Electronic Thesis and Dissertation Repository

Thesis Format



Master of Science


Applied Mathematics


Denniston, Colin


In recent decades, computer experiments have allowed an accurate and fundamental understanding of molecular mechanisms at the microscopic level, such as the process of relaxation at a stable physical state. However, computer simulations may sometimes produce non-physical results or relations due to the incompleteness of mathematical models describing physical systems. In this thesis, we have investigated whether the initial structure in a computer simulation affects the system relaxation time, which is denoted by τsys, in the Langevin NVT ensemble. We found that for an initial structure, which is inhomogeneous in the number density of atoms, the system relaxation time, τsys, is longer, often by more than an order of magnitude, compared to that for the homogeneous initial structure. Moreover, we realized that the system relaxation time for the inhomogeneous initial structure is an increasing function of the Langevin coupling constant γ.

Summary for Lay Audience

One of the fundamental physical processes in nature is the relaxation process of many-body systems towards a stable physical state. Once a system equilibrates, it becomes measurable, and thus, we can define reliable physical quantities, such as temperature. That is why conventional physics is mostly defined in steady-state conditions. In this thesis, we are going to measure the time that it takes for a system to reach a steady state under specified conditions using computer simulations. The original objective of doing so is to examine the effects of the initial structural conditions on this period of time, commonly called the system relaxation time and denoted by τsys. We found that the initial structural conditions have an effect on the system relaxation time. In particular, we have a shorter system relaxation time for homogeneous initial structures than for inhomogeneous initial structures.