Critical behaviour of (2+12+1)-dimensional QED: 1/N_f-corrections in the Landau gauge

The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N<N_c where N_c=3.29, that is only about $1\%$ larger than its value at leading order.Comment: (v2) Accepted for publication in PRD. Some references added. No change in results. 6 pages, 2 figures. (v1) LaTeX file with feynMF package. 6 pages, 2 figure

Some Formulas for Legendre Functions Induced by the Poisson Transform

Using the Poisson transform, which maps any homogeneous and infinitely differentiable function on a cone into a corresponding function on a hyperboloid, we derive some integral representations of the Legendre functions

Automated system for studying feedback regulators

Bundled software intended for realization of different control algorithms constructed on the basis of functional units on medium-priced industrial controllers have been considered. The example of programming in a language of functional block diagrams of algorithm of real processing automation is give

A methodology for the construction of efficient PLC based low-power photovoltaic generation plants

The research of the operation of low-power photovoltaic generation plants used for self-contained electric power supply in Siberian climatic conditions is performed in this paper. It provides an analysis of the operation of individual units of an automated control system, and gives recommendations for the selection of hardware components. The article describes the operational principles, developed based on functional modules of the programmable logic controller, ensuring maximum possible use of solar energy in this continuous power supply system. The results of plant operation have been obtained, in the form of a power counter log, as well as data on the volume of solar energy produced in both overcast and in sunny weather, throughout the observation period. The article provides visual illustration of generated energy, which could be used to assess the efficiency and economic viability of the low-power photovoltaic plant. Authors would like to point out that examples of the proposed methodology for the construction of self-contained power supply systems can be found in existing industrial facilities, on which further scientific research can be based

Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix

Soft elastic composite materials containing particulate rigid inclusions in a soft elastic matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft elastic polymeric gel matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify the scenario by different theoretical tools, i.e., explicit analytical calculations in the framework of linear elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.Comment: 14 pages, 7 figure