Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

Scale-wise evolution of rainfall probability density functions fingerprints the rainfall generation mechanism

© 2010 by the American Geophysical Union.The cross-scale probabilistic structure of rainfall intensity records collected over time scales ranging from hours to decades at sites dominated by both convective and frontal systems is investigated. Across these sites, intermittency build-up from slow to fast time-scales is analyzed in terms of heavy tailed and asymmetric signatures in the scale-wise evolution of rainfall probability density functions (pdfs). The analysis demonstrates that rainfall records dominated by convective storms develop heavier-Tailed power law pdfs toward finer scales when compared with their frontal systems counterpart. Also, a concomitant marked asymmetry build-up emerges at such finer time scales. A scale-dependent probabilistic description of such fat tails and asymmetry appearance is proposed based on a modified q-Gaussian model, able to describe the cross-scale rainfall pdfs in terms of the nonextensivity parameter q, a lacunarity (intermittency) correction and a tail asymmetry coefficient, linked to the rainfall generation mechanism.

Improving the generation of decision objectives

Real decision makers exhibit significant shortcomings in the generation of objectives for decisions that they face. Prior research has illustrated the magnitude of this shortcoming but not its causes. In this paper, we identify two distinct impediments to the generation of decision objectives: not thinking broadly enough about the range of relevant objectives, and not thinking deeply enough to articulate every objective within the range that is considered. To test these explanations and explore ways of stimulating a more comprehensive set of objectives, we present three experiments involving a variety of interventions: the provision of sample objectives, organization of objectives by category, and direct challenges to do better, with or without a warning that important objectives are missing. The use of category names and direct challenges with a warning both led to improvements in the quantity of objectives generated without impacting their quality; other interventions yielded less improvement. We conclude by discussing the relevance of our findings to decision analysis and offering prescriptive implications for the elicitation of decision objectives. © 2010 INFORMS.