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Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.
eBook
How mechanics shaped the modern world
This unique book presents a nontechnical view of the history of mechanics, from the Big Bang to present day. The impact of mechanics on the evolution of a variety of subjects is vividly illustrated, including astronomy, geology, astrophysics, anthropology, archeology, ancient history, Renaissance art, music, meteorology, modern structural engineering, mathematics, medicine, warfare, and sports. While enormous in scope, the subject matter is covered (with ample photographic support) at a level designed to capture the interest of both the learned and the curious. The book concludes with a creative and thoughtful examination of the current state of mechanics and possibilities for the future of mechanics. This book also: Presents an offbeat, nontechnical chronology of the history of mechanics, from the Big Bang to present day Lays out a complicated scientific subject in a rapid-fire narrative that is both interesting and informative for the non-specialist reader Covers subjects ranging from Egyptian civilization, music and musical instruments, art, and climate dynamics and demonstrates how their evolution both impacted and was impacted by humankind's understanding of mechanics Thoughtfully examines the current state of mechanics and possibilities for future research and innovation.
Book
Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona
The goal of the Entropy and the Quantum schools has been to introduce young researchers to some of the exciting current topics in mathematical physics. These topics often involve analytic techniques that can easily be understood with a dose of physical intuition. In March of 2010, four beautiful lectures were delivered on the campus of the University of Arizona. They included Isoperimetric Inequalities for Eigenvalues of the Laplacian by Rafael Benguria, Universality of Wigner Random Matrices by Laszlo Erdos, Kinetic Theory and the Kac Master Equation by Michael Loss, and Localization in Disordered Media by Gunter Stolz. Additionally, there were talks by other senior scientists and a number of interesting presentations by junior participants. The range of the subjects and the enthusiasm of the young speakers are testimony to the great vitality of this field, and the lecture notes in this volume reflect well the diversity of this school.
eBook
Contact mechanics and friction : physical principles and applications
This text introduces the associations between contact mechanics and friction, offering a deep understanding of tribology. It deals with the associated phenomena of contact, adhesion, capillary forces, friction, lubrication, and wear. The book also explores the system dynamic aspects of tribological systems, such as squeal and its suppression, as well as other types of instabilities and spatial patterns. The second edition has been expanded with a more detailed exposition of elastohydrodynamic lubrication, an updated chapter on numerical simulation methods in contact mechanics, and a new section on fretting in the chapter on wear.
Book
Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are
given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest curve, the
Airy
In this paper, we employ the Brownian Gibbs property to make a close
comparison between the Airy line ensemble’s curves after affine shift and Brownian bridge, proving the finiteness of a superpolynomially
growing moment bound on Radon-Nikodym derivatives.
We also determine the value of a natural exponent describing in Brownian last
passage percolation the decay in probability for the existence of several near geodesics that are disjoint except for their common
endpoints, where the notion of ‘near’ refers to a small deficit in scaled geodesic energy, with the parameter specifying this nearness
tending to zero.
To prove both results, we introduce a technique that may be useful elsewhere for finding upper bounds on
probabilities of events concerning random systems of curves enjoying the Brownian Gibbs property.
Several results in this article
play a fundamental role in a further study of Brownian last passage percolation in three companion papers (Hammond 2017a,b,c), in which
geodesic coalescence and geodesic energy profiles are investigated in scaled coordinates.
eBook
Geomechanical behaviors of bimrocks
\"This book is intended as a reference book for advanced graduate students and research engineers in block-in-matrix rocks (bimrocks) or soil and rock mixtures (SRMs) or rock and soil aggregate (RSA). Bimrocks are complex formations characterized by competent rock inclusions floating in a weaker matrix. Typical types of bimrocks include a series of mixed geological or engineering masses such as mélanges, fault rocks, coarse pyroclastic rocks, breccias, sheared serpentines and waste dump mixture. Bimrock is especially different from the general soil and rock material, and the detection of the damage and fracture is still wide open to innovative research. Globally, there is widespread interest in investigating the geomechanical behaviors of bimrocks, such as deformation and strength characteristics, damage and fracture evolution and stability prediction of bimrock construction. However, the meso-structure factors control the whole mechanical properties of bimrocks, the source of the macroscopic deformation phenomenon is the meso-structural changes. Therefore, evaluation of the mesoscopic physical and mechanical properties, together with advanced testing technique, are attractive research topics in rock mechanics. As a result, comprehensive macroscopic and mesoscopic experimental investigations should be conducted to reveal the damage and fracturing mechanical behaviors of bimrock. The readers of this work can gain new insights into the meso-structural changes of bimrocks subjected to different stress paths. The book is expected to improve the understanding of the mesoscopic damage and fracturing mechanisms of bimrocks and can be helpful to predict the stability of rock structures where rock mass is subjected to complex loading conditions\"-- Provided by publisher.
BOOK
Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
eBook
