In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.
<span style="white-space:normal;">This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Poly...<span style="white-space:normal;">This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Polyethylene C</span><sub style="white-space:normal;">2</sub><span style="white-space:normal;">H</span><sub style="white-space:normal;">4</sub><span style="white-space:normal;"> (PE) by the Molecular Dynamics (MD) method with Dreading pair interaction, cyclic boundary conditions and plastic deformation of Polyethylene (PE) be done by stretching method according to the z-axis. The results of structure, plastic deformation of PE are analyzed through size (l), the total energy of the system (E</span><sub style="white-space:normal;">tot</sub><span style="white-space:normal;">), shape and associated energy (E</span><sub style="white-space:normal;">bond</sub><span style="white-space:normal;">), angular binding energy (E</span><sub style="white-space:normal;">angle</sub><span style="white-space:normal;">), energy E</span><sub style="white-space:normal;">dihedral</sub><span style="white-space:normal;">, interactive energy Vander Walls (E</span><sub style="white-space:normal;">non-bonding</sub><span style="white-space:normal;">). When increasing N, t leads to the number of structural units of Face-Centred Cubic (FCC), Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP) increasing, but Amorphous (Amor) decreases while the angle between the atoms is a constant corresponding to 109.5</span>°<span style="white-space:normal;">. Besides, the length of the link (r) increases from r = 1.529 </span>Å<span style="white-space:normal;"> to r = 1.558 </span>Å<span style="white-space:normal;"> while the plastic deformation energy of PE gets an enormous change and the bonding angle at 109.27</span>°<span style="white-space:normal;">. The length of the link r = 1.529 </span>Å<span style="white-space:normal;"> and the size (l) of the PE material increase from l = 3.73 nm to l = 6.63 nm while the total energy of system (E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;">) decreases from E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>1586 eV to E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>7891 eV with the transition temperature is T = 103 K. Increasing the number of atoms leads to increasing the length of the link. The total energy E</span><sub style="white-space:normal;">total </sub><span style="white-space:normal;">of the system decreases, but the number of structural units in FCC, HCP, BCC and Amor increase, which leads to the length of the link increases, the E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> decreases, and there is a change in the plastic deformation characteristics of PE. In contrast, increasing T leads to the plastic deformation increases, and PE moves from the amorphous state to the liquid state. The obtained results are very significant for future experimental research.</span>展开更多
文摘In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.
文摘<span style="white-space:normal;">This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Polyethylene C</span><sub style="white-space:normal;">2</sub><span style="white-space:normal;">H</span><sub style="white-space:normal;">4</sub><span style="white-space:normal;"> (PE) by the Molecular Dynamics (MD) method with Dreading pair interaction, cyclic boundary conditions and plastic deformation of Polyethylene (PE) be done by stretching method according to the z-axis. The results of structure, plastic deformation of PE are analyzed through size (l), the total energy of the system (E</span><sub style="white-space:normal;">tot</sub><span style="white-space:normal;">), shape and associated energy (E</span><sub style="white-space:normal;">bond</sub><span style="white-space:normal;">), angular binding energy (E</span><sub style="white-space:normal;">angle</sub><span style="white-space:normal;">), energy E</span><sub style="white-space:normal;">dihedral</sub><span style="white-space:normal;">, interactive energy Vander Walls (E</span><sub style="white-space:normal;">non-bonding</sub><span style="white-space:normal;">). When increasing N, t leads to the number of structural units of Face-Centred Cubic (FCC), Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP) increasing, but Amorphous (Amor) decreases while the angle between the atoms is a constant corresponding to 109.5</span>°<span style="white-space:normal;">. Besides, the length of the link (r) increases from r = 1.529 </span>Å<span style="white-space:normal;"> to r = 1.558 </span>Å<span style="white-space:normal;"> while the plastic deformation energy of PE gets an enormous change and the bonding angle at 109.27</span>°<span style="white-space:normal;">. The length of the link r = 1.529 </span>Å<span style="white-space:normal;"> and the size (l) of the PE material increase from l = 3.73 nm to l = 6.63 nm while the total energy of system (E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;">) decreases from E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>1586 eV to E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>7891 eV with the transition temperature is T = 103 K. Increasing the number of atoms leads to increasing the length of the link. The total energy E</span><sub style="white-space:normal;">total </sub><span style="white-space:normal;">of the system decreases, but the number of structural units in FCC, HCP, BCC and Amor increase, which leads to the length of the link increases, the E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> decreases, and there is a change in the plastic deformation characteristics of PE. In contrast, increasing T leads to the plastic deformation increases, and PE moves from the amorphous state to the liquid state. The obtained results are very significant for future experimental research.</span>
