Nonlinear Problems of Engineering

Nonlinear Problems of Engineering reviews certain nonlinear problems of engineering. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena.

Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This text then explores nonlinear integral equations, which have long occupied a prominent place in mathematical analysis. Other chapters consider the phenomena associated with essentially divergent small-divisor series, such as may occur in the formal solution of differential equations that represent the oscillations of conservative dynamical systems. This book discusses as well the mechanics of idealized textiles consisting of inextensible filaments. The final chapter deals with the use of the Peaceman-Rachford alternating direction implicit method for solving the finite difference analogs of boundary value problems.

This book is a valuable resource for engineers and mathematicians.

Contenu

Contributors
Foreword
Preface
New Methods in Nonlinear Mechanics
I. Introduction
II. The Comparative Approach
III. Classical Approach
IV. Discussion
V. The New Approach of Invariant Imbedding
VI. Discussion
VII. Variational Processes
VIII. Geodesics
IX. Dynamic Programming and the Calculus of Variations
X. Approximation in Policy Space
XI. Discussion
References
Probability as a Science
On Random Solutions of Nonlinear Integral Equations
Text
References
A Singular Case of Iteration of Analytic Functions: A Contribution to the Small-Divisor Problem
I. The "Center Problem" in the Iteration of Analytic Functions
II. Contexts Leading to Small-Divisor Series
III. Generalities Regarding Iteration of Analytic Functions
IV. Construction of Singular Iterations Zn+1 = f(Zn)
V. Properties of Singular Iterations
References
Networks of Inextensible Cords
I. Introduction
II. Pure Homogeneous Deformation
III. Plane Strain of a Net-Displacement Boundary Conditions
IV. Plane Strain of a Net-Force Boundary Conditions
V. Further Developments
Bibliography
On Integral Operators Generating Stream Functions of Compressible Fluids
Introduction
I. Partial Differential Equations Arising in the Theory of Compressible Fluids
II. The Determination of the Stream Function of a Vortex in the Subsonic Region
III. A Method for Generating Solutions of Equation (1.3.5)
References
Bibliography
Some Problems Concerning Linear Differential Equations Made Nonlinear by Unknown or Moving Boundaries
A. Melting or Solidification
B. Consolidation of an Earth Dam
C. Seepage through a Porous Dam
D. Lubrication in a Journal Bearing, with Oil Cavitation
References
General References
Nonlinear Problems of Combined Conductive-Radiative Heat Transfer
Nomenclature
Introduction
The Single Plate-Type Fin
Radiant Interaction Between Fin and Tube Surfaces
Radiant Interaction Between Fin Surfaces
Radiant Interaction Between Fin and Tube and Between Neighboring Fins
Concluding Remarks
References
Statistical Problems Connected with the Solution of a Nonlinear Partial Differential Equation
I. A Particular Nonlinear Partial Differential Equation and Its Solution by Means of a Geometrical Construction
II. Formulation of a Statistical Problem
III. The Solution of the Auxiliary Differential Equation
Notes
Melting Decelerating Bodies
Introduction
Symbols
Analysis
Results
Concluding Remarks
References
Thermal Radiation Effects on Hypersonic Flow Fields
I. Introduction
II. Fundamentals of Radiant Energy Transfer
III. Fundamental Equations of Radiation Gas Dynamics
IV. Solutions for Radiation Transfer Equation
V. New Parameters of Radiation Gas Dynamics
VI. Wave Motions in Radiation Gas Dynamics
VII. Shock Waves in Radiation Gas Dynamics
VIII. Jet Mixing in Radiation Gas Dynamics
IX. Plane Couette Flow in Radiation Magnetogas Dynamics
References
Mathematical Theory of Compressible Fluids
Introduction
List of Symbols

1. Two-Dimensional Compressible Flow in the Physical Plane
2. Two-Dimensional Compressible Flow in the Hodograph Plane
3. Two-Dimensional Compressible Flow About a Closed Body in a Uniform Subsonic Flow
4. Two-Dimensional Flow through the Sonic Line
   References
   Problems in Nonlinear Nonmechanics
   Introduction
   Information and Communication
   Symbols and Symbolic Structure
   Handicaps and Communication
   Other Observations
   Concluding Remarks
   References
   Nonlinear Problems in Ballistics
   Text
   References
   Alternating Direction Methods for Solving Partial Difference Equations
5. Introduction
6. The Difference Equation
7. The Linear System
8. The Peaceman-Rachford Method
9. The Cummutative Case
10. Laminar Flow Problem
11. Numerical Results and Conclusions
    References
    Subject Index