A Dictionary of art quotations - Ian Crofton

Mathematical models stated as systems of partial di
erential equations (PDEs) are

broadly used in biology, chemistry, physics and medicine (physiology). These models

describe the spatial and temporial variations of the problem system dependent variables,

such as temperature, chemical and biochemical concentrations and cell densities, as a

function of space and time (spatiotemporal distributions).

For a complete PDE model, initial conditions (ICs) specifying how the problem system

starts and boundary conditions (BCs) specifying how the system is de ned at its spatial

boundaries, must also be included for a well-posed PDE model.

In this book, PDE models are considered for which the physical boundaries move with

time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis,

the plaque formation on the arterial wall moves inward, thereby restricting blood ow

with serious consequences such as stroke and myocardial infarction (heart attack).

These two examples are considered as applications of the reported moving boundary

PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of

documented routines coded in R, a quality, open-source scienti c programming system.

The routines are provided as a download so that the teacher/analyst/researcher can

use MFPDE models without having to rst study numerical methods and computer

programming