Let Var(Mplan) denote the variety generated by the class Mplan of planar modular lattices. In 1977, based on his structural investigations, R. Freese proved that Var(Mplan) has continuumly many subvarieties. The present paper provides a new approach to this result utilizing lattice identities. We also show that each subvariety of Var(Mplan) is generated by its planar (subdirectly irreducible) m...

Motivated by experimental observations on CuAlNi single crystals, we present a theoretical investigation of non-planar austenite-martensite interfaces. Our analysis is based on the nonlinear elasticity model for martensitic transformations and we show that, under suitable assumptions on the lattice parameters, non-planar interfaces are possible, in particular for transitions with cubic austenite.

The lattice structure of the AlN/SiC interface has been studied in cross section by high-resolution transmission-electron microscopy. Lattice images show planar and crystallographically abrupt interfaces. The atomic arrangement at the plane of the interface is analyzed based on the image characteristics. Possible bonding configurations are discussed. Variations in local image contrast and inter...

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1 11)-dimensional planar lattice of elastic lines in a random potential and the two-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe Ansatz ~RBA! while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamic...

Numerical simulations are performed to investigate the fundamental acoustics properties of the Lattice–Boltzmann method. The propagation of planar acoustic waves is studied to determine the resolution dependence of numerical dissipation and dispersion. The two setups considered correspond to the temporal decay of a standing plane wave in a periodic domain, and the spatial decay of a propagating...

Let δ0(P, k) denote the degree k dilation of a point set P in the domain of plane geometric spanners. If Λ is the infinite square lattice, it is shown that 1+ √ 2 ≤ δ0(Λ, 3) ≤ (3+2 √ 2) 5−1/2 = 2.6065 . . . and δ0(Λ, 4) = √ 2. If Λ is the infinite hexagonal lattice, it is shown that δ0(Λ, 3) = 1 + √ 3 and δ0(Λ, 4) = 2. All our constructions are planar lattice tilings constrained to degree 3 or 4.