Maple

This project aims to investigate the physical and biological processes that initiate sap flow in maple trees during early spring when maple sap is harvested. Our study will be centered around developing a mathematical model that captures both sap flow and heat transport in the porous wood tissue, and then investigating solutions using a combination of analytical and numerical techniques.

The theoretical and practical aspects of manipulating mathematical expressions on computers are usually referred to as computer algebra or symbolic computation. In this field, calculations are designed to yield exact and complete results, by opposition to numerical analysis which is meant to handle approximate values, potentially producing incomplete results. Exactness and completeness have some significant computational overhead. Computer algebra software is highly demanding in CPU time and memory.

Computer algebra systems such as Maple compute using mathematical formulae as well as numbers, mechanizing the mathematics used in education and research labs. This project focuses on the design and implementation of algorithms for these systems. Emphasis is placed on efficiency that allows large and complex problems of the type encountered in industrial settings to be solved. In the past year the team has made major advances in the core tools that are needed to solve these complex problems.