Abstract
When an electric field is applied to an inhomogeneous material one may have strong spatial variations in the Joule heat distribution. We define a hot spot as a region where the Joule heat distribution is considerably higher than in the surrounding material. In one dimension the Joule heat is determined by the resistance at that point. In two dimensions we know that the Joule heat dissipation is determined by long range effects and it is hard to find an immediate criterion to see where hot spots occur. In three dimensions again the occurrence of hot spots is a more local effect. Here we have investigated, using numerical calculations on resistor networks, which structural properties give rise to hot spots, and what length scales are involved.
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