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This book addresses key conceptual issues relating to the modern scientific and engineering use of computer simulations. It analyses a broad set of questions, from the nature of computer simulations to their epistemological power, including the many scientific, social and ethics implications of using computer simulations. The book is written in an easily accessible narrative, one that weaves together philosophical questions and scientific technicalities. It will thus appeal equally to all academic scientists, engineers, and researchers in industry interested in questions (and conceivable answers) related to the general practice of computer simulations.
A description of computer programs for simulating phenomena in hydrodynamics, gas dynamics, and elastic plastic flow in one, two, and three dimensions. The text covers Maxwell's equations, and thermal and radiation diffusion, while the numerical procedures described permit the exact conservation of physical properties in the solutions of the fundamental laws of mechanics. The author also treats materials, including the use of simulation programs to predict material behavior.
Computer simulation is an essential tool in studying the chemistry and physics of liquids. Simulations allow us to develop models and to test them against experimental data. This book is an introduction and practical guide to the molecular dynamics and Monte Carlo methods.
Computer simulation of systems has become an important tool in scientific research and engineering design, including the simulation of systems through the motion of their constituent particles. Important examples of this are the motion of stars in galaxies, ions in hot gas plasmas, electrons in semiconductor devices, and atoms in solids and liquids. The behavior of the system is studied by programming into the computer a model of the system and then performing experiments with this model. New scientific insight is obtained by observing such computer experiments, often for controlled conditions that are not accessible in the laboratory. Computer Simulation using Particles deals with the simulation of systems by following the motion of their constituent particles. This book provides an introduction to simulation using particles based on the NGP, CIC, and P3M algorithms and the programming principles that assist with the preparations of large simulation programs based on the OLYMPUS methodology. It also includes case study examples in the fields of astrophysics, plasmas, semiconductors, and ionic solids as well as more detailed mathematical treatment of the models, such as their errors, dispersion, and optimization. This resource will help you understand how engineering design can be assisted by the ability to predict performance using the computer model before embarking on costly and time-consuming manufacture.
Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.
Proceedings of the NATO Advanced Study Institute, Albena, Bulgaria, from 9 to 20 September 2002
Computer simulation was first pioneered as a scientific tool in meteorology and nuclear physics in the period following World War II, but it has grown rapidly to become indispensible in a wide variety of scientific disciplines, including astrophysics, high-energy physics, climate science, engineering, ecology, and economics. Digital computer simulation helps study phenomena of great complexity, but how much do we know about the limits and possibilities of this new scientific practice? How do simulations compare to traditional experiments? And are they reliable? Eric Winsberg seeks to answer these questions in Science in the Age of Computer Simulation. Scrutinizing these issue with a philosophical lens, Winsberg explores the impact of simulation on such issues as the nature of scientific evidence; the role of values in science; the nature and role of fictions in science; and the relationship between simulation and experiment, theories and data, and theories at different levels of description. Science in the Age of Computer Simulation will transform many of the core issues in philosophy of science, as well as our basic understanding of the role of the digital computer in the sciences.
This book is written to introduce computer simulations to undergraduate college students, freshmen to seniors, in STEM fields. The book starts with concepts from Basic Mathematics: Geometry, Algebra and Calculus, Properties of Elementary Functions (Polynomials, Exponential, Hyperbolic and Trigonometric Functions) are studied and simple differential equations representing these functions are derived. Numerical approximations of first and second order differential equations are studied in terms of finite differences on uniform grids. Computer solutions are obtained via recursive relations or solutions of simultaneous algebraic equations. Comparisons with the exact solutions (known a priori) allow the calculations of the error due to discretization. After the students build confidence in this approach, more problems where the solutions are not known a priori are tackled with applications in many fields. Next, the book gradually addresses linear differential equations with variable coefficients and nonlinear differential equations, including problems of bifurcation and chaos.Applications in Dynamics, Solid Mechanics, Fluid Mechanics, Heat Transfer, Chemical Reactions, and Combustion are included. Biographies of 50 pioneering mathematicians and scientists who contributed to the materials of the book are briefly sketched, to shed light on the history of these STEM fields.Finally, the main concepts discussed in the book, are summarized to make sure that the students do not miss any of them. Also, references for further readings are given for interested readers.
The study of natural phenomena using computer simulation is a major new research tool in the physical, chemical, biological and social sciences. It is useful for studying simple systems, and it is essential for the study of complex systems. Using Mathematica, an integrated software environment for scientific programming, numerical analysis and visualization, this book describes computer simulations applicable to a wide range of phenomena.