On asymptotic properties of solutions to σ\sigma-evolution equations with general double damping

In this paper, we would like to consider the Cauchy problem for semi-linear $\sigma$-evolution equations with double structural damping for any $\sigma\ge 1$. The main purpose of the present work is to not only study the asymptotic profiles of solutions to the corresponding linear equations but also describe large-time behaviors of globally obtained solutions to the semi-linear equations. We want to emphasize that the new contribution is to find out the sharp interplay of ``parabolic like models" corresponding to $\sigma_1 \in [0,\sigma/2)$ and ``$\sigma$-evolution like models" corresponding to $\sigma_2 \in (\sigma/2,\sigma]$, which together appear in an equation. In this connection, we understand clearly how each damping term influences the asymptotic properties of solutions.Comment: 29 page

Applications of Lp−LqL^p-L^q estimates for solutions to semi-linear σ\sigma-evolution equations with general double damping

In this paper, we would like to study the linear Cauchy problems for semi-linear $\sigma$-evolution models with mixing a parabolic like damping term corresponding to $\sigma_1 \in [0,\sigma/2)$ and a $\sigma$-evolution like damping corresponding to $\sigma_2 \in (\sigma/2,\sigma]$. The main goals are on the one hand to conclude some estimates for solutions and their derivatives in $L^q$ setting, with any $q\in [1,\infty]$, by developing the theory of modified Bessel functions effectively to control oscillating integrals appearing the solution representation formula in a competition between these two kinds of damping. On the other hand, we are going to prove the global (in time) existence of small data Sobolev solutions in the treatment of the corresponding semi-linear equations by applying $(L^{m}\cap L^{q})- L^{q}$ and $L^{q}- L^{q}$ estimates, with $q\in (1,\infty)$ and $m\in [1,q)$, from the linear models. Finally, some further generalizations will be discussed in the end of this paper.Comment: 38 page

Model of neutrino effective masses

It is shown that an effective (nonrenormalizable) coupling of lepton multiplets to scalar triplets in the 331 model with sterile/exotic neutrinos, can be a good way for generating neutrino masses of different types. The method is simple and avoids radiative/loop calculations which, sometimes, are long and complicated. Basing on some astrophysical arguments it is also stated that the scale of SU(3)L symmetry breaking is at TeV scale, in agreement with earlier investigations. Or equivalently, starting from this symmetry breaking scale we could have sterile/exotic neutrinos with mass of a few keV's which could be used to explain several astrophysical and cosmological puzzles, such as the dark matter, the fast motion of the observed pulsars, the re-ionization of the Universe, etc

Optimization of Weld Parameters in Wire and Arc-Based Directed Energy Deposition of High Strength Low Alloy Steels

This paper aims to investigate the fabrication of high strength low alloy (HSLA) steels by wire and arc-based directed energy deposition (WADED). Firstly, the relationship between the process variables (including the travel speed-V, the current-C, and the voltage-U) and the geometrical characteristics of weld beads (including the bead height (BH), bead width (BW), and melting pool length (MPL)) was investigated. Secondly, the optimal process variables were identified using the desirability approach. The results indicate that voltage-U has the highest impact on BW and MPL, meanwhile the travel speed-V is the most impacting factor on BH. The optimal variables for the WADED process of HSAL steels are V = 0.3 m/min, C = 160 A, and U = 19 V. The component fabricated with the optimal variables is fully dense without spatters and defects, confirming the efficiency of the WADED process for HSLA steels

Material Design for Concrete Using Low-Quality Recycled Aggregate

Since the 19th century, concrete has been a fundamental construction material. It is the most popular manmade material in the world because of its more reliable workability, greater durability, and lower cost compared with other construction materials. However, because of its durability, demolishing or renovating old structures generates a huge amount of concrete waste, which, if not properly treated or reused, can adversely affect the environment. Therefore, the development of concrete-recycling technology is a necessary and pressing requirement for all the countries. This study concerns material design with concrete using low-quality recycled aggregates prepared via an aggregate replacement method. To evaluate the quality of the aggregates in recycled aggregate concrete, experiments were conducted using specimen groups characterized by various mix proportions. Accordingly, when low-quality recycled aggregate is used, by employing the relative quality index method for material design, the manufacturing of recycled aggregate concrete with required performance could be achieved