Pde models

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  • This Second Edition of the go-to reference combines the classical analysis and modern applications of applied mathematics for chemical engineers. The book introduces traditional techniques for solving ordinary differential equations (ODEs), adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions. It also includes analytical methods to deal with important classes of finite-difference equations. The last half discusses numerical solution techniques and partial differential equations (PDEs). The read...

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  • The following chapters contain core material supported by pen and paper exercises together with computer-based exercises where appropriate. In addition there are web links to: worked solutions, computer codes, audio-visual presentations, case studies, further reading. Codes are written using Scilab (a Matlab clone, downloadable for free from http://www.scilab.org/) and also Matlab.

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  • Solving PDEs generally means you must take the time to set up the underlying equations, material properties, and boundary conditions for a given problem. COMSOL Multiphysics, however, relieves you of much of this work. The package provides a number of application modes that consist of predefined templates and user interfaces already set up with equations and variables for specific areas of physics. Special properties allow the selection of, for instance, analysis type and model formulations.

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  • The CIME-EMS Summer School in applied mathematics on “Multiscale and Adaptivity:Modeling, Numerics and Applications” was held in Cetraro (Italy) from July 6 to 11, 2009. This course has focused on mathematical methods for systems that involve multiple length/time scales and multiple physics. The complexity of the structure of these systems requires suitable mathematical and computational tools. In addition, mathematics provides an effective approach toward devising computational strategies for handling multiple scales and multiple physics.

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  • The dynamics of flexible mechanical systems that require vibration reduction are usually mathematically represented by partial differential equations (PDEs). Specifically, flexible systems are modeled by a PDE that is satisfied over all points within a domain and a set of boundary conditions. These static or dynamic boundary conditions must be satisfied at the points bounding the domain. Traditionally, PDE-based models for flexible systems have been discretized via modal analysis in order to...

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  • 16 Vibration Reduction via the Boundary Control Method 16.1 16.2 16.3 Siddharth P. Nagarkatti Lucent Technologies Introduction Cantilevered Beam System Model • Model-Based Boundary Control Law • Experimental Trials Axially Moving Web System Model • Model-Based Boundary Control Law • Experimental Trials 16.4 16.5 Flexible Link Robot Arm System Model • Model-Based Boundary Control Law • Experimental Trials Darren M. Dawson Clemson University Summary 16.

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  • Partial differential equations (PDEs) are very important in modelling as their solutions unlock the secrets to a range of important phenomena in engineering and physics. The PDE known as the wave equation models sound waves, light waves and water waves. It arises in fields such as acoustics, electromagnetics and fluid dynamics.

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  • Wavelets in Nonlinear Semiconductor Devices Semiconductor device behavior can be described by a system of coupled partial differential equations (PDEs) with associated boundary conditions, requiring the conservation of charge and energy. In physics one is more interested in the quantities of charge concentration, average velocity, and mean energy, for example. From an engineering standpoint, potential, fields, current, and I -V curves are the desired parameters.

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