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Gas saturation degree and flow patterns are key factors for modeling and designing multiphase systems and operations. In turn, these factors are strongly related to the flow dynamics, which are controlled largely by the fluid and media properties. However, predicting the gas distribution and flow pattern remains elusive. Data from 11 series of steady air injection experiments into initially water‐saturated granular media, conducted with different media and flow geometries, are analyzed to identify the main factors governing air saturation and flow patterns. For air injection into otherwise water‐saturated granular media, the flow pattern is affected mainly by the ratio between the Capillary number (ratio of viscous to capillary forces) and the Bond number (ratio of gravitational to capillary forces), that is, by the ratio of viscous to gravitational forces. Moreover, the meta‐analysis presented here indicates that the steady air saturation degree is correlated strongly to flow velocity and grain diameter. Furthermore, analysis of experimental results from different studies of air injection into coarse, homogeneous, granular media (glass beads, sand) also suggests a significant effect of inertial forces. Both viscous and buoyancy forces increased air saturation, while capillary forces decreased the saturation degree. The ratio between capillary and buoyancy forces determines the air flow pattern during air injection into otherwise water‐saturated media. Key Points: Capillary, viscous, gravity, and inertial forces control air flow regime and content, the latter increases with velocity and grain sizeA new phase diagram depicts the effect of Ca and Bo on air flow patternsThe effect of the background saturation degree cannot be easily decoupled from the Bo‐Ca‐flow pattern phase diagram [ABSTRACT FROM AUTHOR]

This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime. [ABSTRACT FROM AUTHOR]

Reviews the book "Equilibrium Theory in Infinite Dimensional Spaces," edited by M. A. Kahn and N. C. Yannelis.

Reviews the book 'Dimensional Analysis for Economists,' by F.J. de Jong.

Climate Mathematics - Theory and Application Samuel S. P. Shen and Richard C. J. Somerville Cambridge University Press, 2019 Hardback £57.99456 ppISBN 978-1108476874 Climate change is one of the most pressing issues of our time. The mathematics of matrices and linear algebra are presented using space-time climate data, which makes it instantly relevant to climate scientists. This book teaches mathematics but with the climate system at its heart, for example, teaching matrices and linear algebra using space-time climate data. [Extracted from the article]

Reviews the book 'Dimensional Analysis for Economists,' by Frits J. DeJong.

The article reviews the book "Multiple Solution Methods for Teaching Science in the Classroom: Improving Quantitative Problem Solving Using Dimensional Analysis and Proportional Reasoning," by Stephen DeMeo.

The article reviews the book "Dimensional Analysis Through Perspective: A Reference Manual," 2nd Edition, by James R. Williamson and Michael H. Brill.

This article focuses on the book " Scaling," by G.I. Barenblatt. This book describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are given a modern treatment here. By considering examples of various degrees of complexity, the development spirals to a conclusion. General ideas are illustrated in a final chapter that describes in detail the structure of an important class of turbulent flows and explains why controversies surrounding them can be attributed to an inadequate understanding of the use of scaling.

This article focuses on the book "Dimensional Management," by Mark A. Curtis. This book is designed to provide a comprehensive systems approach to all facets of dimension and tolerance development, analysis, inspection and documentation. Often referred to as dimensional management, this systems approach focuses on optimizing the interchangeability of multicomponent manufactured products. It demonstrates that through the detailed description of known manual and computer-aided tolerance analysis techniques, an understanding of manufacturing variation and the mitigation of its undesirable effects can be achieved. The author includes a chapter on geometric dimensioning and tolerancing as specified in the national dimensioning and tolerancing standard, ASME Y14.