arXiv subjects
Publications and source records attributed to S. Vakhrushev.
In 1991 Bollobás and Frieze found the threshold for the emergence of a spanning triangulation of a triangle in the binomial random graph, up to a logarithmic factor. In this paper, we find the threshold probability for the emergence of a spanning triangulation of a $k$-gon for any $3\leq k\leq n$, up to a constant factor.
We propose a simple phenomenological picture to explain the unusual dielectric properties of the proto-typical ferroelectric relaxor lead magnesium niobate-titanate (PMN-PT). Our model assumes a specific, slowly changing, displacement pattern of the lead ion, which is indirectly controlled by the low-energy acoustic phonons of the system. The model qualitatively explains in great detail the temperature, pressure, and electric field dependence of diffuse neutron- and x-ray scattering, as well as the existence of hierachy in the relaxation times of these materials. We furthermore show that the widely used concept of polar nanoregions as indiviudal static entities is incompatible with the available body of experimental diffuse scattering results.
Inelastic neutron scattering measurements of the relaxor ferroelectric PbMg$_{1 / 3}$Nb$_{2 / 3}$O$_{3}$ (PMN) in the temperature range 490~K$<$T$<$880~K directly observe the soft mode (SM) associated with the Curie-Weiss behavior of the dielectric constant $\varepsilon $(T). The results are treated within the framework of the coupled SM and transverse optic (TO1) mode and the temperature dependence of the SM frequency at q=0.075 a* is determined. The parameters of the SM are consistent with the earlier estimates and the frequency exhibits a minimum near the Burns temperature ($\approx $ 650K)