24 research outputs found
Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2
We give a presentation by generators and relations of a certain monoid
generating a subgroup of index two in the group Aut(F_2) of automorphisms of
the rank two free group F_2 and show that it can be realized as a monoid in the
group B_4 of braids on four strings. In the second part we use Christoffel
words to construct an explicit basis of F_2 lifting any given basis of the free
abelian group Z^2. We further give an algorithm allowing to decide whether two
elements of F_2 form a basis or not. We also show that, under suitable
conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure
High Pressure Thermoelasticity of Body-centered Cubic Tantalum
We have investigated the thermoelasticity of body-centered cubic (bcc)
tantalum from first principles by using the linearized augmented plane wave
(LAPW) and mixed--basis pseudopotential methods for pressures up to 400 GPa and
temperatures up to 10000 K. Electronic excitation contributions to the free
energy were included from the band structures, and phonon contributions were
included using the particle-in-a-cell (PIC) model. The computed elastic
constants agree well with available ultrasonic and diamond anvil cell data at
low pressures, and shock data at high pressures. The shear modulus and
the anisotropy change behavior with increasing pressure around 150 GPa because
of an electronic topological transition. We find that the main contribution of
temperature to the elastic constants is from the thermal expansivity. The PIC
model in conjunction with fast self-consistent techniques is shown to be a
tractable approach to studying thermoelasticity.Comment: To be appear in Physical Review