On the existence of traveling waves in the 3D Boussinesq system

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic

Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method

We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in L-2 for a class of large perturbations and for any bounded time interval. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. This is the first application of the relative entropy method developed by N. Leger [Arch. Ration. Mech. Anal., 199 (2011), pp. 761-778] and N. Leger and A. Vasseur [Arch. Ration. Mech. Anal., 201 (2011), pp. 271-302] to the study of an inviscid limit to a shock.open1

On the variational limits of lattice energies on prestrained elastic bodies

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\Gamma$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$

Existence and stability of viscoelastic shock profiles

We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic--parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributions are treatment of the compressible case, formulation of a rigorous nonlinear stability theory, including verification of stability of small-amplitude Lax shocks, and the systematic incorporation in our investigations of numerical Evans function computations determining stability of large-amplitude and or nonclassical type shock profiles.Comment: 43 pages, 12 figure

Discovery of mating in the major African livestock pathogen Trypanosoma congolense

The protozoan parasite, Trypanosoma congolense, is one of the most economically important pathogens of livestock in Africa and, through its impact on cattle health and productivity, has a significant effect on human health and well being. Despite the importance of this parasite our knowledge of some of the fundamental biological processes is limited. For example, it is unknown whether mating takes place. In this paper we have taken a population genetics based approach to address this question. The availability of genome sequence of the parasite allowed us to identify polymorphic microsatellite markers, which were used to genotype T. congolense isolates from livestock in a discrete geographical area of The Gambia. The data showed a high level of diversity with a large number of distinct genotypes, but a deficit in heterozygotes. Further analysis identified cryptic genetic subdivision into four sub-populations. In one of these, parasite genotypic diversity could only be explained by the occurrence of frequent mating in T. congolense. These data are completely inconsistent with previous suggestions that the parasite expands asexually in the absence of mating. The discovery of mating in this species of trypanosome has significant consequences for the spread of critical traits, such as drug resistance, as well as for fundamental aspects of the biology and epidemiology of this neglected but economically important pathogen

Foreword

It was July 1938 when Louis Wirth published his “Urbanism as a Way of Life” in the American Journal of Sociology. The paper was seen by many as the one defining the city as a social phenomenon. Looking beyond its physical structure, economic product or cultural institutions, the author discovers those “elements of urbanism which mark it as a distinctive mode of human group life” (Wirth 1938: 4). Wirth argues that three key characteristics of cities — large population size, social heterogeneity, and population density — contribute to the development of a peculiarly “urban way of life” and a distinct “urban personality”. In his opinion, for centuries casual observers have noted deep personality differences between urban and rural people and between nature-based and machinebased styles of living

In place of an end

Cities, since first of them were to be established centuries ago, have always been spaces full of social actions, mass activities and collective behaviors. It is because they had an unusual power to attract people. They were and still are influential, inspiring and they arouse interest. For many reasons cities are important for common dwellers, but also for artists and thinkers. In 20th century Louis Wirth described urbanized areas in terms of high population density, social diversity and large size of population — features which seem to be obvious and natural

Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.Comment: 29 page

Shape programming for narrow ribbons of nematic elastomers

Using the theory of Γ-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e., ribbons exhibiting spontaneous curvature and twist. We apply the models to shape-selection problems for thin films of nematic elastomers with twist and splay-bend texture of the nematic director. For the former, we discuss the possibility of helicoid-like shapes as an alternative to spiral ribbons

A case of multiple abnormalities of the azygos venous system: a praeaortic interazygos vein

The posterior thoracic wall, an area drained by the azygos venous system, is a common site for surgical intervention. Since the venous part of the cardiovascular system is subject to most common variation, abnormalities in the azygos venous system are often reported. Some of the anatomical variants have significant clinical implications for computed tomography image assessment and mediastinal surgery. During dissection of the posterior mediastinum in a 76 year-old Caucasian male cadaver we found a rare variation in the azygos venous system. The hemiazygos vein drained the left 9th to 11th left posterior intercostal veins. While passing ventrally to the aorta at the level of the body of the eighth thoracic vertebra it was joined by two separate vessels found to be the continuations of the 7th and 8th left posterior intercostal veins. The resultant dilated vessel, termed the "interazygos vein", then opened into the azygos vein on the right side of the vertebral column. Variation in the azygos venous system has often been reported, but the abnormality observed by us appears to be extremely rare. The interazygos vein passing ventrally to the aorta may mimic enlarged lymph nodes and cause misinterpretation of a computed tomography image or, if accidentally damaged during mediastinal surgery, may lead to intraoperative haemorrhage. To the best of our knowledge this report provides new data of potential clinical significance