Theory for Thermal Bi/Multistability: Nonlinear Thermal Conductivity

Abstract

AbstractIn this chapter, we theoretically design diffusive bistability (and even multistability) in the macroscopic scale, which has a similar phenomenon but a different mechanism from its microscopic counterpart (Wang et al., Phys. Rev. Lett. 101, 267203 (2008)); the latter has been extensively investigated in the literature, e.g., for building nanometer-scale memory components. By introducing second- and third-order nonlinear terms (opposite in sign) into diffusion coefficient matrices, bistable energy or mass diffusion occurs with two different steady states, identified as “0” and “1”. In particular, we study heat conduction in a two-terminal three-body system. This bistable system exhibits a macro-scale thermal memory effect with tailored nonlinear thermal conductivities. Finite-element simulations confirm the theoretical analysis. Also, we suggest experiments with metamaterials based on shape memory alloys. This framework blazes a trail in constructing intrinsic bistability or multistability in diffusive systems for macroscopic energy or mass management.