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Online 1. A lattice model of the translational dynamics of nonrotating rigid rods [electronic resource] [2011]
 Tse, Ying Lung.
 2011.
 Description
 Book — 1 online resource.
 Summary

We present a lattice model of oriented, nonrotating, rigid rods in three dimensions with random walk dynamics and an algorithm to simulate the model. We use the ideas of the DoiEdwards (DE) theory, which was originally developed for a system of rods that both translate and rotate in continuous space, to predict the dependence of the translational diffusion constant of the rods in the perpendicular direction, on the (dimensionless) concentration in the semidilute regime. We find that the transnational perpendicular diffusion constant is proportional to the inverse square of the concentration. The theory is based on a `tube model' for the constraints imposed on the motion of a rod by the surrounding rods. Simulations of the model confirm that the scaling predicted by DE ideas and that the nature of the agreement is similar to that for the rotational diffusion constant in the original DE theory. We formulate a quantitative theory for the prefactor in the scaling relationship using only DE ideas, but it predicts a proportionality constant that is much too small. To explain this discrepancy, we modify the DE approach to obtain a more accurate estimate of the average tube radius, and we take into account two effects, called `leakage' and `drift', that are caused by perpendicular motions of rods that are ignored by the original DE theory. The theory of leakage takes into account the fact that the ends of a rod are less effective than the middle of the rod for blocking the motion of nearby rods. The theory of drift takes into account that the tube that any one rod is in can move in the perpendicular direction without changing its structure as a result of the perpendicular motion of the rods that form the tube. With these changes, the theory predicts a prefactor that is in much better agreement with the simulations. The simulations find that, as the concentration is increased, the approach to the limit of DE scaling is slow, and the 2 power in the DE scaling law is never quite achieved even at the highest concentration simulated. We propose a new scaling relationship that explains the deviations from the DE scaling relationship. Finally, we study the self and total densitydensity space time correlation functions for this model and propose a simple theory for the short time behavior of these functions based on a onedimensional twocomponent lattice gas model.
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Online 2. Statistical mechanical basis and algorithms for constructing coarse grained models of molecular liquids and biological structures [electronic resource] [2011]
 Das, Avisek.
 2011.
 Description
 Book — 1 online resource.
 Summary

Computer simulation of condensed phases have been on the forefront of the scientific research in varieties of disciplines including but not limited to chemistry, physics, biophysics and material science. In spite of impressive success, standard computational techniques such as molecular dynamics and Monte Carlo run into serious limitations in the system sizes and temporal durations accessible in simulations when an atomically detailed description of the system is employed, for any given choice of computational technology. One obvious way of surmounting this problem is to construct a reduced representation of the original system of interest with the hope that reduction in number of degrees of freedom will cut down the computational cost at the same time retaining some essential features. This approach, known as coarsegrained modelling, has attracted a great deal of attention in recent years and a varieties of methods have been reported in the literature. The multiscale coarsegraining (MSCG) method is a method for determining the effective potential energy function for a coarsegrained (CG) model of a system using data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The method has been given a rigorous statistical mechanical basis and the coarsegrained potential obtained using the MSCG method is an approximate variational solution for the exact manybody potential of mean force for the coarsegrained sites. In this thesis we extend the formal theory behind the method to situations that were not considered in the original version, thereby expanding the applicability of the method. We also develop new algorithms for practical implementation of the MSCG method. The algorithmic developments consist of introduction of new basis functions for representing the CG potential energy functions and construction of new numerical techniques for the optimization problem associated with the MSCG method. We apply the MSCG method, with a new set of basis functions, to study the many body potential of mean force among solutes in a simple model of a solution of LennardJones particles. For this model, pairwise additivity of the many body potential of mean force is a very good approximation when the solute concentration is low, and it becomes less accurate for high concentrations, indicating the importance of many body contributions to the coarsegrained potential. We propose and test a version of the MSCG method suitable for the isothermalisobaric ensemble. The method shows how to construct an effective potential energy function for a coarsegrained system that generates the correct volume fluctuations as well as correct distribution functions in the configuration space of the CG sites. We present a new numerical algorithm with automatic basis set selection and noise suppression capabilities for the solution of the MSCG variational problem. We also develop new basis functions that are similar to multiresolution Haar functions and that have the differentiability properties that are appropriate for representing CG potentials. The new method, allows us to construct a large basis set, and the method automatically chooses a subset of the basis that is most important for representing the MSCG potential. It provides regularization to mitigate potential numerical problems in the associated linear least squares calculation, and it provides a way to avoid fitting statistical error. We use this technology to construct a systematic method for including three body terms as well as two body terms in the nonbonded part of the CG potential energy. Inclusion of three body terms can lead to significant improvement in the accuracy of CG potentials and hence of CG simulations as shown by the test calculations on two very different model systems. We construct basis functions for representing the CG potential energy functions for molecular systems. We also discuss the problem arising from insufficient sampling of certain parts of the atomistic configuration space and develop methods for surmounting this problem that require very little human intervention. We test our algorithms on a simple but nontrivial test problem that involves constructing coarse grained models of liquid hexane.
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3781 2011 D  Inlibrary use 
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