Computational Modeling By Case Study

Computational Modeling by Case Study

Mathematical models power the modern world; they allow us to design safe buildings, investigate changes to the climate, and study the transmission of diseases through a population. However, all models are uncertain: building contractors deviate from the planned design, humans impact the climate unpredictably, and diseases mutate and change. Modern advances in mathematics and statistics provide us with techniques to understand and quantify these sources of uncertainty, allowing us to predict and design with confidence. This book presents a comprehensive treatment of uncertainty: its conceptual nature, techniques to quantify uncertainty, and numerous examples to illustrate sound approaches. Several case studies are discussed in detail to demonstrate an end-to-end treatment of scientific modeling under uncertainty, including framing the problem, building and assessing a model, and answering meaningful questions. The book illustrates a computational approach with the Python package Grama, presenting fully reproducible examples that students and practitioners can quickly adapt to their own problems.

COMPUTATIONAL MODELING BY CASE STUDY

Computational Modelling of Nanomaterials

Due to their small size and their dependence on very fast phenomena, nanomaterials are ideal systems for computational modelling. This book provides an overview of various nanosystems classified by their dimensions: 0D (nanoparticles, QDs, etc.), 1D (nanowires, nanotubes), 2D (thin films, graphene, etc.), 3D (nanostructured bulk materials, devices). Fractal dimensions, such as nanoparticle agglomerates, percolating films and combinations of materials of different dimensionalities are also covered (e.g. epitaxial decoration of nanowires by nanoparticles, i.e. 0D+1D nanomaterials). For each class, the focus will be on growth, structure, and physical/chemical properties. The book presents a broad range of techniques, including density functional theory, molecular dynamics, non-equilibrium molecular dynamics, finite element modelling (FEM), numerical modelling and meso-scale modelling. The focus is on each method's relevance and suitability for the study of materials and phenomena in the nanoscale. This book is an important resource for understanding the mechanisms behind basic properties of nanomaterials, and the major techniques for computational modelling of nanomaterials. - Explores the major modelling techniques used for different classes of nanomaterial - Assesses the best modelling technique to use for each different type of nanomaterials - Discusses the challenges of using certain modelling techniques with specific nanomaterials