The author's previous theory of elasticity and consolidation for isotropic materials m. Appl. Phys. 12, 15.5-164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.

The number of local optima is an important characteristic of a landscape. It appears to depend on the pair-correlation of the landscape as well as on its deviations from statistical isotropy. We use Tanaka and Edward's XY Hamiltonian as an example for an investigation of the relationships between ruggedness, metastable states, and isotropy.

The Landau theory' of continuous phase transitions provides a powerful tool for understanding transitions between solid phases whose symmetries have a group-subgroup relationship. In the Landau theory, the thermodynamic free energy F of the crystal is written as a function of an order parameter Q. In the high-symmetry phase, the minimum of F is at Q = 0. In the low-symmetry phase, the minimum o...

We discuss the problem of the stability of the isotropy of the universe in the space of ever-expanding spatially homogeneous universes with a compact spatial topology. The anisotropic modes which prevent isotropy being asymptotically stable in Bianchi-type V IIh universes with non-compact topologies are excluded by topological compactness. Bianchi type V and type V IIh universes with compact to...

Let F be an arbitrary field (of arbitrary characteristic). Let A be a central simple F -algebra endowed with a quadratic pair σ (if charF 6= 2 then σ is simply an orthogonal involution on A). We show that the Witt index of σ over the function field of the Severi-Brauer variety of A is divisible by the Schur index of the algebra A.

We report a new type of restoration of macroscopic isotropy (homogenization) in fractals with microscopic anisotropy. The phenomenon is observed in various physical setups, including diffusions, random walks, resistor networks, and Gaussian field theories. The mechanism is unique in that it is absent in uniform media, while universal in that it is observed in a wide class of fractals. 05.40+j, ...