Browsing by Author "Muhammad Sohail"

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    Bi-doping of Alkali Metals M2 (M2=Li2, Na2, and K2) on Al12N12 Nano-cage: A New Effective Approach to Design Nonlinear Optical Material
    (library Information Services CUI Lahore Campus, 2020-02-16) Muhammad Sohail; FA18-R06-025; Dr. Mazhar Amjad Gilani; LHR TP 5966
    Under the framework of density functional theory (DFT), M2@x-Al12N12 (M2=Li2, Na2, and K2; x=b66, Ntop, and r6) complexes have been designed. These highly stable complexes are formed through doping of bi-alkali metals at the surface of inorganic Al12N12 nano-cage. Both alkali metal atoms were doped in a trans-fashion over nitrogen atoms of Al12N12 (Ntop) or Al-N fused bond (b66) and over six-membered rings (r6). For the b66 and Ntop positions, the trend of stability for the complexes is Li2->Na2->K2-complexes. However, in cage doping position of r6, the stability is increased in the order of Li2->K2->Na2-complexes. The analysis of our computed data revealed that the large band-gap between HOMO (Highest occupied molecular orbital) and LUMO (Lowest unoccupied molecular orbital) of pure Al12N12 nano-cage can be decreased significantly within the range of 0.74-1.67 eV through doping of bi-alkali metals, thus showing the fascinating n-type behavior. A new HOMO orbital formed between the original band-gap of pure Al12N12 is responsible for the reduction in band gap. The doping of bi-alkali metals M2 on Al12N12 nano-cage results in a remarkable nonlinear optical response (β0). The calculated highest first hyperpolarizability values are 127397.94 au for K2@Ntop-Al12N12, 670.67 au for K2@r6-Al12N12, and 1028 au for Na2@b66-Al12N12 respectively. The hyperpolarizability values are increased with the increase in the atomic number of bi-alkali metals when bi-alkali metals are doped over Ntop and r6 positions. These intriguing results would be helpful to pursue future uses of modified doped Al12N12-based nano-cages in the latest kind of electronic and high efficient NLO (Nonlinear optical) nano-devices.
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    Study of Chirp Solitons and Rogue Wave Solutions
    (Library Information Services COMSATS University Lahore Campus, 2023-03-13) Muhammad Sohail; LHR TP 8738; Dr. Syed Tahir Raza Rizvi
    Nonlinear Evolution Equations (NLEEs) are a type of mathematical equation, commonly a partial differential equation (PDE), that describe the evolution of physical phenomena with nonlinear behaviours across time. These equations are critical in many scientific disci plines, including mathematical modelling and soliton theory. The solutions of the NLEEs represent the solitary waves (SW) called solitons. The solitary waves or solitons have a very unique history.Solitons are observed as a dispersion and nonlinearity balance. They are common in many different sectors and have intriguing qualities that make them use ful in a variety of applications. The chirped solitons are a recently popular solitary wave phenomenon. Chirp is used in spread spectrum communications as well as some sonar and radar devices. In this thesis, firstly we will obtain some chirped periodic and solitons wave by using Jaco bian elliptic function (JEF) for for higher order NLSE with anomalous dispersion regime. We also obtain some solitary waves (SW) like dark, bright, kink, hyperbolic, periodic and other solutions for the governing model. The chirp that corresponds to each of these optical solitons is also determined. We will also display the graph of our solutions in different di mensions. Secondly we will study different analytical solutions for Susceptible-Infectious Recovered (SIR) epidemic model with specific nonlinear incidence rate and spatial diffu sion like lump waves (LW), rogue waves (RW), periodic wave (PW) and periodic-cross lump waves (PCLW). This model offers useful information for containment methods by simulating and understanding the geographical spread of infectious illnesses. It advances our knowledge of how the dynamics of an epidemic are influenced by the movement of infected and susceptible people across space