Depth-dependent critical behavior in V2H

Using X-ray diffuse scattering, we investigate the critical behavior of an order-disorder phase transition in a defective "skin-layer" of V2H. In the skin-layer, there exist walls of dislocation lines oriented normal to the surface. The density of dislocation lines within a wall decreases continuously with depth. We find that, because of this inhomogeneous distribution of defects, the transition effectively occurs at a depth-dependent local critical temperature. A depth-dependent scaling law is proposed to describe the corresponding critical ordering behavior.Comment: 5 pages, 4 figure

Depth-dependent ordering, two-length-scale phenomena and crossover behavior in a crystal featuring a skin-layer with defects

Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of the central peak by scattering from a near-surface region of a V2H crystal, which has a first-order transition in the bulk. As the temperature is lowered toward the critical temperature, a crossover in critical behavior is seen, with the temperature range nearest to the critical point being characterized by mean field exponents. Near the transition, a small two-phase coexistence region is observed. The values of transition and crossover temperatures decay with depth. An explanation of these experimental results is here proposed by means of a theory in which edge dislocations in the near-surface region occur in walls oriented in the two directions normal to the surface. The strain caused by the dislocation lines causes the ordering in the crystal to occur as growth of roughly cylindrically shaped regions. After the regions have reached a certain size, the crossover in the critical behavior occurs, and mean field behavior prevails. At a still lower temperature, the rest of the material between the cylindrical regions orders via a weak first-order transition.Comment: 12 pages, 8 figure

On linear combinations of generalized involutive matrices

Let X(dagger) denotes the Moore-Penrose pseudoinverse of a matrix X. We study a number of situations when (aA + bB)(dagger) = aA + bB provided a, b is an element of C\{0} and A, B are n x n complex matrices such that A(dagger) = A and B(dagger) = B. (C) 2011 Taylor & FrancisLiu, X.; Wu, L.; Benítez López, J. (2011). On linear combinations of generalized involutive matrices. Linear and Multilinear Algebra. 59(11):1221-1236. doi:10.1080/03081087.2010.496111S12211236591

The lattice of the CERN Large Hadron Collider

The lattice of the CERN Large Hadron Collider is designed with 23 regular cells per arc, each containing 6 tightly packed 14.2 m long dipoles. This allows to reach 7 TeV per beam with a dipole field of 8.4 Tesla. There are four experimental insertions, two of which are devoted to high luminosity experiments with ± 23 m of free space for the detector. The other two experimental insertions are combined with injection. The value of ß* at the interaction points is tunable from 6 m at injection to 0.5 m in collision. The energy deposition in the inner triplets is carefully reduced to sustain the nominal luminosity of 1034 cm-2s-1. Two insertions are devoted to collect the halo particles with large emittance and momentum spread surrounding the beam core: escaping rates of the protons are estimated to be less than 4·106 sec-1m-1. Finally, one insertion is used to extract the particles in the vertical direction with a minimized deflecting strength

X-ray scattering study of two length scales in the critical fluctuations of CuGeO3

The critical fluctuations of CuGeO$_3$ have been measured by synchrotron x-ray scattering, and two length scales are clearly observed. The ratio between the two length scales is found to be significantly different along the $a$ axis, with the $a$ axis along the surface normal direction. We believe that such a directional preference is a clear sign that surface random strains, especially those caused by dislocations, are the origin of the long length scale fluctuations.Comment: 5 pages, 4 figures, submitted to PR

Author Correction: Federated learning enables big data for rare cancer boundary detection.

10.1038/s41467-023-36188-7NATURE COMMUNICATIONS14