Well-posedness and general energy decay of solutions for a Petrovsky equation with a nonlinear strong dissipation

We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.

Asymptotic structure with vanishing cosmological constant

This is the first of two papers [1] devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant Λ. This first paper is concerned with the case of Λ = 0. Our approach is fully based on the tidal nature of the gravitational field and therefore on the ‘tidal energies’ built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with Λ > 0 covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of super- translation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.

COUNTER-ROTATING DUAL ROTOR WIND TURBINE LAYOUT OPTIMISATION

General energy demand is continuously increasing, thus the energy generating assets need to be optimised for higher efficiency. Wind turbines are no exception. Their maximum efficiency can be determined on a theoretical basis. The limit is approached by researches day by day, utilizing the latest developments in airfoil design, blade structure and new and improved ideas in conventional and unconventional wind turbine layouts. In this paper, we are reviewing the conventional and unconventional wind turbines and their place in smart cities. Then, an unconventional wind turbine design, the CO-DRWT (counter-rotating dual rotor wind turbine) is analysed with a CFD (computational fluid dynamics) code, varying the axial and radial distances between the two turbines. After the simulations, the power coefficients for the different turbine configurations is calculated. At the end of this paper, the simulations results are summarized and consequences are drawn for the CO-DRWT layouts.

Correction: Camiola, V.D., et al. Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation. Entropy 2020, 22, 1023

In Section 5 of Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation [...]

General decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan-Taylor damping with nonlinear delay and acoustic boundary conditions

In this paper, we consider the general energy decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan-Taylor damping with nonlinear delay and acoustic boundary conditions. By introducing suitable energy and Lyapunov functionals, we establish the general decay estimates for the energy, which depends on the behavior of both sigma and g.

Determination features of fuel and energy complex critically important facilities in fuel and energy supply reliability studies

The purpose of the study is to identify industrial facilities that are critically important for the fuel and energy complex in the conditions of joint functioning of industries, taking into account the system effect and existing mechanisms of structural redundancy. To identify critically important facilities of the fuel and energy complex based on its operation models derived as a result of stage-by-stage sectoral and general energy studies, a methodology is proposed. It is based on the identification methods of critically important industry facilities on the principles of assessing vulnerability of critically important infrastructure elements. The presented methodology is characterized by the complex and flexible assessment of the critical importance of sectoral facilities, which is carried out on the basis of scenario options of fuel and ener gyomplex operation. The methodology is supplemented with a formalized representation of a typical general energy optimization model, which unifies the relationship between the territorial-production structure of the sectoral systems modeled in it, its information base with the corresponding technical and economic indicators, and the research problems solved with its help. The assessment of the critical importance of gas industry facilities is given for 80 constituent entities of the Russian Federation. The approbation results of the proposed methodology are given on the example of the identification of the critically important gas industry facilities using a model of fuel and energy complex operation with a detailed scheme of the Unified Gas Supply System of Russia. The approbation has revealed the differences in the priority of critically important facilities of the gas industry and the fuel and energy complex. It has also shown a significant influence of the system effect of the mutually coordinated functioning of industries on the fuel and energy supply of consumers. The results obtained confirm the efficiency of the methodology, prove the possibility of its use for assessing the critical importance of power industry branch facilities. The research scheme implemented in the methodology allows to obtain an adequate state of matters with the fuel and energy supply to consumers under cut-out critically important sectoral facilities.