### Table of Contents

Preface

1. Spatial Structure of Random Dispersion of Equal Spheres in One-Dimension

1.1 Discrete System

1.2 Continuous System

2. Spatial Structure of Random Dispersion of Equal Spheres in Two-Dimension

2.1 Outline of Computer Simulation Experiments

2.2 Structure of Random Dispersion

3. Preliminary Mathematics

3.1 Laplace Transform and Inversion Formula

3.2 Fourier Transform and Spectral Density

4. Radial Distribution Function

4.1 RDF Definition

4.2 Ornstein-Zernike Equation

4.3 Solving Procedure

4.4 Analytic Solution by Percus-Yevick Approximation

A. xg_{n}(x)

B. state at contact

4.5 Multi-Sized Particle System

4.6 Binary-Sized Particle System

4.6.1 Influence by the Presence of a Vessel Wall

4.6.2 Pore Size Distribution in Random Assemblies of Equal Spheres

4.6.3 Size Distribution of Aggregates Inherent in Random Dispersion of Equal Spheres

5. Sample Size for Measuring Particle Concentration

5.1 Distribution Functions

5.2 Sample Size of Measurement

6. Introduction to Statistical Thermodynamics

6.1 Quantum States of Steady Thermal Vibration

6.2 Analytical Dynamics and Generalized Coordinates

6.3 Stationary Distribution and Partition Function

6.4 Number Density and Distribution Function

6.5 Equation of State for Gases

7. Structural Comparison of Molecular System and particle Assemblies: Particle Morphology

7.1 Random Packing

7.2 Random Dispersion

7.3 Molecular System and Particle Assemblies

Closing Remarks