Modeling the remnants of core-collapse supernovae from luminous blue variable stars

Context. Luminous blue variable stars (LBVs) are massive evolved stars that suffer sporadic and violent mass-loss events. They have been proposed as the progenitors of some core-collapse supernovae (SNe), but this idea is still debated because of a lack of strong evidence. As supernova remnants (SNRs) can carry in their morphology the fingerprints of the progenitor stars as well as of the inhomogeneous circumstellar medium (CSM) sculpted by the progenitors, the study of SNRs from LBVs could help to place core-collapse SNe in context with the evolution of massive stars. Aims. We investigate the physical, chemical, and morphological properties of the remnants of SNe originating from LBVs in order to search for signatures in the ejecta distribution and morphology of the remnants that could reveal the nature of the progenitors. Methods. As a template of LBVs, we considered the LBV candidate Gal 026.47+0.02. We selected a grid of models that describe the evolution of a massive star with properties consistent with those of Gal 026.47+0.02 and its final fate as a core-collapse SN. We developed a three-dimensional hydrodynamic model that follows the post-explosion evolution of the ejecta from the breakout of the shock wave at the stellar surface to the interaction of the SNR with a CSM characterized by two dense nested toroidal shells, parametrized in agreement with multi-wavelength observations of Gal 026.47+0.02. Results. Our models show a strong interaction of the blast wave with the CSM which determines an important slowdown of the expansion of the ejecta in the equatorial plane where the two shells lay, determining a high degree of asymmetry in the remnant. After ≈10 000 yr of evolution, the ejecta show an elongated shape forming a broad jet-like structure caused by the interaction with the shells and oriented along the axis of the toroidal shells. Models with high explosion energy show Fe-rich internal ejecta distributions surrounded by an elongated Si-rich structure with a more diffuse O-rich ejecta all around. Models with low explosion energy instead show a more homogeneous distribution of chemical elements with a very low presence of Fe-group elements. Conclusions. The geometry and density distribution of the CSM where a LBV star goes SN are fundamental in determining the properties of the resulting SNR. For all the LBV-like progenitors explored here, we found that the remnants show a common morphology, namely elongated ejecta with an internal jet-like structure, which reflects the inhomogeneous and dense pre-SN CSM surrounding the star.

Toroidal uniformly stressed pressure vessel shell formed by the meridian and ring filament winding

The paper outlines the prospects for the use of composite toroidal high-pressure cylinders for the breathing apparatus of the Ministry of Emergency Situations, fire brigades, industrial workers, which are more ergonomic in comparison with their cylindrical counterparts. Relying on the analytical solution of the equilibrium equations, we determined the shape of the cross-section of toroidal shells reinforced along the meridians and representing intersecting loop-like curves that form an infinitely long corrugated pipe. The study introduces a solution for a toroidal composite pressure vessel formed by the intersection of the upper and lower branches of the shell, reinforced along the meridians, and a profiled ring layer of filaments installed at the point of their intersection. The parameters of the toroidal uniformly stressed pressure vessel shell made by ring and meridian filament winding are calculated.

To the Question of Designing Baromembrane Combined Type Apparatus

The paper considers works on methods for calculating design and technological parameters, design of membrane equipment, research of technological features of membrane devices, selection of design schemes, methods for calculating strength and stiffness. A method has been developed for calculating mechanical loads and determining the thickness of plates and toroidal shells of a membrane apparatus of the combined type, which makes it possible to assess the strength properties of apparatus of this class. An example of a calculation, which makes it possible to assess the adequacy of the application of this technique to devices of the combined type, is given.

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

Thin-walled toroidal shells are widely used in the construction During operation, various defects appear on the surface of the shells, in particular, local depressions on the outer and inner surfaces, causing stress concentration in the structure. A three-dimensional spline option of the finite element method was developed to determine the stress-strain state of a toroidal shell with a local deepening on the outer and inner surface. The numerical experiments were carried out. The regularities of the changes in a stress-strain state of the shell with the change in the geometric parameters of the deepening were noted.

Buckling of Externally Pressurized Toroidal Shell With Stiffened Ribs

The buckling characteristics of toroidal shells with closed circular cross sections loaded with a static external pressure were investigated. Eight toroidal shell test models were developed: two ribless, two semicircular discrete ribs, two rectangular discrete ribs, and two rectangular continuous ribs. The geometry, toroidal shell thickness, buckling load, and failure of each model were measured and compared. The effects of different ribbing methods (discrete, continuous unidirectional single-wire, continuous unidirectional multiwire wound, and continuous bidirectional wound ribs) on the buckling behavior of a ribbed toroidal shell were investigated, and the results provide guidance for practical engineering.

On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.