Analysis and Simulation of Molecular Systems: Memory Function Approach and Uncertainty Quantification Kim, Changho creator 2015 xvi, 292 p. born digital Thesis (Ph.D. -- Brown University (2015) Karniadakis, George Director Matzavinos, Anastasios Reader Stratt, Richard Reader Borodin, Oleg Reader Brown University. Applied Mathematics sponsor theses The mesoscopic description of molecular systems is investigated by using the memory function approach, and uncertainty quantification methods are developed for the evaluation of time correlation functions and transport coefficients from molecular dynamics (MD) simulations. All theoretical predictions are carefully examined by large-sized-ensemble MD runs. First, the Brownian motion of a colloidal particle suspended in a simple molecular fluid is considered, and it is demonstrated that its mesoscopic description can be improved by incorporating the microscopic information through the memory function. The microscopic origin of friction force and thermal noise in the Langevin description is explained by introducing two types of dynamics where the colloidal particle is fixed or moves at an infinitesimal constant velocity due to its infinite mass. Subsequently, in the near-Brownian-limit regime, where the particle has large but finite mass, asymptotic expansions of its time correlation functions are derived, and hence the finite-mass effects in the mesoscopic description are quantified. For a Rayleigh particle (i.e., a colloidal particle in an ideal gas), it is shown that confinement enhances the tail of the memory function, which may change the diffusion behavior of the particle. Second, a theoretical and computational framework for the analysis of statistical errors and finite-system-size effects in MD simulation results is presented, and applied to the MD procedure evaluating the diffusion coefficient of a tracer particle. It is shown that the velocity autocorrelation function (VACF) and mean-squared displacement (MSD) methods produce the same mean value of the time-dependent diffusion coefficient (TDDC) with the same level of the statistical errors. Under the Gaussian process approximation of the velocity process, theoretical statistical-error estimates of the VACF, MSD, and TDDC are derived. Subsequently, it is shown that in order to apply a finite-system-size correction on the diffusion coefficient, the evaluation time of the TDDC should be linearly increased as the system size increases. An asymptotic expression for the memory function with respect to the system size is proposed from the computational results, and the corresponding expressions for the VACF and the diffusion coefficient are derived. Generalized Langevin equation Brownian motion Molecular dynamics simulation Brownian motion processesMolecular dynamics--Simulation methods RPB 20150601 engEnglish10.7301/Z05D8Q7MIn CopyrightCollection is open for research.dissertations