On the cumulants of affine equivariant estimators in elliptical families

AbstractGiven a statistical model for data which take values in Rd and have elliptically distributed errors, and affine equivariant estimators μ̂ and μ̂ of a mean vector in Rd⊗Rn and a d × d scatter matrix, expressions are given for the covarances of the estimators in terms of their expectations and some unknown constants that depend on the model and the estimator. Higher order cumulants are also developed. These results place considerable constraints on the possible cumulants of μ̂ and μ̂, as wel as those of estimators of higher order behavior such as multivariate skewness and kurtosis. These expressions are obtained using tensor methods

Ultrafast relaxation dynamics of the antiferrodistortive phase in Ca doped SrTiO3

The ultrafast dynamics of the octahedral rotation in Ca:SrTiO3 is studied by time resolved x-ray diffraction after photo excitation over the band gap. By monitoring the diffraction intensity of a superlattice reflection that is directly related to the structural order parameter of the soft-mode driven antiferrodistortive phase in Ca:SrTiO3, we observe a ultrafast relaxation on a 0.2 ps timescale of the rotation of the oxygen octahedron, which is found to be independent of the initial temperaure despite large changes in the corresponding soft-mode frequency. A further, much smaller reduction on a slower picosecond timescale is attributed to thermal effects. Time-dependent density-functional-theory calculations show that the fast response can be ascribed to an ultrafast displacive modification of the soft-mode potential towards the normal state, induced by holes created in the oxygen 2p states

Watching the birth of a charge density wave order: diffraction study on nanometer-and picosecond-scales

Femtosecond time-resolved X-ray diffraction is used to study a photo-induced phase transition between two charge density wave (CDW) states in 1T-TaS$_2$, namely the nearly commensurate (NC) and the incommensurate (I) CDW states. Structural modulations associated with the NC-CDW order are found to disappear within 400 fs. The photo-induced I-CDW phase then develops through a nucleation/growth process which ends 100 ps after laser excitation. We demonstrate that the newly formed I-CDW phase is fragmented into several nanometric domains that are growing through a coarsening process. The coarsening dynamics is found to follow the universal Lifshitz-Allen-Cahn growth law, which describes the ordering kinetics in systems exhibiting a non-conservative order parameter.Comment: 6 pages, 5 figure

Relaxation and reconstruction on (111) surfaces of Au, Pt, and Cu

We have theoretically studied the stability and reconstruction of (111) surfaces of Au, Pt, and Cu. We have calculated the surface energy, surface stress, interatomic force constants, and other relevant quantities by ab initio electronic structure calculations using the density functional theory (DFT), in a slab geometry with periodic boundary conditions. We have estimated the stability towards a quasi-one-dimensional reconstruction by using the calculated quantities as parameters in a one-dimensional Frenkel-Kontorova model. On all surfaces we have found an intrinsic tensile stress. This stress is large enough on Au and Pt surfaces to lead to a reconstruction in which a denser surface layer is formed, in agreement with experiment. The experimentally observed differences between the dense reconstruction pattern on Au(111) and a sparse structure of stripes on Pt(111) are attributed to the details of the interaction potential between the first layer of atoms and the substrate.Comment: 8 pages, 3 figures, submitted to Physical Review

Structure of self-organized Fe clusters grown on Au(111) analyzed by Grazing Incidence X-Ray Diffraction

We report a detailed investigation of the first stages of the growth of self-organized Fe clusters on the reconstructed Au(111) surface by grazing incidence X-ray diffraction. Below one monolayer coverage, the Fe clusters are in "local epitaxy" whereas the subsequent layers adopt first a strained fcc lattice and then a partly relaxed bcc(110) phase in a Kurdjumov-Sachs epitaxial relationship. The structural evolution is discussed in relation with the magnetic properties of the Fe clusters.Comment: 7 pages, 6 figures, submitted to Physical Review B September 200

Asymmetrically cut crystals as optical elements for highly collimated x‐ray beams

Asymmetrically cut perfect crystals, in both the Laue and Bragg geometries, are examined as single crystal monochromators for x‐ray beams that are collimated to a small fraction of the Darwin width, as is typical in experiments with coherent x rays. Both the Laue and asymmetric Bragg geometries are plagued by an inherent chromatic aberration that increases the beam divergence much beyond that of the symmetric Bragg geometry. Measurements from a recent experiment at the ESRF are presented to compare Si(220) (symmetric Bragg), diamond(111) (asymmetric Laue), and diamond(111) (symmetric Bragg inclined) geometries. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70952/2/RSINAK-66-2-1506-1.pd