"Mathematica's ability to handle arbitrary precision has enabled me to use Mathematica where other languages and programs have failed. In my calculations, I often encounter exponentials of large negative numbers. The limited numerical precision of the Fortran language would substitute zeros in place of these numbers, so I would often obtain overflow errors. With Mathematica, my problem is solved."

A Bottle of Soap, A Bar of Shampoo?

Who ever heard of a bar of Suave shampoo? No one, we hope! That's because the scientists at Helene Curtis make sure it flows out of the bottle with the precise consistency we all expect from our shampoo. Michelle Long is one of the researchers who use Mathematica to understand why shampoos, conditioners, and other personal care products work the way they do.

Long performs probability calculations with Mathematica to predict the phase behavior and flow of various ingredients, combined at various temperatures. Soap molecules pack together to carry away dirt and oil. The shape and size of these aggregates depend on the concentration of this surfactant and affect whether the end result is a fluid or solid, or somewhere in between.

"Mathematica helps us explain these thermodynamic phenomena sometimes after the lab staff produce a successful combination during formulation," explains Long. Why Mathematica? "Our research is quantitative, and involves iterative calculations that require a high level of precision."

Key features of Mathematica used:

• Numeric--arbitrary precision, fitting routines (FindRoot, FindMinimum, Fit), all trigonometric functions
  
• Graphic--3D plots, ListPlot, MultipleListPlot
  
• Programming--routines that read input data and output results to Fortran ("The numerical functions and packages that are included in Mathematica are very simple to understand and incorporate into my routine," says Long. "Also the structure and language of Mathematica allow a single line to contain commands that would have been 10 or more lines in a Fortran program. The concise commands greatly enhance the readability of my programs.")
• Notebook
• MathLink for Excel and Mathematica