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 nanomaterialsClearly explains important models, such as the Lennard-Jones potential, in a carbon nanomaterials contextIncludes worked examples and exercises to help readers reinforce what they have read

Modelling and Mechanics of Carbon-based Nanostructured Materials (Micro and Nano Technologies)

Science & Math

Hill, James M.

Baowan, Duangkamon

Cox, Barry J

Hilder, Tamsyn A

Thamwattana, Ngamta

Physics

William Andrew

Solution of Differential Equations by Means of One-parameter Groups (Research Notes in Mathematics)

Mathematics

Pitman Advanced Pub. Program

<p>One of the most important partial differential equations in applied mathematics is the heat or diffusion equation. Its importance in the modeling of heat conduction, diffusional processes, and flow through a porous medium is well known. It arises from a probabilistic framework and emerges as the simplest approximation to bulk processes governed at the microscopic level by random spatial variations. Heat Conduction provides a balanced account of solutions and results for the heat equation and serves as a modern undergraduate text that reflects the importance of the heat equation in applied mathematics and mathematical modeling. The first two chapters of the book are introductory and summarize the essential elements of heat flow, diffusion, the mathematical formulation, and simple general results. The next two chapters develop exact analytical solutions, obtained by Laplace transforms and Fourier series, for infinite and finite media problems respectively. Other chapters deal with approximate analytical solutions based on the heat-balance integral method, numerical methods for the heat equation, and simple heat conduction moving boundary problems.</p>

Heat Conduction (Electrical Engineering Handbook)

Dewynne, Jeff

CRC-Press

Differential Equations and Group Methods for Scientists and Engineers presents a basic introduction to the technically complex area of invariant one-parameter Lie group methods and their use in solving differential equations. The book features discussions on ordinary differential equations (first, second, and higher order) in addition to partial differential equations (linear and nonlinear). Each chapter contains worked examples with several problems at the end; answers to these problems and hints on how to solve them are found at the back of the book. Students and professionals in mathematics, science, and engineering will find this book indispensable for developing a fundamental understanding of how to use invariant one-parameter group methods to solve differential equations.

Differential Equations and Group Methods for Scientists and Engineers

Mines of Cherry Creek, Ely Range and other Eastern Nevada Districts

Nevada Pubns

Mathematics of Particle-Wave Mechanical Systems

Springer

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Books by Hill, James M.