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(abridged) This thesis presents theoretical and statistical techniquesbroadly related to systems of dynamically-interacting particles composed ofseveral different types of populations. They are applied to observations ofdense star clusters (SCs) in order to study gravitational interactions betweenstars. We present a new analytic method of quantifying the frequency ofencounters involving single, binary and triple stars. With this technique, wehave shown that dynamical encounters involving triple stars occur commonly inat least some SCs, and that they are likely to be an important dynamicalchannel for stellar mergers to occur. We have also used our techniques toanalyze observational data for a large sample of SCs taken from the ACS Surveyfor Globular Clusters. The results of this analysis are as follows: (1) We havecompiled a homogeneous catalogue of stellar populations for every cluster inour sample, including main-sequence (MS), red giant branch, horizontal branchand blue straggler (BS) stars. (2) With this catalogue, we have quantified theeffects of the cluster dynamics in determining the relative sizes and spatialdistributions of these stellar populations. (3) These results are particularlyinteresting for BSs since they provide compelling evidence that they aredescended from binary stars. (4) Our analysis of the MS populations isconsistent with a remarkably universal initial stellar mass function in oldmassive SCs in the Milky Way. This is a new result with important implicationsfor our understanding of star formation in the early Universe and, moregenerally, the history of our Galaxy. Finally, we describe how our techniquesare ideally suited for application to a number of other outstanding puzzles ofmodern astrophysics, including chemical reactions in the interstellar mediumand mergers between galaxies in galaxy clusters.

The Physics of Mergers: Theoretical and Statistical Techniques Applied to Stellar Mergers in Dense Star Clusters