Water plays a critical role in the function and structure of biological systems. Current techniques to study biologically relevant events that span many length and time scales are limited by the prohibitive computational cost of including accurate effects from the aqueous environment. The aim of this work is to expand the reach of current molecular dynamics techniques by reducing the computational cost for achieving an accurate description of water and its effects on biomolecular systems. This work builds from the assumption that the “local” effect of water (e.g. the local orientational preferences and hydrogen bonding) can be effectively modelled considering only the atomistic detail in a very limited region. A recent adaptive resolution simulation technique (AdResS) has been developed to practically apply this idea; in this work it will be extended to systems of simple hydrophobic solutes to determine a characteristic length for which thermodynamic, structural, and dynamic properties are preserved near the solute. This characteristic length can then be used for simulation of biomolecular systems, specifically those involving protein dynamics in water. Before this can be done, current coarse grain models must be adapted to couple with a coarse grain model of water. This thesis is organized in to five chapters. The first will give an overview of water, and the current methodologies used to simulate water in biological systems. The second chapter will describe the AdResS technique and its application to simple test systems. The third chapter will show that this method can be used to accurately describe hydrophobic solutes in water. The fourth chapter describes the use of coarse grain models as a starting point for targeted search with all-atom models. The final chapter will describe attempts to couple a coarse grain model of a protein with a single-site model for water, and it’s implications for future multi-resolution studies.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.