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When can one say that a small cluster of atoms is in a molten state? Characterization of the melting transition in a small cluster poses many challenges. Firstly, the very concept of a phase transition in a small cluster is not as sharply defined as in the thermodynamic limit, i. e., for bulk systems. For example, the singularity in specific heat of a bulk system at the transition temperature is seen as a finite and often broad peak when a small cluster melts. Moreover, existing theories of melting in small clusters are often inadequate because strong size-dependent variations in cluster properties, a hallmark of cluster physics, are impossible to model in a purely theoretical framework in a detailed fashion.
How does one characterize cluster melting, in particular, in a molecular dynamics simulation of a cluster? Classic indicators of melting include, e. g., the specific heat, the diffusion coefficient, and the root-mean-squre deviation (relative to the ground state or a reference configuration) in pairwise distances. The goal of this exploratory project is to devise other indicators of melting that are well-suited for a molecular dynamics simulation, and guage their relative merit, efficasy, and usefuleness as compared to the traditional ones. In particular, considering that the system is highly nonlinear near the melting transition, we wish to investigate the behaviour of dynamical quantities such as the Lyapunov exponents (which, indeed, have been occasionally reported in the literature) and other entities from dynamical systems theory. Other possibilities include quantities with nice physical interpretations and whose bulk behaviour is well-understood (e. g., structure factors), and perhaps purely statistical indicators with good statistical properties.
Necessary: Masters degree in Physics, Chemistry, or a related field, with minimum 55% or equivalent grade. Those who have appeared for their degree examination in 2004 are welcome to apply. Familiarity with statistical mechanics and thermodynamics. Knowledge of a programming language suitable for scientific computing such as fortran, C or C++. Strong interest, motivation, enthusiasm, and the ability to learn new things as required. Desirable: Familiarity with the theory of phase transitions, dynamical systems theory and molecular dynamics simulations. Any scientific computing experience.