Proton-proton collisions at the Large Hadron Collider provide insight into fundamental dynamics at unprecedented energy scales. After the discovery of the Higgs boson by the ATLAS and CMS experiments completed the Standard Model picture of particle physics in 2012, the focus turned to investigation of new phenomena beyond the Standard Model. Variations on Supersymmetry, which has strong theoretical underpinnings and a wide potential particle phenomenology, garnered attention in particular. Preliminary results, however, yielded no new particle discoveries and set limits on the possible physical properties of supersymmetric models. This thesis describes a search for supersymmetric particles that could not have been detected by earlier efforts. The study probes collisions with a center of mass energy of 13 TeV detected by ATLAS from 2015 to 2016 that result in events with a large number of jets. This search is sensitive to decays of heavy particles via cascades, which result in at least seven hadronic jets and some missing energy. Constraints on the properties of reclustered large-radius jets are used to improve the sensitivity. The main Standard Model backgrounds are removed using a template method that extrapolates background behavior from final states with fewer jets. No excess is observed over prediction, so limits are set on supersymmetric particle masses in the context of two different theoretical models. Gluino masses below 1500 and 1600 GeV, respectively, are excluded, a significant extension of the limits set by previous analyses.

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Various methods and approximation schemes are used to study many-electron interacting systems. Two important many-particle models, the Anderson model and the Hubbard model, and their electromagnetic properties have been investigated in many parameter regimes, and applied to physical systems. An Anderson single-impurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the Non-Crossing Approximation proposed by Zwicknagl et.al., incorporating parameters obtained from ab initio band structure calculations. It yields good agreement with experimental data. For the Anderson lattice model, a variational scheme which uses specific many-electron wavefunctions as basis is applied to both one- and two-dimensional systems represented by symmetric Anderson lattice Hamiltonians. Without much computational effort, the ground state energy is well approximated, especially in strong-coupling limit. Some electronic properties are examined using the variational ground state wavefunction. The one-dimensional Hubbard model has been solved exactly for small-size clusters by diagonalizing the Hamiltonian in the basis of many-electron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and low-lying excited states are presented. Also, mean field calculations of the two-dimensional single-band Hubbard model and Cu-O lattice model (three-band Hubbard model) are carried out for various physical quantities including the energy, occupation probability, staggered magnetization, momentum distribution Fermi surface and density of states, by using a projection operator formalism. To develop a systematic approach to solving many-electron problems, the many-particle partition function for the free electron gas system is explored using a cumulant expansion scheme. Starting from the ground state, the partition function can be approximated to any order in terms of excitation energy. Its application to interacting systems such as the Anderson model and the Hubbard model is briefly discussed. / Ph. D.