We consider the conformally invariant cubic wave equation on the Einstein cylinder R×S 3 for small rotationally symmetric initial data. This simple equation captures many key challenges of nonlinear wave dynamics in confining geometries, while a conformal transformation relates it to a self-interacting conformally coupled scalar in four-dimensional anti-de Sitter spacetime (AdS 4 ) and connects it to various questions of AdS stability. We construct an effective infinite-dimensional time-averaged dynamical system accurately approximating the original equation in the weak field regime. It turns out that this effective system, which we call the conformal flow, exhibits some remarkable features, such as low-dimensional invariant subspaces, a wealth of stationary states (for which energy does not flow between the modes), as well as solutions with nontrivial exactly periodic energy flows. Based on these observations and close parallels to the cubic Szegő equation, which was shown by Gérard and Grellier to be Lax-integrable, it is tempting to conjecture that the conformal flow and the corresponding weak field dynamics in AdS 4 are integrable as well.
In this article we describe a novel method for the detection of explosives and other hazardous substances in the marine environment using neutron activation. Unlike the other considered methods based on this technique we propose to use guides for neutron and gamma quanta which speeds up and simplies identication. Moreover, it may provide a determination of the density distribution of a dangerous substance. First preliminary results of Monte Carlo simulations dedicated for design of a device exploiting this method are also presented.
We report a discovery of a 1.3 Mpc diffuse radio source with extremely steep spectrum fading radio structures in the vicinity of the Abell 449 cluster of galaxies. Its extended diffuse lobes are bright only at low radio frequencies and their synchrotron age is about 160 Myr. The parent galaxy of the extended relic structure, which is the dominant galaxy within the cluster, is starting a new jet activity. There are three weak X-rays sources in the vicinity of the cluster as found in the ROSAT survey, however it is not known if they are connected with this cluster of galaxies. Just a few radio galaxy relics are currently known in the literature, as finding them requires sensitive and high angular resolution low-frequency radio observations. Objects of this kind, which also are starting a new jet activity, are important for understanding the life cycle and evolution of active galactic nuclei. A new 613 MHz map as well as the archival radio data pertaining to this object are presented and analyzed.
We present status of simulations used to design a novel device for the detection of hazardous substances in the aquatic environment using neutron activation. Unlike the other considered methods based on this technique we propose to use guides for neutron and gamma quanta which speeds up and simplifies identification. First preliminary results show that both the neutron guide and the γ ray guide increase the performance of underwater threats detection.
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