How heater filaments burn out: A new type of phase transitions

A simple model combining the most typical features of the physical phenomena involved in Ohmic heating of conductors is proposed. The instability associated with the one-dimensional Helmholtz equation used in the model sets in when boundary conditions are imposed at the ends of a section whose length coincides with the characteristic scale governing the change in the transport properties of the system. It has been found that this mechanism gives rise to formation of spatial structures as a result of a “dimensional” phase transition.