Minimal surfaces and multifunctionality

Abstract

Triply periodic minimal surfaces are objects of great interest to physical scientists, biologists and mathematicians. It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. More importantly, here we further establish the multifunctionality of such two-phase systems by showing that they are also extremal when a competition is set up between the effective bulk modulus and the electrical (or thermal) conductivity of the composite. The implications of our findings for materials science and biology, which provides the ultimate multifunctional materials, are discussed.