Interdisciplinary applications of mathematical modeling

Abstract

We demonstrate applications of numerical integration and visualization algorithms in diverse fields including psychological modeling (biometrics); in high energy physics for the study of collisions of elementary particles; and in medical physics for regulating the dosage of proton beam radiation therapy. We discuss the problems and solution methods, as supported by numerical results.

Dimensional recursion for multivariate adaptive integration

“…. , ) for the computation of loop integrals in high energy physics, e.g., in [1,2,3,4,5], and for other mathematical modeling problems in [6], where the focus was on the applications and the interface problem was not addressed. The technique is implemented recursively using the lower-dimensional code across successive groups of dimensions.…”