Time-dependent radio emission from evolving jets

We investigated the time-dependent radiative and dynamical properties of light supersonic jets launched into an external medium, using hydrodynamic simulations and numerical radiative transfer calculations. These involved various structural models for the ambient media, with density profiles appropriate for galactic and extragalactic systems. The radiative transfer formulation took full account of emission, absorption, re-emission, Faraday rotation and Faraday conversion explicitly. High time-resolution intensity maps were generated, frame-by-frame, to track the spatial hydrodynamical and radiative properties of the evolving jets. Intensity light curves were computed via integrating spatially over the emission maps. We apply the models to jets in active galactic nuclei (AGN). From the jet simulations and the time-dependent emission calculations we derived empirical relations for the emission intensity and size for jets at various evolutionary stages. The temporal properties of jet emission are not solely consequences of intrinsic variations in the hydrodynamics and thermal properties of the jet. They also depend on the interaction between the jet and the ambient medium. The interpretation of radio jet morphology therefore needs to take account of environmental factors. Our calculations have also shown that the environmental interactions can affect specific emitting features, such as internal shocks and hotspots. Quantification of the temporal evolution and spatial distribution of these bright features, together with the derived relations between jet size and emission, would enable us to set constraints on the hydrodynamics of AGN and the structure of the ambient medium.Comment: 16 pages, 18 figures, MNRAS in press

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view

Trefftz Difference Schemes on Irregular Stencils

The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions -- local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro & Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils.Comment: 28 pages, 12 figures; to be published in J Comp Phy