  Physical strands or sheets that can be modelled as curves or surfaces
embedded in three dimensions are ubiquitous in nature, and are of fundamental
importance in mathematics, physics, biology and engineering. Often the physical
interpretation dictates that self-avoidance should be enforced in the continuum
model, i.e. finite energy configurations should not self-intersect. Current
continuum models with self-avoidance frequently employ pairwise repulsive
potentials, which are of necessity singular. Moreover the potentials do not
have an intrinsic length scale appropriate for modelling the finite thickness
of the physical systems. Here we develop a framework for modelling
self-avoiding strands and sheets which avoids singularities, and which provides
a way to introduce a thickness length scale. In our approach pairwise
interaction potentials are replaced by many-body potentials involving three or
more points, and the radii of certain associated circles or spheres.
Self-interaction energies based on these many-body potentials can be used to
describe the statistical mechanics of self-interacting strands and sheets of
finite thickness.
