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Since the 1960s, it has been known that the protons and neutrons in nuclei are composed of more fundamental particles called quarks. To date, there is no evidence that quarks have a substructure. Experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab, on Long Island, New York, study the particle emerging from very energetic collisions between heavy nuclei like gold (each made up of 197 protons and neutrons), and offer a unique means for investigating the properties of quarks and the particles associated with the forces between quarks. The most high-profile scientific breakthrough so far at the RHIC accelerator was the discovery of quark-gluon plasma (QGP). The existence of this new phase of matter had been predicted on theoretical grounds, and it is believed to have existed briefly during the first microsecond after the Big Bang. Its discovery was further confirmation of the Standard Model – a unified description of matter in terms of quarks, particles in the electron family (leptons), and the fields mediating their interactions. Until recently, the available evidence always pointed to a smooth transition between ordinary matter and QGP, unlike the familiar discontinuous change of state (phase transition) when ice turns to liquid water, or when liquid water turns to steam. Changes of phase like in water are called first-order phase transitions. Theorists had anticipated that the normal maximum energy of the RHIC accelerator is too high to observe a first-order phase transition, and they predicted that it might be seen at a lower energy. This insight prompted a multi-year effort at RHIC, known as the Beam Energy Scan (BES), to investigate a wide range of beam energies and search for such phenomena. One of the challenges that arise in interpreting BES measurements is to investigate if a bombarding energy exists where a maximum occurs in the nuclear compression during the early stages of the collision. Naively, one might expect compression to keep increasing indefinitely as the beam energy increases, but nuclei, even if they collide exactly head-on, will transparently pass through each other without stopping at the highest energies, and this counteracts the above- mentioned increase in nuclear compression. Therefore, there probably exists an optimum beam energy where compression is a maximum. Nuclear compression during a nucleus-nucleus collision cannot be measured experimentally, and a model calculation is needed. This thesis involves study of the nuclear transport model AMPT (A Multi-Phase Transport). More specifically, the goal is to study nuclear compression as a function of time during the collision at a given collision energy, extract the maximum compression, then study this maximum as a function of collision energy over the range of energies being scanned at RHIC. The basic computer code to implement the AMPT model is freely available for investigation by any interested user, but various modifications and pieces of additional code need to be developed in order to probe the specific questions of relevance to the scientific objectives explained above.