# Browsing by Subject "Molecular simulation"

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Item Efficient computational strategies for predicting homogeneous fluid structure(2014-08) Hollingshead, Kyle Brady; Truskett, Thomas Michael, 1973-Show more A common challenge in materials science is the "inverse design problem," wherein one seeks to use theoretical models to discover the microscopic characteristics (e.g., interparticle interactions) of a system which, if fabricated or synthesized, would yield a targeted material property. Inverse design problems are commonly addressed by stochastic optimization strategies like simulated annealing. Such approaches have the advantage of being general and easy to apply, and they can be effective as long as material properties required for evaluating the objective function of the optimization are feasible to accurately compute for thousands to millions of different trial interactions. This requirement typically means that "exact" yet computationally intensive methods for property predictions (e.g., molecular simulations) are impractical for use within such calculations. Approximate theories with analytical or simple numerical solutions are attractive alternatives, provided that they can make sufficiently accurate predictions for a wide range of microscopic interaction types. We propose a new approach, based on the fine discretization (i.e., terracing) of continuous pair interactions, that allows first-order mean-spherical approximation theory to predict the equilibrium structure and thermodynamics of a wide class of complex fluid pair interactions. We use this approach to predict the radial distribution functions and potential energies for systems with screened electrostatic repulsions, solute-mediated depletion interactions, and ramp-shaped repulsions. We create a web applet for introductory statistical mechanics courses using this approach to quickly estimate the equilibrium structure and thermodynamics of a fluid from its pair interaction. We use the applet to illustrate two fundamental fluid phenomena: the transition from ideal gas-like behavior to correlated-liquid behavior with increasing density in a system of hard spheres, and the water-like tradeoff between dominant length scales with changing temperature in a system with ramp-shaped repulsions. Finally, we test the accuracy of our approach and several other integral equation theories by comparing their predictions to simulated data for a series of different pair interactions. We introduce a simple cumulative structural error metric to quantify the comparison to simulation, and find that according to this metric, the reference hypernetted chain closure with a semi-empirical bridge function is the most accurate of the tested approximations.Show more Item Iterative milestoning(2016-12) Bello Rivas, Juan Manuel; Elber, Ron; Engquist, Bjorn; Makarov, Dmitrii E; Rodin, Gregory J; Zariphopoulou, ThaleiaShow more Computer simulation of matter using Molecular Dynamics (MD) is a staple in the field of Molecular Biophysics. MD yields results suitable for comparison with laboratory experiments and, in addition, it serves as a computational microscope by providing insight into a variety of molecular mechanisms. However, some of the most interesting problems pertaining to the investigation of biomolecules remain outside of the scope of MD due to the long time scales at which they occur. Milestoning is a method that addresses the long time simulation of biomolecular systems without giving up the fully-atomistic spatial resolution necessary to understand biological processes such as signalling and biochemical reactions. The method works by partitioning the phase space of the system into regions whose boundaries are called milestones. The dynamics of the system restricted to the milestones defines a stochastic process whose transition probabilities and exit times can be efficiently computed by numerical simulation. By calculating the transition probabilities and exit times of this process, we can obtain global thermodynamic and kinetic properties of the original system such as its stationary probability, free energy, and reaction rates. The calculation of these properties would be unfeasible for many systems of interest if we were to approach the problem by plain MD simulation. The success of milestoning computations relies on certain modeling assumptions. In this dissertation we introduce an iterative variant of the Milestoning method that relaxes the assumptions required by the original method and can be applied in the non-equilibrium setting. The new method works by iteratively approximating the transition probabilities and exit times until convergence is attained. In addition to a detailed description of the method, we give various pedagogical examples, showcase its practical applications to molecular systems, and provide an alternative formulation of the method in terms of boundary value problems.Show more