Are adobe walls optimal phase-shift filters?

The adobe house construction gives an automatic, air conditioning effect because the rooms tend to be cool at midday and warm at night. Presumably this is brought about by the walls acting as a heat filter so that there is nearly a 12-hour phase lag. This raises the question of how to optimize the adobe phenomenon by a suitable design of the walls. In this study it is supposed possible to make the walls of layered construction with layers having different thermal resistivity. Such a layered wall can be modeled electrically as a ladder filter of capacitors and resistors. The input to the ladder is a sinusoidal voltage. Then the following question arises: If the filter capacitors have given values, how should the resistors be chosen so that the output voltage has a given phase lag but least attenuation? It is found possible to answer this question by use of a special variational principle. Applying this analysis to building construction shows how to maximize oscillation of interior temperature with a phase lag of a prescribed number of hours.