## Simulated annealing algorithm

The simulated annealing algorithm is an optimization method that mimics the slow cooling of metals, which is characterized by a progressive reduction in the atomic movements that reduce the density of lattice defects until a lowest-energy state is reached [143]. Similarly, at each virtual annealing temperature, the simulated annealing algorithm generates a new potential solution (or neighbor of the current state) to the problem considered by altering the current state, according to a predefined criterion. The acceptance of the new state is then based on the satisfaction of the Metropolis criterion, and this procedure is iterated until convergence. The simulated annealing algorithm performs the following steps: The algorithm generates a random trial point. The algorithm chooses the distance of the trial point from the current point by a probability distribution with a scale depending on the current temperature.

## Finite element analysis

The Finite Element Analysis (FEA) is the simulation of any given physical phenomenon using the numerical technique called the Finite Element Method (FEM). Engineers use FEA software to reduce the number of physical prototypes and experiments and optimize components in their design phase to develop better products, faster while saving on expenses. It is necessary to use mathematics to comprehensively understand and quantify any physical phenomena such as structural or fluid behavior, thermal transport, wave propagation, the growth of biological cells, etc. Most of these processes are described using Partial Differential Equations (PDEs). However, for a computer to solve these PDEs, numerical techniques have been developed over the last few decades and one of the prominent ones, today, is the Finite Element Analysis.

## Superalloys

Superalloys are a group of nickel, iron-nickel, and cobalt alloys used in jet engines. These metals have excellent heat-resistant properties and retain their stiffness, strength, toughness, and dimensional stability at temperatures much higher than the other aerospace structural materials. Superalloys also have good resistance against corrosion and oxidation when used at high temperatures in jet engines. The most important type of superalloy is the nickel-based material that contains a high concentration of chromium, iron, titanium, cobalt, and other alloying elements. Nickel superalloys can operate for long periods at temperatures of 800–1000 °C, which makes them suitable for the hottest sections of gas turbine engines. Superalloys are used in engine components such as the high-pressure turbine blades, discs, combustion chamber, afterburners, and thrust reversers

## Spectroscopy analysis

Spectroscopic analysis might be utilized to elucidate the structure of this surface complex. The Se could serve as a bridging atom, reducing the double bond to Sc to a single bond. Also, Se may have relatively less shielded access to Os. On the other hand, Sc could be the participating atom since it would simply be exchanging one S–O bond for another. The spectroscopic evidence that would be needed would include the presence of S-S bond stretch (difference between a single and double bond) and S–O decoupling; in one configuration, Sc is bonded to three O atoms and Se to none, and in the other, Sc is bonded to two O atoms and Se to one. The pattern of bond bending spectral information may be different due to the iso structure of one configuration and the test structure of the other. The maximum bonded chain length may also be evident in spectral data (the Sc bonded configuration has a chain length of three atoms, while the Se bonded configuration has a four-atom chain length). Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) was recently applied to the confirmation of inner-sphere complexation of B(OH)30 and BOH4− to various minerals, including amorphous iron hydroxide (Su and Suarez, 1995). By systematically subtracting reference spectra from the spectra of more complex samples, ATR-FTIR information about the surface coordination of salicylic acid on aluminum and iron(III) oxides was obtained (Biber and Stumm, 1994).

## Structural mechanics

Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (stress equivalents) within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads, the structure’s geometric representation and support conditions, and the materials’ properties. Output quantities may include support reactions, stresses, and displacements. Advanced structural mechanics may include the effects of stability and non-linear behaviors. Mechanics of structures is a field of study within applied mechanics that investigates the behavior of structures under mechanical loads, such as the bending of a beam, buckling of a column, torsion of a shaft, deflection of a thin shell, and vibration of a bridge. There are three approaches to the analysis: the energy method, flexibility method, or direct stiffness method which later developed into the finite element method, and the plastic analysis approach.

## Catalytic uses for metal nanoparticles synthesized from natural polymers

Green nanotechnology has consistently incorporated biopolymers into its development. They have improved the process of making biocatalysts. The majority of these biopolymers play the dual roles of stabilizing and reducing agents in aqueous conditions, which allows them to be used in the environmentally friendly production of numerous noble metal NPs. The scope of biopolymers’ applications is increased by their biodegradability and biocompatibility. Effective catalysts can be created by combining biopolymers with additional biopolymers or other components, such as biodegradable synthetic polymers. Metal or metal oxide nanoparticles (NPs) with surface decorations, such as Au, Ag, Cu, Pd, Pt, TiO2, and Fe3O4, are used to improve the catalytic activity of biopolymers, resulting in the creation of efficient catalysts for a variety of chemical processes.