Materials Characterisation Vi: Computational Methods And Experiments vi

Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2.

Microcirculation is a key area of interest within the realms of biology and medicine. As a vital discipline, microcirculatory biology forms a significant part of established medical fields like cardiovascular medicine and oncology, and is increasingly relevant in emerging fields such as neuroscience. With its multifaceted nature, the study of microcirculation has evolved from basic observations and experiments to embrace cutting-edge imaging technologies, quantitative methods, and the power of data science. This volume brings together a series of insightful chapters that highlight the latest trends in modeling microcirculation. It casts a spotlight on the vital role of microcirculation in brain function modeling and the innovative applications of microvascular models in oncology. Readers will be introduced to state-of-the-art methodologies of microcirculation modeling. A key focus is on mixed-dimensional models, mathematical methods adept at describing complex interactions within lower dimensional manifolds. Each chapter thoughtfully navigates the mathematical, computational, and practical challenges of these approaches, underscoring their effectiveness in capturing the essence of microcirculation. This book offers a window into the latest advancements and methodologies that are shaping the future of this vital field.

This book includes selected, peer-reviewed contributions from the 2018 International Conference on “Physics and Mechanics of New Materials and Their Applications”, PHENMA 2018, held in Busan, South Korea, 9–11 August 2018. Focusing on manufacturing techniques, physics, mechanics, and applications of modern materials with special properties, it covers a broad spectrum of nanomaterials and structures, ferroelectrics and ferromagnetics, and other advanced materials and composites. The authors discuss approaches and methods in nanotechnology; newly developed, environmentally friendly piezoelectric techniques; and physical and mechanical studies of the microstructural and other properties of materials.

The present book contains the 20 articles accepted and published in the Special Issue "Computational Methods and Applications for Numerical Analysis" of the MDPI "Mathematics" journal, which surround the theory, algorithms, programming, software, numerical simulation, and/or novel applications of computational methods to solve problems in engineering, science, and other disciplines related to computations. These topics include finite element methods, finite difference methods, meshless/meshfree methods, physics-informed neural networks, interpolation, approximation, optimization, numerical methods for ordinary/partial differential equations, etc. Their applications include crack propagation, acoustic analysis, elastodynamic analysis, free vibration analysis, structure and topology optimization, fractional equations, eigenvalue problems, inverse problems, etc.

This book includes selected, peer-reviewed contributions from the 2018 International Conference on “Physics and Mechanics of New Materials and Their Applications”, PHENMA 2018, held in Busan, South Korea, 9–11 August 2018. Focusing on manufacturing techniques, physics, mechanics, and applications of modern materials with special properties, it covers a broad spectrum of nanomaterials and structures, ferroelectrics and ferromagnetics, and other advanced materials and composites. The authors discuss approaches and methods in nanotechnology; newly developed, environmentally friendly piezoelectric techniques; and physical and mechanical studies of the microstructural and other properties of materials.

This book includes selected, peer-reviewed contributions from the 2018 International Conference on “Physics and Mechanics of New Materials and Their Applications”, PHENMA 2018, held in Busan, South Korea, 9–11 August 2018. Focusing on manufacturing techniques, physics, mechanics, and applications of modern materials with special properties, it covers a broad spectrum of nanomaterials and structures, ferroelectrics and ferromagnetics, and other advanced materials and composites. The authors discuss approaches and methods in nanotechnology; newly developed, environmentally friendly piezoelectric techniques; and physical and mechanical studies of the microstructural and other properties of materials.