Superclusters from velocity divergence fields

ABSTRACT Superclusters are a convenient way to partition and characterize the large-scale structure of the Universe. In this Letter, we explore the advantages of defining superclusters as watershed basins in the divergence velocity field. We apply this definition on diverse data sets generated from linear theory and N-body simulations, with different grid sizes, smoothing scales, and types of tracers. From this framework emerges a linear scaling relation between the average supercluster size and the autocorrelation length in the divergence field, a result that holds for one order of magnitude from 10 up to 100 Mpc h−1. These results suggest that the divergence-based definition provides a robust context to quantitatively compare results across different observational or computational frameworks. Through its connection with linear theory, it can also facilitate the exploration of how supercluster properties depend on cosmological parameters, paving the way to use superclusters as cosmological probes.

Hydroelastic Instability of Infinite Strips Under Shearing Load on an Elastic Foundation

The paper examines the hydroelastic instability of an infinitely long plate subjected to shearing load with two different boundary conditions, one side of which is exposed to an incompressible inviscid flow, and the other side supported on an elastic foundation. The analysis is based on the small deflection plate theory and the classical linearized potential flow theory. The Galerkin method and Fourier transforms are used. It is found that the effects of the shearing load and the elastic foundation on the divergence velocity can be illustrated by a single curve for both clamped and simply supported cases.

Effects of Shearing Loads and In-Plane Boundary Conditions on the Stability of Thin Tubes Conveying Fluid

The hydroelastic stability of short, simply supported, thin-walled tubes conveying fluid is examined with an emphasis on the effects of shearing loads and in-plane boundary conditions. The Donnell shell equation is used in conjunction with linearized, potential flow theory. The solution is obtained by using Fourier integral theory and Galerkin’s method. It is found that an increase of the shearing load reduces the critical divergence velocity and raises the corresponding number of circumferential waves. A change in the in-plane boundary conditions exerts the significant effect on the critical divergence velocity of short tubes.