Mathematical Tools for Changing Scale in the Analysis of Physical Systems
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A01=Anton Leijnse
A01=Cheryl A. Blain
A01=Randall L. Kolar
A01=William G. Gray
Author_Anton Leijnse
Author_Cheryl A. Blain
Author_Randall L. Kolar
Author_William G. Gray
Averaging Theorems
balance equations
Balance Laws
Category=PBW
Category=PH
Cellular Automata
Channel Axis
continuum mechanics
Control Volume Approach
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eq_isMigrated=2
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Gauss Divergence Theorem
generalized functions
Global Coordinate System
Heaviside Step Function
integral theorems
Integration Theorems
Mass Balance Equation
mathematical tools
Megascopic Scale
Microscopic Coordinates
Microscopic Function
multiphase systems
Orthogonal Unit Vectors
Partial Time Derivative
physical systems
Rev
Reynolds Transport Theorem
spatial scale transformation methods
spatial scales
Surface Integral
tensor analysis
Time Derivative
Total Time Derivative
Transport Theorem
Undergraduate Calculus Courses
Unit Vector
Unit Vector Tangent
vector calculus
Product details
- ISBN 9780849389344
- Weight: 680g
- Dimensions: 178 x 254mm
- Publication Date: 06 Jul 1993
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale.
Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.
Gray, William G.; Leijnse, Anton; Kolar, Randall L.; Blain, Cheryl A.
