Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models

We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional for which we prove explicit inequality between the relative entropy and the production of entropy to get exponential convergence to equilibrium with explicit rate. The proof is based on inequalities between the entropy production functional for hard spheres and Maxwell molecules. Mathematical proof of the convergence to some heat equation in the diffusive limit is also given. From the last two points we deduce the first explicit estimates on the diffusive coefficient in the Fick's law for (inelastic hard-spheres) dissipative gases.Comment: 25 page

Quiet City, trumpet manuscript

Trumpet part for Aaron Copland's "Quiet City", copied out and annotated by Roger Voisin for use in performance. Top right corner signed by Copland: "For Roger Voisin who plays this like a dream. A Copland 1957"

On the non-integrability of the Popowicz peakon system

We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlev\'e analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension 3N.Comment: 8 pages, AIMS class file. Proceedings of AIMS conference on Dynamical Systems, Differential Equations and Applications, Arlington, Texas, 200

Into the Wide – Into the Deep: Manuscript Research in the Digital Age. Introduction

Manuscript research is a wide field of scholarship which is integrated in core disciplines such as history, philology, or library science. Yet manuscript research is also crucial in other fields such as archaeology, history of arts, musicology or Egyptology, to name but a few. For all these disciplines, manuscripts are fundamental sources. There are different approaches to different types of manuscripts, but questions and perspectives, methodologies and tools are often quite similar. Innovations and new research strategies from one discipline can be transferred to and adopted by others. This article is an introduction to the second volume of the anthology "Codicology and Palaeography in the Digital Age" and gives an overview of current aspects in the field of manuscript studies in both theory and practice by showing the relatedness of the contributions to the volume at hand as well as its predecessor. The texts are roughly assigned to five interrelated areas of manuscript research: (I) the photographic capturing of the manuscript surface, (II) the description of the manuscript for a catalogue, (III) the scientific examination of material aspects, (IV) the analysis of the script and (V) the deep encoding of the text itself

Guidance on Noncorticosteroid Systemic Immunomodulatory Therapy in Noninfectious Uveitis : Fundamentals Of Care for UveitiS (FOCUS) Initiative

Supplemental material available at www.aaojournal.org. Supported by AbbVie, Inc., and the Fundamentals of Care for Uveitis Initiative National Faculty. This manuscript was developed subsequent to an AbbVie-sponsored literature review of noninfectious, nonanterior uveitis. The meeting was conducted to understand the available literature regarding the management of patients with noninfectious, nonanterior uveitis. The program involved a total of 139 experts from 28 countries, who were selected for participation by AbbVie. However, AbbVie was not involved in the development of the manuscript. The authors maintained complete control over the content and this manuscript reflects the opinions of the authors. AbbVie selected the discussion participants and reviewed the final manuscript draft for scientific accuracy, but the authors determined the final content. All authors made substantial contributions to the article or critically revised it for important intellectual content and approved the final manuscript. AbbVie provided funding to invited participants, including honoraria for their attendance at the meetings. Travel to and from the meetings was reimbursed. No payments were made to the authors for the development of this manuscript. Dhinakaran Sambandan, PhD, and Shula Sarner, PhD, of Lucid Partners, Burleighfield House, Buckinghamshire, United Kingdom, provided medical writing and editorial support to the authors in the development of this manuscript; financial support for these services was provided by AbbVie. AbbVie reviewed the manuscript, but was not involved in the methodology, data collection and analysis, or completion of this manuscript.Peer reviewedPublisher PD

Manuscript Collections

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