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Nature of the Equations

  • Donald A. Drew
  • Stephen L. Passman
Part of the Applied Mathematical Sciences book series (AMS, volume 135)

Abstract

It should be recognized that any system of equations that is expected to describe the behavior of a physical system is a model, and will, at best, describe the subset of phenomena that falls under the limitations of the model. These limitations are often unwritten and, unfortunately, are often unrecognized As an example in a classi­cal context, the equations of (linear) elasticity provide an excellent description of a large body of phenomena. However, the model fails to describe such com­mon phenomena as permanent bending, crack propagation, and shear bands. For dispersed multicomponent flows, if the initial conditions, or the evolving fields, predict a high concentration of dispersed phase units in some region, we must consider the likely possibility that the predictions are not valid. In this situation, it is sometimes difficult to decide whether the model is incorrect, or whether the solution method led to an approximation that is invalid. Thus, we consider some general properties of the equations in order to understand the behavior in more complicated situations.

Keywords

Shear Band Reynolds Stress Lift Force Pressure Force Disperse Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Donald A. Drew
    • 1
  • Stephen L. Passman
    • 2
  1. 1.Department of Mathematical ScienceRensselaer Polytechnic InstituteTroyUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA

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