Applied dimensional analysis and modeling

  title={Applied dimensional analysis and modeling},
  author={Thomas Szirte and Sheldon I. Green},
Chapter 1: Mathematical Preliminaries by Pal Rozsa Chapter 2: Formats and Classification Chapter 3: Dimensional Systems Chapter 4: Transformation of Dimensions Chapter 5: Arithmetic of Dimensions Chapter 6: Dimensional Homogeneity Chapter 7: Structure of Physical Relations Chapter 8: Systematic Determination of Complete Set of Products of Variables Chapter 9: Transformations Chapter 10: Number of Sets of Dimensionless Products of Variables Chapter 11: Relevancy of Variables Chapter 12: Economy… 
Static Dimensional Analysis
Science and engineering mathematical formulas are based on proportionality, principle of superposition, and dimensional homogeneity. This chapter reviews the development of the concept of dimensions
A graphical and topological combination is presented to illustrate the applicability of dimensional analysis as a state equation generation tool and acts as a learning instrument where complex engineering equations are derived and interpreted through visual perception similar to a block diagram or flow chart.
Dimensional Analysis Using Toric Ideals: Primitive Invariants
A selection of computer algebra packages are used to show the considerable ease with which both a simple basis and a Graver basis can be found within the use of toric ideal theory from algebraic geometry.
Dimensional Analysis and Its Applications in Statistics
Dimensional analysis (DA) is a well-developed, widely-employed methodology in the physical and engineering sciences. The application of dimensional analysis in statistics leads to three advantages:
Dimensional analysis and qualitative methods in problem solving
We show that the underlying mathematical structure of dimensional analysis (DA), in the qualitative methods in problem-solving context, is the algebra of the affine spaces. In particular, we show
Characteristic quantities and dimensional analysis
Phenomena in the physical sciences are described with quantities that have a numerical value and a dimension, i.e., a physical unit. Dimensional analysis is a powerful aspect of modeling and
A review of dimensional assessment for statistics and probability
Dimensional awareness contributes to a broader system-level foundation for utilizing statistics and probability concepts as tools in applied scenarios and is explored in this article.
Dimensional Analysis of Matrices State-Space Models and Dimensionless Units [Lecture Notes]
Physical dimensions and units, such as mass (kg), length (m), time (s), and charge (C), provide the link between mathematics and the physical world. It is well known that careful attention to
Reduction of Non-Monomial Basis in the Dimensional Analysis of a Dynamical System
Dimensional Analysis (DA) is a tool often used to relate models and specimens to the actual product or system based on the hypothesis that the two regimes follow the same physical laws and are hence
Model order reduction using neural network principal component analysis and generalized dimensional analysis
A novel computational intelligence technique to generate concise neural network models for distributed dynamic systems based on artificial neural network architectures that incorporate linear and nonlinear principal component analysis, combined with generalized dimensional analysis.