Improving the Lagrangian perturbative solution for cosmic fluid: Applying Shanks transformation

We study the behavior of Lagrangian perturbative solutions. For a spherical void model, the higher order the Lagrangian perturbation we consider, the worse the approximation becomes in late-time evolution. In particular, if we stop to improve until an even order is reached, the perturbative solution describes the contraction of the void. To solve this problem, we consider improving the perturbative solution using Shanks transformation, which accelerates the convergence of the sequence. After the transformation, we find that the accuracy of higher-order perturbation is recovered and the perturbative solution is refined well. Then we show that this improvement method can apply for a $\Lambda$CDM model and improved the power spectrum of the density field.Comment: 17 pages, 7 figures; accepted for publication in Phys.Rev.D; v2: Evolution of power spectrum in LCDM model is added; v3: References are correcte

Beyond Zel'dovich-Type Approximations in Gravitational Instability Theory --- Pad\'e Prescription in Spheroidal Collapse ---

Among several analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate scheme is known to be unusually accurate even in mildly non-linear regime. This approximation is very similar to the Pad\'e approximation in appearance. We first establish, however, that these two are actually different and independent approximations with each other by using a model of spheroidal mass collapse. Then we propose Pad\'e-prescribed Zel'dovich-type approximations and demonstrate, within this model, that they are much accurate than any other known nonlinear approximations.Comment: 4 pages, latex, 3 figures include

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

Performance of the optimized Post-Zel'dovich approximation for CDM models in arbitrary FLRW cosmologies

We investigate the performance of the optimized Post-Zel'dovich approximation in three cold dark matter cosmologies. We consider two flat models with $\Omega_0=1$ (SCDM) and with $\Omega_0=0.3$ ($\Lambda$CDM) and an open model with $\Omega_0=0.3$ (OCDM). We find that the optimization scheme proposed by Wei{\ss}, Gottl\"ober & Buchert (1996), in which the performance of the Lagrangian perturbation theory was optimized only for the Einstein-de Sitter cosmology, shows the excellent performances not only for SCDM model but also for both OCDM and $\Lambda$CDM models. This universality of the excellent performance of the optimized Post-Zel'dovich approximation is explained by the fact that a relation between the Post-Zel'dovich order's growth factor $E(a)$ and Zel'dovich order's one $D(a)$, $E(a)/D^2(a)$, is insensitive to the background cosmologies.Comment: 8 pages, 3 figures, LaTex using aaspp4.sty and epsf.sty, Accepted for publication in ApJ Letter

Effect of edge conditions on buckling of stiffened and framed shells

"October 20, 1967.""A series of stiffened shells made of plastic were tested to verify the theoretical equations for the effect of edge conditions on the buckling of stiffened and framed shells. The theory was developed by calculating the deflections during loading and prior to buckling, and by using a large deflection stability approach. The agreement between the test results and the theory was good. Tests also confirmed that the edges could be stiffened and relatively high buckling loads could be obtained by increasing the meridional curvature near the edge of the shell."--Summary

Space Research Spinoff to Structural Engineering

Research for space applications has resulted in a considerable amount of valuable spinoff information to practicing structural engineers outside the space related fields. The spinoff has not been limited to any one field, but cuts across the lines of many industries serving the public, For example, specific applications can be traced to the agricultural industry, commercial power generation, school and building construction, and hydrospace applications. Examples are given where funds from NASA and other space oriented organizations have been combined with funds from private organizations such as the American Iron aid Steel Institute, the American Institute of Steel Construction and from private corporations to produce results that are applicable to both space efforts and commercially oriented efforts

How is the local-scale gravitational instability influenced by the surrounding large-scale structure formation?

We develop the formalism to investigate the relation between the evolution of the large-scale (quasi) linear structure and that of the small-scale nonlinear structure in Newtonian cosmology within the Lagrangian framework. In doing so, we first derive the standard Friedmann expansion law using the averaging procedure over the present horizon scale. Then the large-scale (quasi) linear flow is defined by averaging the full trajectory field over a large-scale domain, but much smaller than the horizon scale. The rest of the full trajectory field is supposed to describe small-scale nonlinear dynamics. We obtain the evolution equations for the large-scale and small-scale parts of the trajectory field. These are coupled to each other in most general situations. It is shown that if the shear deformation of fluid elements is ignored in the averaged large-scale dynamics, the small-scale dynamics is described by Newtonian dynamics in an effective Friedmann-Robertson-Walker (FRW) background with a local scale factor. The local scale factor is defined by the sum of the global scale factor and the expansion deformation of the averaged large-scale displacement field. This means that the evolution of small-scale fluctuations is influenced by the surrounding large-scale structure through the modification of FRW scale factor. The effect might play an important role in the structure formation scenario. Furthermore, it is argued that the so-called {\it optimized} or {\it truncated} Lagrangian perturbation theory is a good approximation in investigating the large-scale structure formation up to the quasi nonlinear regime, even when the small-scale fluctuations are in the non-linear regime.Comment: 15pages, Accepted for publication in Gravitation and General Relativit

Hydrodynamic approach to the evolution of cosmological structures

A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed irrelevance of short-range (``collisional'') interactions, the way to tackle the hydrodynamic equations is essentially different from the usual case. The main assumption is that the influence of the small scales over the large-scale evolution is weak: this idea is implemented in the form of a large-scale expansion for the coarse-grained equations. This expansion builds a framework in which to derive in a controlled manner the popular ``dust'' model (as the lowest-order term) and the ``adhesion'' model (as the first-order correction). It provides a clear physical interpretation of the assumptions involved in these models and also the possibility to improve over them.Comment: 14 pages, 3 figures. Version to appear in Phys. Rev.