing research on the prediction of career indecision by examining potential mediating and moderating relationships.