The study of two-dimensional interfaces and membranes to help understand their properties is an important area of research for many fields of science, including biology (cell membranes), chemistry and chemical physics (reactions at interfaces, cosmetics, medicine), and theoretical physics (condensed matter, particle physics). It is remarkable that the surface behavior of red blood cells in the body can be described by theories very similar to the string theories of particle physics. We aim to produce modules that will bring out the generality of membrane models. They will provide a range of explorations from the biology of life processes through materials to cosmology. We hope to leverage interest in the abstract physics from the more accessible biological contexts.
Simulations of real membranes are designed to probe the underlying microscopic dynamics. In particular, the study of artificial membranes composed of amphiphilic phospholipids (see, for example, [8]) is a lively research field with applications in industry and medicine. For example, such membranes are able to close in on themselves forming spherical vesicles, and may be tailored to open up and release their load when the `correct' physical and chemical conditions are found. In this way, they have potential as drug carriers [9].
In the area of particle physics, string theories can be thought of as theories of random surfaces. Thermal fluctuations in the biological context are then replaced by quantum fluctuations. To illustrate concepts in particle physics, we hope to draw on the common thread with real membranes. However, it is hard to see how we can explain any meaningful particle physics, other than to the high-end of K-12. At present, we are concentrating on real membranes and the biological context in particular.
We consider two classes of membrane: fluid membranes, where the constituent molecules can freely flow around each other for any shape of the membrane surface, and crystalline or polymerized membranes, where the molecules are held in place by strong covalent bonds. At any finite temperature, these membranes undergo thermal fluctuations and the physical properties of the surface depend on the interplay between these disordering effects and the ordering associated with a curvature-suppressing energy term. Complex phase structures exist between `smooth' surfaces, `crumpled' surfaces, and other more exotic arrangements.