Deuterated hydrogen molecule and search for early structure-formation signatures in the Universe

Possible detection of signatures of structure formation at the end of the 'dark age' epoch  ( z ∼ 40–20)  is examined. We discuss the spectral–spatial fluctuations in the cosmic microwave background radiation (CMBR) temperature produced by elastic resonant scattering of CMBR photons on deuterated hydrogen (HD) molecules located in protostructures moving with peculiar velocity. Detailed chemical kinematic evolution of HD molecules in the expanding homogeneous medium is calculated. Then, the HD abundances are linked to protostructures at their maximum expansion, whose properties are estimated by using the top-hat spherical approach and the Λ cold dark matter (ΛCDM) cosmology. We find that the optical depths in the HD three lowest pure rotational lines for high-peak protohaloes at their maximum expansion are much higher than those in LiH molecule. The corresponding spectral–spatial fluctuation amplitudes, however, are probably too weak to be detected by current and forthcoming millimetre telescope facilities. We extend our estimates of spectral–spatial fluctuations to gas clouds inside collapsed CDM haloes by using results from a crude model of HD production in these clouds. The fluctuations for the highest peak CDM haloes at redshifts ∼20–30 could be detected in the future. Observations will be important to test model predictions of early structure formation in the Universe.     

Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.