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Learning to Read: Navigating the Ebook Reader Market

The latest “Scholarly Kitchen” blog post by Robert Harington, AED of Publishing at the AMS, explores the confusing landscape of ebook readers, presenting a few of the options available along with their pros and cons.

Bulletin of the AMS

Bulletin of the AMS Hilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations
( view abstract )
Hilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations
The problem of the derivation of hydrodynamics from the Boltzmann equation and related dissipative systems is formulated as the problem of a slow invariant manifold in the space of distributions. We review a few instances where such hydrodynamic manifolds were found analytically both as the result of summation of the Chapman-Enskog asymptotic expansion and by the direct solution of the invariance equation. These model cases, comprising Grad's moment systems, both linear and nonlinear, are studied in depth in order to gain understanding of what can be expected for the Boltzmann equation. Particularly, the dispersive dominance and saturation of dissipation rate of the exact hydrodynamics in the short-wave limit and the viscosity modification at high divergence of the flow velocity are indicated as severe obstacles to the resolution of Hilbert's 6th Problem. Furthermore, we review the derivation of the approximate hydrodynamic manifold for the Boltzmann equation using Newton's iteration and avoiding smallness parameters, and compare this to the exact solutions. Additionally, we discuss the problem of projection of the Boltzmann equation onto the approximate hydrodynamic invariant manifold using entropy concepts. Finally, a set of hypotheses is put forward where we describe open questions and set a horizon for what can be derived exactly or proven about the hydrodynamic manifolds for the Boltzmann equation in the future.

Browse the archive 1891 - 2014.

Featured Publication

Really Big Numbers
by Richard Evan Schwartz, Brown University, Providence, RI

In the American Mathematical Society’s first-ever book for kids (and kids at heart!), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. This book is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.

Featured Series

Student Mathematical Library Series
The books presented in this series serve as pivotal stepping stones in a student’s journey from mathematical coursework to research. Beneficial to beginning and advanced mathematicians alike.

Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction by Mark Levi
Primality Testing for Beginners by Lasse Rempe-Gillen and Rebecca Waldecker
The Joy of Factoring
by Samuel S. Wagstaff, Jr.

Featured Series

Graduate Studies in Mathematics Series
Volumes in this series are specifically designed as graduate studies texts, but are also suitable for supplemental course reading and make ideal independent study resources.

Mathematics of Probability by Daniel W. Stroock
The Joys of Haar Measure by Joe Diestel and Angela Spalsbury
Introduction to 3-Manifolds by Jennifer Schultens

Research Journals Spotlight