Effective Hamiltonian study of excitations in a boson- fermion mixture with attraction between components

An effective Hamiltonian for the Bose subsystem in the mixture of ultracold atomic clouds of bosons and fermions with mutual attractive interaction is used for investigating collective excitation spectrum. The ground state and mode frequencies of the $^{87}$Rb and $^{40}$K mixture are analyzed quantitatively at zero temperature. We find analytically solutions of the hydrodynamics equations in the Thomas- Fermi approximation. We discuss the relation between the onset of collapse and collective modes softening and the dependence of collective oscillations on scattering length and number of boson atoms.Comment: 9 pages, 5 figure

Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new references added, fixed typo

Metal Ion-Mediated DNA-Protein Interactions

The dramatic changes in the environmental conditions that organisms encountered during evolution and adaptation to life in specific niches, have influenced intracellular and extracellular metal ion contents and, as a consequence, the cellular ability to sense and utilize different metal ions. This metal-driven differentiation is reflected in the specific panels of metal-responsive transcriptional regulators found in different organisms, which finely tune the intracellular metal ion content and all metal-dependent processes. In order to understand the processes underlying this complex metal homeostasis network, the study of the molecular processes that determine the protein-metal ion recognition, as well as how this event is transduced into a transcriptional output, is necessary. This chapter describes how metal ion binding to specific proteins influences protein interaction with DNA and how this event can influence the fate of genetic expression, leading to specific transcriptional outputs. The features of representative metal-responsive transcriptional regulators, as well as the molecular basis of metal-protein and protein-DNA interactions, are discussed on the basis of the structural information available. An overview of the recent advances in the understanding of how these proteins choose specific metal ions among the intracellular metal ion pool, as well as how they allosterically respond to their effector binding, is given