On Capital Dependent Dynamics of Knowledge

We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of physical and human capital. First, we study model with constant savings. The model with optimised behaviour of households is also considered. We show that the model where the rate of change of knowledge depends only on the rate of change of physical capital can be reduced to the form of the two-dimensional autonomous dynamical system. All possible evolutional paths and the stability of solutions in the phase space are discussed in details. We obtain that the rate of growth of capital, consumption and output are greater in the case of capital dependent rate of change of knowledge.Comment: 11 pages, 5 figures; presented at 2nd Polish Symposium on Econo- and Sociophysics, Krakow, Poland, 21-22 April 2006; to be published in Acta Phys. Pol.

Phantom cosmology as a simple model with dynamical complexity

We study the Friedmann-Robertson-Walker model with phantom fields modelled in terms of scalar fields. We apply the Ziglin theory of integrability and find that the flat model is nonintegrable. Then we cannot expect to determine simple analytical solutions of the Einstein equations. We demonstrate that there is only a discrete set of parameters where this model is integrable. For comparison we describe the phantoms fields in terms of the barotropic equation of state. It is shown that in the contrast to the phantoms modelled as scalar fields, the dynamics is always integrable and phase portraits are constructed. In this case we find the duality relation.Comment: RevTeX4, 11 pages, 2 figures; rewritten (v.2); new section on complex dynamics in cases with and without spontaneous symmetry breaking (v.3); this new section on numerical analysis of complex dynamics was dropped, upload to match version in PRE (v.4

Mini-documentaries

Thesis (M.S.V.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1979.Includes index.The considerations, potential and limit ations of very short films as exemplified by the production of thirty- eight Mini-Documentaries for the Aspen Movie Map Project. The films are included on videotape.by Marek Zalewski.M.S.V.S

Deconstructing 5D supersymmetric U(1) gauge theories on orbifolds

We investigate deconstruction of five dimensional supersymmetric abelian gauge theories compactified on $S_1/Z_2$, with various sets of bulk and matter multiplets. The problem of anomalies, chirality and stability in the deconstructed theories is discussed. We find that for most of the 5d brane/bulk matter assignments there exists the deconstructed version. There are, however, some exceptions.Comment: Discussion of mixed anomalies and some clarifying commments added. Version to appear in Phys.Lett.