We present an improvement over the Wang-Teter, Perrot, and Smargiassi-Madden kinetic-energy functionals without going beyond linear-response theory and without introducing a density-dependent kernel. The improved functionals were tested on bulk aluminum, and excellent results were obtained. Accurate densityfunctional calculations using the new functionals on systems larger than one can study by...

We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems – we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.

In this paper, we improve the approach of the previous paper about the domino problem in the hyperbolic plane[8, 9]. This time, we prove that the general problem of tiling the hyperbolic plane withà la Wang tiles is undecidable.

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not necessarily local) transformations called flips. This study allows us to formulate an exhaustive generation algorithm and a uniform random sampling algorithm. We fina...