Atomistic potential for graphene and other sp2^2 carbon systems

We introduce a torsional force field for sp$^2$ carbon to augment an in-plane atomistic potential of a previous work (Kalosakas et al, J. Appl. Phys. {\bf 113}, 134307 (2013)) so that it is applicable to out-of-plane deformations of graphene and related carbon materials. The introduced force field is fit to reproduce DFT calculation data of appropriately chosen structures. The aim is to create a force field that is as simple as possible so it can be efficient for large scale atomistic simulations of various sp$^2$ carbon structures without significant loss of accuracy. We show that the complete proposed potential reproduces characteristic properties of fullerenes and carbon nanotubes. In addition, it reproduces very accurately the out-of-plane ZA and ZO modes of graphene's phonon dispersion as well as all phonons with frequencies up to 1000~cm$^{-1}$.Comment: 9 pages, 6 figure

Beta Functions study and Unification in the Standard Model and the Minimal Supersymmetric Standard Model of elementary particles

67 σ.Ο σκοπός της παρούσης διπλωματικής είναι η μελέτη της συμπεριφοράς των σταθερών σύζευξης των κβαντικών θεωριών πεδίου του Καθιερωμένου Προτύπου μέσω των συναρτήσεων β της ομάδας επανακανονικοποίησης. Επιβεβαιώνεται η αδυναμία ενοποίησης των σταθερών σύζευξης στο Καθιερωμένο Πρότυπο, αλλά και η επίτευξή της στα πλαίσια του Ελάχιστου Υπερσυμμετρικού Προτύπου των στοιχειωδών σωματιδίων.The purpose of this diploma thesis is the study of the behavior of the Standard Model QFT coupling constants via the renormalisation group beta functions. Results are obtained regarding the Standard Model and the Minimal Supersymmetric Standard Model. Failure of coupling constant unification is verified in the former case, successful unification of coupling constants in the latter.Γεώργιος Δ. Χατζηδάκη

Atomistic potential for graphene and other sp2 carbon systems

We introduce a torsional force field for sp2 carbon to augment an in-plane atomistic potential of a previous work (Kalosakas et al, J. Appl. Phys. 113, 134307 (2013)) so that it is applicable to out-of-plane deformations of graphene and related carbon materials. The introduced force field is fit to reproduce DFT calculation data of appropriately chosen structures. The aim is to create a force field that is as simple as possible so it can be efficient for large scale atomistic simulations of various sp2 carbon structures without significant loss of accuracy. We show that the complete proposed potential reproduces characteristic properties of fullerenes and carbon nanotubes. In addition, it reproduces very accurately the out-of-plane ZA and ZO modes of graphene’s phonon dispersion as well as all phonons with frequencies up to 1000 cm−1.</div