The Physics Behind Nanotechnology Mathematical Modelling

Nanotechnology is a multidisciplinary field that involves the manipulation and control of matter at the nanoscale, typically ranging from 1 to 100 nanometers. At this scale, the properties of materials can significantly differ from their bulk counterparts, leading to unique and enhanced functionalities. The physics behind nanotechnology encompasses various principles and phenomena that govern the behavior of matter at the nanoscale. In this book, we can see how these principles help explain phenomena related to heat transfer, phase transitions, and fluctuations at the nanoscale. Understanding these principles is crucial for designing and optimizing nanoscale devices and systems. One of the fundamental concepts in nanotechnology is quantum mechanics. Quantum mechanics describes the behavior of particles at the atomic and subatomic levels. It provides a framework for understanding phenomena such as wave-particle duality, quantization of energy levels, and tunneling. In nanotechnology, quantum mechanics plays a crucial role in explaining the electronic properties of nanomaterials. Mathematical modelling plays a vital role in understanding and predicting the behavior of nanoscale systems. It provides a quantitative framework for describing complex phenomena and optimizing device performance. Mathematical models in nanotechnology often involve differential equations, statistical methods, and computational simulations.It is crucial for understanding the mechanical properties of nanomaterials. Models based on continuum mechanics, such as elasticity theory and plasticity theory, can predict the behavior of nanomaterials under different loading conditions. These models help in designing materials with desired mechanical properties and optimizing their performance. Mathematical models also aid in the design and optimization of nanoscale devices such as sensors, transistors, and solar cells. By simulating device behavior using mathematical models, researchers can optimize device parameters to achieve desired performance characteristics.

Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical–physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way.

This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.

Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical–physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way.

Computational Multiscale Modeling of Multiphase Nanosystems: Theory and Applications presents a systematic description of the theory of multiscale modeling of nanotechnology applications in various fields of science and technology. The problems of computing nanoscale systems at different structural scales are defined, and algorithms are given for their numerical solutions by the quantum/continuum mechanics, molecular dynamics, and mesodynamics methods. Emphasis is given to the processes of the formation, movement, and interaction of nanoparticles; the formation of nanocomposites; and the processes accompanying the application of nanocomposites. The book concentrates on different types of nanosystems: solid, liquid, gaseous, and multi-phase, consisting of various elements interacting with each other, and with other elements of the nanosystem and with the environment. The book includes a large number of examples of numerical modeling of nanosystems. The valuable information presented here will be useful to engineers, researchers, and postgraduate students engaged in the design and research in the field of nanotechnology.

This new book focuses on nanomaterial development as well as investigations of combustion and explosion processes. It presents valuable information on the modeling of processes and on quantum chemical calculations and leading-edge research from around the world in this dynamic field, focusing on concepts above formal experimental techniques and theoretical methods of chemical physics for micro- and nanotechnologies. Also presented are non-linear kinetic appearances and their possible applications.

This book is devoted to researchers and teachers, as well as graduate students, undergraduates and bachelors in engineering mechanics, nano-mechanics, nanomaterials, nanostructures and applied mathematics. It presents a collection of the latest developments in the field of nonlinear (chaotic) dynamics of mass distributed-parameter nanomechanical structures, providing a rigorous and comprehensive study of modeling nonlinear phenomena. It is written in a unique pedagogical style particularly suitable for independent study and self-education. In addition, the book achieves a good balance between Western and Eastern extensive studies of the mathematical problems of nonlinear vibrations of structural members.

Modelling and Mechanics of Carbon-based Nanostructured Materials sets out the principles of applied mathematical modeling in the topical area of nanotechnology. It is purposely designed to be self-contained, giving readers all the necessary modeling principles required for working with nanostructures. The unique physical properties observed at the nanoscale are often counterintuitive, sometimes astounding researchers and thus driving numerous investigations into their special properties and potential applications. Typically, existing research has been conducted through experimental studies and molecular dynamics simulations. This book goes beyond that to provide new avenues for study and review. Explores how modeling and mechanical principles are applied to better understand the behavior of carbon nanomaterials Clearly explains important models, such as the Lennard-Jones potential, in a carbon nanomaterials context Includes worked examples and exercises to help readers reinforce what they have read