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Study of Cosmic Issues in Modified Gauss-Bonnet Theories

Thesis Info

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Author

Ikram, Ayesha

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10016/1/Ayesha%20Ikram_Maths_2018_UoP_punjab_18.03.2019.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727367710

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This thesis is devoted to study some interesting cosmic issues in the context of modi- ¯ed Gauss-Bonnet theories. Firstly, we explore the instability ranges of a spherically symmetric anisotropic collapsing °uid under expansion-free condition in f(G) grav- ity. We apply the ¯rst order perturbation scheme to the metric components as well as °uid variables and construct the corresponding ¯eld equations for both static as well as perturbed con¯gurations using viable power-law f(G) model. We establish dynamical equations using contracted Bianchi identities to discuss the dynamical in- stability in both Newtonian and post-Newtonian regimes. It is found that instability ranges depend on energy density, anisotropic pressures and Gauss-Bonnet terms but independent of adiabatic index for expansion-free collapsing °uid. Secondly, we generalize f(G) gravity by introducing non-minimal coupling be- tween Gauss-Bonnet invariant and trace of the energy-momentum tensor named as f(G; T) gravity and explore energy conditions for two reconstructed models in the background of homogeneous and isotropic universe. It is found that the massive test particles move along geodesic trajectories due to the presence of extra force originated from non-zero divergence of the energy-momentum tensor. The energy bounds are expressed in terms of deceleration, jerk and snap cosmological parameters. We study energy conditions for reconstructed models corresponding to de Sitter and power-law cosmological background using pressureless °uid and obtain feasible constraints on free parameters. Thirdly, we discuss stability of the Einstein static universe against homogeneous as well as inhomogeneous scalar perturbations in f(G; T) gravity. We investigate sta- bility regions for particular f(G; T) models corresponding to zero as well as non-zero covariant divergence of the energy-momentum tensor. The graphical analysis shows that stable Einstein universe exists for both spatially closed as well as open universe xi xii models against homogeneous and inhomogeneous perturbations for appropriate choice of parameters. Finally, we analyze stability of some cosmic evolutionary models against linear per- turbations in Hubble parameter and energy density of matter distribution in f(G; T) gravity. We establish the ¯eld equations for both general and particular f(G; T) forms in the context of FRW universe model. We apply the reconstruction technique and found that this theory describes the de Sitter universe, power-law solutions as well as phantom/non-phantom eras cosmological backgrounds. We also discuss stability of de Sitter and power-law reconstructed f(G; T) models and ¯nd stable results against linear perturbations.
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یہ عشق میں نہ سوچ تو کہ کیا نہیں ملا

یہ عشق میں نہ سوچ، تُجھے کیا نہیں ملا
ہے کر لیا، تو خاک میں اپنی جبیں ملا

ہم راہ دیکھتے ہی رہے جس کی عمر بھر
آیا وہ شہر میں بھی تو ہم سے نہیں ملا

بچپن میں دل کی بستی میں رہتے تھے کتنے لوگ
دیکھا شباب میں تو فقط اک مکیں ملا

اگلے جہاں کے عہد پہ ہم کو دیا ہے ٹال
کم بخت ہم کو وہ تو بلا کا ذہیں ملا

کہتے رہے تھے یار جسے ہم تمام عمر
اک دن عدو کی بزم میں وہ نازنیں ملا

گر یاں دیا نہ تُو نے تو نہ لوں گا حشر میں
یارب اسے اگر ہے ملانا، یہیں ملا

PENERAPAN TEORI KONSTRUKTIVIS DALAM PEMBELAJARAN

Constructivism is the basis for thinking of a contextual approach, namely that knowledge is built not a set of facts, concepts, or rules that are ready to be remembered. Students must construct that knowledge and give meaning through real experience. Students need to be accustomed to solving problems, finding something useful for themselves, and struggling with ideas. The teacher will not be able to give all knowledge to students. Students must construct knowledge in their own minds. Knowledge is not static, but is constantly evolving and changing as students construct new experiences that force them to base themselves and modify previous knowledge. Learning must be packaged into the process of constructing knowledge rather than receiving knowledge. In the learning process, students build their own knowledge through active involvement in the learning and teaching process. Students become the center of activities, not teachers. Critical thinking is an attempt by someone to check the truth of information using the availability of evidence, logic, and awareness of bias. Critical thinking skills are the cognitive processes of students in analyzing systematically and specifically the problems faced, distinguishing these problems carefully and thoroughly, as well as identifying and reviewing information to plan problem solving strategies.

Dft Studies of Carbon and Nitrogen Based Cubic Antiperovskite Materials.

In this thesis, we present theoretical studies of antiperovskites ANCa3 (A=Ge, Sn, Pb), BCFe3 (B=Al, Zn, Ga), SnCD3 (D=Co and Fe) and MXY3 (M=Al, Ga, Ir, Mg, Pd, Pt, Rh; X=C, N; Y=Mn, Ni, Sc, Ti, Cr, Fe) as well as SbNCa3, BiNCa3, SbNSr3 and BiNSr3. The calculations are carried out with the full-potential linearized augmented plane waves plus local orbital (FPLAPW+lo) method within the framework of density functional theory (DFT) as well as Boltzmann’s theory. The exchange–correlation effects are treated by the local density approximation (LDA), generalized gradient approximation (GGA-PBEsol) and Engel and Vosko GGA (EV-GGA). Furthermore, the modified Becke and Johnson (mBJ) as well as improved mBJ potentials are used for the exact band gaps of the semiconductors. The relativistic effects in some of the compounds under study are explored by spin-orbit coupling. The consistency of the calculated results of the thermoelectric properties of SnCCo3 and SnCFe3 with the experimental results confirms the reliability of our theoretical calculations for the other investigated metallic antiperovskites, ANCa3 (A=Ge, Sn, Pb), BCFe3 (B=Al, Zn, Ga), SnCD3 (D=Co and Fe) and MXY3 (M=Al, Ga, Ir, Mg, Pd, Pt, Rh; X=C, N; Y=Mn, Ni, Sc, Ti, Cr, Fe). Our results for ANCa3 (A=Ge, Sn, Pb), BCFe3 (B=Al, Zn, Ga) and SnCD3 (D=Co, Fe) indicate that the thermopower of these materials can be enhanced by changing the chemical potential. The dimensionless figure of merit for the three nitrides approaches to 0.96 at room temperature, which predicts the usefulness of these materials in thermoelectric devices. Furthermore, the thermal conductivity of these compounds is minimum at room temperature for chemical potential of -0.25 eV to 0.25 eV, with maximum values of dimensionless figure of merit in this range. The striking feature of these studies is identifying a metallic compound, SnNCa3, with the highest value of Seebeck coefficient at room temperature out of all metals. Furthermore, electronic and thermoelectric properties of carbon and nitrogen based twenty metallic antiperovskites MXY3 (M=Al, Ga, Ir, Mg, Pd, Pt, Rh; X=C, N; Y=Mn, Ni, Sc, Ti, Cr, Fe) are investigated. We find high values of Seebeck coefficient and small values of electronic thermal conductivity for AlCTi3, AlNSc3, AlCNi3, AlNTi3, GaCCr3 and MgCNi3 between -0.25 and 0.25 eV chemical potential. These results show high dimensionless figure of merit in metallic materials and therefore, we predict these materials can be potential candidates for low temperature thermoelectric applications. Figure of merit for AlNTi3, GaCCr3, AlCNi3, AlNSc3, MgCNi3 and AlCTi3 materials reaches to 0.32, 0.25, 0.19, 0.19, 0.2 and 0.25 respectively, and hence are predicted to be low temperature thermoelectric materials. The structural, electronic and optical properties of antiperovskite semiconductors, SbNCa3, BiNCa3, SbNSr3 and BiNSr3 are also studied. The calculated lattice constants for these compounds are found consistent with the available experimentally measured values and other theoretical results. The band profiles show that all of these materials are direct band gap semiconductors with the band gap values of 1.1 eV, 1.09 eV, 0.92 eV and 0.81 eV for SbNCa3, BiNCa3, SbNSr3 and BiNSr3 respectively. The direct band gap nature reveals that they may be effective in optical devices and therefore the optical properties of these compounds like the real and imaginary parts of dielectric function, refractive index and absorption coefficient are calculated and discussed. Furthermore, the thermoelectric properties of these semiconductors are also calculated. Our results show high values of Seebeck coefficient for these materials between -0.25 eV and 0.25 eV chemical potential values.