Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions

In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of different mesoscopic distributions. Second, a new variant of the sigma model for interacting electrons in disordered normal and superconducting systems is presented, with demonstrating how to reduce it, under certain controlled approximations, to known ``phase-only'' actions, including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 2001; to be published by Kluwe

Simple de Sitter Solutions

We present a framework for de Sitter model building in type IIA string theory, illustrated with specific examples. We find metastable dS minima of the potential for moduli obtained from a compactification on a product of two Nil three-manifolds (which have negative scalar curvature) combined with orientifolds, branes, fractional Chern-Simons forms, and fluxes. As a discrete quantum number is taken large, the curvature, field strengths, inverse volume, and four dimensional string coupling become parametrically small, and the de Sitter Hubble scale can be tuned parametrically smaller than the scales of the moduli, KK, and winding mode masses. A subtle point in the construction is that although the curvature remains consistently weak, the circle fibers of the nilmanifolds become very small in this limit (though this is avoided in illustrative solutions at modest values of the parameters). In the simplest version of the construction, the heaviest moduli masses are parametrically of the same order as the lightest KK and winding masses. However, we provide a method for separating these marginally overlapping scales, and more generally the underlying supersymmetry of the model protects against large corrections to the low-energy moduli potential.Comment: 37 pages, harvmac big, 4 figures. v3: small correction

Trophic macrophages in development and disease

Specialized phagocytes are found in the most primitive multicellular organisms. Their roles in homeostasis and in distinguishing self from non-self have evolved with the complexity of organisms and their immune systems. Equally important, but often overlooked, are the roles of macrophages in tissue development. As discussed in this Review, these include functions in branching morphogenesis, neuronal patterning, angiogenesis, bone morphogenesis and the generation of adipose tissue. In each case, macrophage depletion impairs the formation of the tissue and compromises its function. I argue that in several diseases, the unrestrained acquisition of these developmental macrophage functions exacerbates pathology. For example, macrophages enhance tumour progression and metastasis by affecting tumour-cell migration and invasion, as well as angiogenesis

Borocarbide Thin Films and Tunneling Measurements

The results obtained by their group in thin film fabrication and STM tunneling on superconducting borocarbides YNi{sub 2}B{sub 2}C have been be briefly reviewed. Results concerning the microwave surface impedance and the S/N planar junctions on LuNi{sub 2}B{sub 2}C thin films have been also presented and analyzed. These new data unambiguously confirm the full BCS nature of the superconducting gap in borocarbides and the absence of significant pair-breaking effects in LuNi{sub 2}B{sub 2}C