Atomistic-to-continuum coupling

Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale schemes that combine the accuracy of atomistic models with the efficiency of continuum elasticity. They are increasingly being utilized in materials science to study the fundamental mechanisms of material failure such as crack propagation and plasticity, which are governed by the interaction between crystal defects and long-range elastic fields. In the construction of a/c coupling methods, various approximation errors are committed. A rigorous numerical analysis approach that classifies and quantifies these errors can give confidence in the simulation results, as well as enable optimization of the numerical methods for accuracy and computational cost. In this article, we present such a numerical analysis framework, which is inspired by recent research activity

Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane

We give an analysis of the stability and displacement error for linear and circular atomistic chains in the plane when the atomistic energy is approximated by the Cauchy-Born continuum energy and by the quasi-nonlocal atomistic-to-continuum coupling energy. We consider atomistic energies that include Lennard-Jones type nearest neighbor and next nearest neighbor pair-potential interactions. Previous analyses for linear chains have shown that the Cauchy-Born and quasi-nonlocal approximations reproduce (up to the order of the lattice spacing) the atomistic lattice stability for perturbations that are constrained to the line of the chain. However, we show that the Cauchy-Born and quasi-nonlocal approximations give a finite increase for the lattice stability of a linear or circular chain under compression when general perturbations in the plane are allowed. We also analyze the increase of the lattice stability under compression when pair-potential energies are augmented by bond-angle energies. Our estimates of the largest strain for lattice stability (the critical strain) are sharp (exact up to the order of the lattice scale). We then use these stability estimates and modeling error estimates for the linearized Cauchy-Born and quasi-nonlocal energies to give an optimal order (in the lattice scale) {\em a priori} error analysis for the approximation of the atomistic strain in $\ell^2_\epsilon$ due to an external force.Comment: 27 pages, 0 figure

Adaptive Multiscale Coupling Methods of Molecular Mechanics based on a Unified Framework of a Posteriori Error Estimates

Multiscale coupling methods are significant methodologies for the modeling and simulation of materials with defects, intending to achieve the (quasi-)optimal balance of accuracy and efficiency. The a posteriori analysis and corresponding adaptive algorithms play a crucial role in the efficient implementation of multiscale coupling methods. This paper proposes a unified framework for residual-based a posteriori error estimates that can be applied to general consistent multiscale coupling methods. In particular, we prove that the error estimator based on the residual force can provide the upper bound of the true approximation error. As prototypical examples, we present a variety of adaptive computations based on this reliable error estimator for the blended atomistic-to-continuum (a/c) coupling methods, including the energy-based blended quasi-continuum (BQCE), the force-based blended quasi-continuum (BQCF) and the recently developed blended ghost force correction (BGFC) methods. We develop a coarse-grained technique for the efficient evaluation of the error estimator. A robust adaptive algorithm is therefore proposed and validated with different types of crystalline defects, some of which are not considered in previous related literature on the adaptive a/c coupling methods. The results demonstrate that the adaptive algorithm leads to the same optimal convergence rate of the error as the a priori error estimate, but with considerable computational efficiency. This study provides valuable insights into the design and implementation of adaptive multiscale methods, and represents a significant contribution to the literature on a/c coupling methods

A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field. © 2020 The Authors

Advances in Vibration Analysis Research

Vibrations are extremely important in all areas of human activities, for all sciences, technologies and industrial applications. Sometimes these Vibrations are useful but other times they are undesirable. In any case, understanding and analysis of vibrations are crucial. This book reports on the state of the art research and development findings on this very broad matter through 22 original and innovative research studies exhibiting various investigation directions. The present book is a result of contributions of experts from international scientific community working in different aspects of vibration analysis. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area

Ensemble methods in computational protein and ligand design : applications to the Fc[gamma] immunoglobulin, HIV-1 protease, and ketol-acid reductoisomerase systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2012.In title on title-page, "[gamma]" appears as the lower-case Greek letter. Cataloged from PDF version of thesis.Includes bibliographical references (p. 170-192).This thesis explores the use of ensemble, free energy models in the study and design of molecular, biochemical systems. We use physics based computational models to analyze the molecular basis of binding affinity in the context of protein-protein and protein-ligand binding as well as reaction rate enhancement in enzyme catalysis. First, we evaluate the solvent screened energetics of immunoglobulin G (IgG):Fc[gamma] receptor binding using molecular mechanics, Poisson-Boltzmann surface area (MMPBSA) models. We assess the role IgG1 linked glycans play in binding to human Fc[gamma]-III and computationally evaluate experimentally designed Fe mutations that recover binding affinity in the absence of glycosylation. Using the insight gained from this study, we developed novel murine IgG variants with engineered Fc[gamma] receptor binding patterns via the computational design and experimental validation of Fc mutations that are predicted to knock out binding to Fc[gamma]R-IV. Our design and analysis highlight the importance of solvent screened electrostatic interactions and electrostatic complementarity in protein-protein binding. Second, we develop novel, ensemble methods to measure configurational free energy and entropy changes in protein-ligand binding and use it to predict the relative binding affinity of a series of previously designed HIV-1 protease inhibitors. We find that using configurational free energies to evaluate inhibitor efficacy significantly improves relative ranking of inhibitors over traditional, single-point energy metrics, but that only a relatively small number of low energy configurations are necessary to capture the ensemble effect. Finally, we present a joint study of the redesign and dynamic analysis of ketol-acid isomeroreductase (KARI). We first develop and apply a novel, end-point method to rationally design enzyme variants that reduce the free energy of activation, and present the computational and experimental analysis of a series of designed KARI mutants. Our analysis reveals that this transition-state theory based approach is effective at reducing the enthalpy of activation, but also increases entropic activation penalties that ultimately overpower the enthalpic gains. A dynamic analysis of these KARI variants is also presented, in which the transition path ensemble is explored using transition path sampling. We find that this ensemble approach is better able to predict relative enzyme activities and suggests a conserved, dynamic mechanism for catalysis. The results and analysis presented herein demonstrate novel, computational approaches to account for ensemble effects in the study and design of effective biomolecules.by Nathaniel White Silver.Ph.D

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version