Browsing by Subject "Representative case"

Now showing 1 - 2 of 2

Open Access
Consensus as a Nash equilibrium of a dynamic game
(IEEE, 2016) Niazi, Muhammad Umar B.; Özgüler, Arif Bülent; Yıldız, Aykut
Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.
Open Access
Systematic spatial and stoichiometric screening towards understanding the surface of ultrasmall oxygenated silicon nanocrystal
(Elsevier, 2016-11) Niaz, S.; Zdetsis, A. D.; Koukaras, E. N.; Gülseren, O.; Sadiq, I.
In most of the realistic ab initio and model calculations which have appeared on the emission of light from silicon nanocrystals, the role of surface oxygen has been usually ignored, underestimated or completely ruled out. We investigate theoretically, by density functional theory (DFT/B3LYP) possible modes of oxygen bonding in hydrogen terminated silicon quantum dots using as a representative case of the Si29 nanocrystal. We have considered Bridge-bonded oxygen (BBO), Doubly-bonded oxygen (DBO), hydroxyl (OH) and Mix of these oxidizing agents. Due to stoichiometry, all comparisons performed are unbiased with respect to composition whereas spatial distribution of oxygen species pointed out drastic change in electronic and cohesive characteristics of nanocrytals. From an overall perspective of this study, it is shown that bridge bonded oxygenated Si nanocrystals accompanied by Mix have higher binding energies and large electronic gap compared to nanocrystals with doubly bonded oxygen atoms. In addition, it is observed that the presence of OH along with BBO, DBO and mixed configurations further lowers electronic gaps and binding energies but trends in same fashion. It is also demonstrated that within same composition, oxidizing constituent, along with their spatial distribution substantially alters binding energy, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gap (up to 1.48 eV) and localization of frontier orbitals.