Luttinger model approach to interacting one-dimensional fermions in a harmonic trap

A model of interacting one--dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first application, the particle density is evaluated and the behavior of Friedel oscillations under the influence of interactions is studied. It is found that attractive interactions tend to suppress the Friedel oscillations while strong repulsive interactions enhance the Friedel oscillations significantly. The momentum distribution function and the relation of the model interaction to realistic pair interactions are also discussed.Comment: 12 pages latex, 1 eps-figure in 1 tar file, extended Appendix, added and corrected references, new eq. (53), corrected typos, accepted for PR

On complex-valued 2D eikonals. Part four: continuation past a caustic

Theories of monochromatic high-frequency electromagnetic fields have been designed by Felsen, Kravtsov, Ludwig and others with a view to portraying features that are ignored by geometrical optics. These theories have recourse to eikonals that encode information on both phase and amplitude -- in other words, are complex-valued. The following mathematical principle is ultimately behind the scenes: any geometric optical eikonal, which conventional rays engender in some light region, can be consistently continued in the shadow region beyond the relevant caustic, provided an alternative eikonal, endowed with a non-zero imaginary part, comes on stage. In the present paper we explore such a principle in dimension $2.$ We investigate a partial differential system that governs the real and the imaginary parts of complex-valued two-dimensional eikonals, and an initial value problem germane to it. In physical terms, the problem in hand amounts to detecting waves that rise beside, but on the dark side of, a given caustic. In mathematical terms, such a problem shows two main peculiarities: on the one hand, degeneracy near the initial curve; on the other hand, ill-posedness in the sense of Hadamard. We benefit from using a number of technical devices: hodograph transforms, artificial viscosity, and a suitable discretization. Approximate differentiation and a parody of the quasi-reversibility method are also involved. We offer an algorithm that restrains instability and produces effective approximate solutions.Comment: 48 pages, 15 figure

Information and digital literacies; a review of concepts

A detailed literature reviewing, analysing the multiple and confusing concepts around the ideas of information literacy and digital literacy at the start of the millennium. The article was well-received, and is my most highly-cited work, with over 1100 citations

Histones from dying renal cells aggravate kidney injury via TLR2 and TLR4.

In AKI, dying renal cells release intracellular molecules that stimulate immune cells to secrete proinflammatory cytokines, which trigger leukocyte recruitment and renal inflammation. Whether the release of histones, specifically, from dying cells contributes to the inflammation of AKI is unknown. In this study, we found that dying tubular epithelial cells released histones into the extracellular space, which directly interacted with Toll-like receptor (TLR)-2 (TLR2) and TLR4 to induce MyD88, NF-κB, and mitogen activated protein kinase signaling. Extracellular histones also had directly toxic effects on renal endothelial cells and tubular epithelial cells in vitro. In addition, direct injection of histones into the renal arteries of mice demonstrated that histones induce leukocyte recruitment, microvascular vascular leakage, renal inflammation, and structural features of AKI in a TLR2/TLR4-dependent manner. Antihistone IgG, which neutralizes the immunostimulatory effects of histones, suppressed intrarenal inflammation, neutrophil infiltration, and tubular cell necrosis and improved excretory renal function. In summary, the release of histones from dying cells aggravates AKI via both its direct toxicity to renal cells and its proinflammatory effects. Because the induction of proinflammatory cytokines in dendritic cells requires TLR2 and TLR4, these results support the concept that renal damage triggers an innate immune response, which contributes to the pathogenesis of AKI

Die nur fast gelingende Schließung des Personalentwicklungszyklus

Kühl S. Die nur fast gelingende Schließung des Personalentwicklungszyklus. Organisationsberatung, Supervision, Coaching (OSC ). 2008;15(2):137-155