Search for: All records

The Universe is neither homogeneous nor isotropic, but it is close enough that we can reasonably approximate it as such on suitably large scales.The inflationary-Λ-Cold Dark Matter (ΛCDM) concordance cosmology builds on these assumptions to describe the origin and evolution of fluctuations. With standard assumptions about stress-energy sources, this system is specified by just seven phenomenological parameters,whose precise relations to underlying fundamental theories are complicated and may depend on details of those fields.Nevertheless, it is common practice to set the parameter that characterizes the spatial curvature, Ω_K, exactly to zero.This parameter-fixed ΛCDM is awarded distinguished status as separate model, “flat ΛCDM.”Ipso factothis places the onus on proponents of “curved ΛCDM” to present sufficient evidence that Ω_K≠ 0, and is needed as a parameter.While certain inflationary model Lagrangians, with certain values of their parameters, and certain initial conditions, will lead to a present-day universe well-described as containing zero curvature, this does not justify distinguishing that subset of Lagrangians, parameters and initial conditions into a separate model.Absent any theoretical arguments, we cannot use observations that suggest small Ω_Kto enforce Ω_K= 0.Our track record in picking inflationary models and their parametersa priorimakes such a choice dubious, andconcerns about tensions in cosmological parameters and large-angle cosmic-microwave-background anomalies strengthens arguments against this choice.We argue that Ω_Kmust not be set to zero, and that ΛCDM remains a phenomenological model with at least 7 parameters.

An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for its performance prediction, prognosis and optimization. X‐ray tomography has provided a nondestructive means for microstructure characterization in 3D and 4D (i.e. structural evolution over time), in which a material is typically reconstructed from a large number of tomographic projections using filtered‐back‐projection (FBP) method or algebraic reconstruction techniques (ART). Here, we present in detail a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of absorption contrast x‐ray tomographic projections. This discrete tomography reconstruction procedure is in contrast to the commonly used FBP and ART, which usually requires thousands of projections for accurate microstructure rendition. The utility of our stochastic procedure is first demonstrated by reconstructing a wide class of two‐phase heterogeneous materials including sandstone and hard‐particle packing from simulated limited‐angle projections in both cone‐beam and parallel beam projection geometry. It is then applied to reconstruct tailored Sn‐sphere‐clay‐matrix systems from limited‐angle cone‐beam data obtained via a lab‐scale tomography facility at Arizona State University and parallel‐beam synchrotron data obtained at Advanced Photon Source, Argonne National Laboratory. In addition, we examine the information content of tomography data by successively incorporating larger number of projections and quantifying the accuracy of the reconstructions. We show that only a small number of projections (e.g. 20–40, depending on the complexity of the microstructure of interest and desired resolution) are necessary for accurate material reconstructions via our stochastic procedure, which indicates its high efficiency in using limited structural information. The ramifications of the stochastic reconstruction procedure in 4D materials science are also discussed.