In this research, the numerical calculation for elastic and nonlinear strains of Fe metal and FeC alloy under different pressures has been performed by the statistical moment method SMM with Mie–-Lennard–Jones potential (MLJ) and Embedded-Jones potential Atom Method (EAM). The analysis reveals that an enhancement in the concentration (cC) from 0 to 5% causes a decrement in the Young’s modulus (E) at room temperature (T = 300 K) for FeC. These calculated results are consistent with the experimental results. In addition, the obtained stress-strain curves for Fe are in perfect agreement with the experimental curves. Besides, increasing the cC for a continuous strain decreases the stress, showing that adding C to Fe to form FeC steel will increase strength and hardness, but decrease elasticity and hardness. The results obtained will be very useful not only for experimental studies but also for theoretical studies of metals and their interstitial alloys.

The paper studies the effect of temperature ([Formula: see text]), ([Formula: see text], 3200, 4000, 5000, 6000, 7000[Formula: see text]K) at pressure [Formula: see text][Formula: see text]GPa; pressure ([Formula: see text]), ([Formula: see text], 100, 200, 300, 350, 400[Formula: see text]GPa) at [Formula: see text][Formula: see text]K and thermal annealing time ([Formula: see text]), [Formula: see text][Formula: see text]ps (after 105 steps) at [Formula: see text][Formula: see text]K, [Formula: see text][Formula: see text]Gpa) on the structure of MgSiO3 bulk 3000 atoms by Molecular Dynamics (MD) simulation using Born–Mayer (BM) pair interaction potential and periodic boundary conditions. The structural results are analyzed through the Radial Distribution Function (RDF), the Coordination Number (CN), the angle distribution, size ([Formula: see text]), total energy of the system ([Formula: see text]) and the bonding lengths. The results show that the temperature and pressure had influenced the structural properties of MgSiO3 bulk and formation process geology of the Earth. In addition, the center of the Earth with [Formula: see text][Formula: see text]K and [Formula: see text][Formula: see text]GPa has appearance and disappearance of the Si–Si, Si–O, O–O, Si–Mg, O–Mg, Mg–Mg bonds and SiO4, SiO5, SiO6, MgO3, MgO4, MgO5, MgO6, MgO7, MgO8, MgO9, MgO[Formula: see text], MgO[Formula: see text], MgO[Formula: see text] angle distributions. When increasing the depth of the Earth’s surface [Formula: see text] lead to size [Formula: see text] of MgSiO3 decreases, total energy of the system ([Formula: see text]) increases, position of first peak of Radial Distribution Function (RDF) is [Formula: see text], height of RDF is [Formula: see text] varies greatly with [Formula: see text] from [Formula: see text][Formula: see text]km to [Formula: see text][Formula: see text]km, gradually decreasing with [Formula: see text] from [Formula: see text][Formula: see text]km to [Formula: see text][Formula: see text]km and the smallest structural change with [Formula: see text][Formula: see text]km that shows has influence affects on the geological formation of the Earth.

We study the pair production of scalar quark in a muon collider within the MSSM with CP violation. We show that including the CP phases can strongly affect the cross section of the process: μ + μ − →q iqj . This could have an important impact on the search for squarks and the determination of the MSSM parameters at future colliders.

We discuss the pair production of scalar quarks in e + e − annihilation within the MSSM with complex parameters. We calculate the SU SY -QCD corrections to the cross section e + e − →q iq j (i, j = 1, 2) and show that the effect of the CP phases of these complex parameters on the cross section can be quite strong in a large region of the MSSM parameter space. This could have important implications for squarks searches and the MSSM parameter determination in future collider experiments.

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