Fundamental method and its hardware implementation for the generic prediction and analysis of multiple scattering of waves in particulate composites

A method of predicting physical attributes of a highly concentrated composite of particulate phases with known attributes included in a continuous phase with known attributes, in their interaction with acoustic waves, electromagnetic waves, or elastic waves, the method comprising:

• statistically describing through a probability density function an exciting field, a scattered field, and an incident field in said highly concentrated composite by averaging said exciting field, said scattered field, and said incident field throughout all possible spatial distributions of particles and all possible distributions of particle attributes;
• expressing deterministically the relation between the exciting field and the scattered field around a particle with mathematical formalism for all acoustic, electromagnetic, and elastic fields;
• statistically describing through a probability density function local spatial and attribute correlations between particles;
• expressing the exciting field around a fixed particle in terms of the incident field and the scattered field produced by the rest of the particles;
• averaging throughout all possible particle attribute distributions of the said fixed particle to thereby arrive to a set of integral equations relating said exciting field, said scattered field, and said incident field around all particles, wherein each integral equation comprises multiple integrals;
• calculating said integrals in the set of integral equations and specifying the operating conditions to thereby arrive to a finite set of homogeneous equations in said exciting field, said scattered field, and said incident field;
• finding a complex root for a determinant of said integral equations thereby to determine an expected propagation constant for said highly concentrated composite;
• calculating expected values of said physical attributes of said composite from said expected propagation constant and the known attributes of said particulate phases and said continuous phase;
• and
• displaying one or more of the expected values of said physical attributes of said composite;
• and
• utilizing one or more of the expected values of said physical attributes to evaluate the highly concentrated composite.

An apparatus for enabling a human operator to conduct complex simulation, parametric studies, analysis and synthesis of systems in which there exists interaction between acoustic waves, electromagnetic waves, or elastic waves and a composite of particulate phases included in a continuous phase, with physical attributes, comprising:

• a general-purpose computer;
• data-carrier media to store, distribute, and install software and experimental data into said computer;
• predicting means, in combination with said computer and said carrier media, for predicting the physical attributes of said composite from a knowledge of the physical attributes of said particulate phases and said continuous phase, using a mathematical model, to thereby obtain predictions that can be contrasted with actual experimental values;
• inverting means, in combination with said computer and carrier media, for inverting said mathematical model whereby a selected subset of said physical attributes of said particulate phases, said continuous phase, and said composite can be estimated from the knowledge of the rest of said physical attributes of said particulate phases, said continuous phase, and said composite, to thereby obtain particle size distribution, concentration, and other said selected physical attributes;
• measuring means to measure the particle size distribution, concentration, and other said selected physical attributes of said constituent phases of the composite by analyzing experimental raw data produced by commercially available spectrometers;
• means for connecting said computer to the commercially available spectrometers;
• and
• means for displaying the measured particle size distribution, concentration, and other said selected physical attributes of said constituent phases of the composite on a graphical interface;
• and
• utilizing the measured particle size distribution, concentration, and other said selected physical attributes to evaluate the composite of particulate phases included in a continuous phase.