Homogenization of linear transport equations in a stationary ergodic setting

We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random and stationary. We identify the asymptotic microscopic and macroscopic profiles of the density, and we derive formulas for these profiles when the space dimension is equal to one.Comment: 24 page

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics

A computational study of the influence of surface roughness on material strength

In machine component stress analysis, it usually assumed that the geometry specified in CAD provides a fair representation of the geometry of the real component. While in particular circumstances, tolerance information, such as minimum thickness of a highly stressed region, might be taken into consideration, there is no standard practice for the representation of surface quality. It is known that surface roughness significantly influences fatigue life, but for this to be useful in the context of life prediction, there is a need to examine the nature of surface roughness and determine how best to characterise it. Non-smooth geometry can be represented in mathematics by fractals or other methods, but for a representation to have a practical value for a manufactured component, it is necessary to accept that there is a lower limit to surface profile measurement resolution. Resolution and mesh refinement also play a part in any computational analysis undertaken to assess surface profile effects: in the analyses presented, a nominal axi-symmetric geometry has been taken, with a finite non-smooth region on the boundary. Various surface roughness representations are modelled, and the significance of the characterized surface roughness type is investigated. It is shown that the applied load gives rise to a nominally uni-axial stress state of 90% of the yield, although surface roughness features have the effect of modifying the load path, and give rise to localized regions of plasticity near to the surface. The material of the test model is assumed to be elasto-plastic, and the development and evolution of plastic zones formed within the geometry are shown for multiple load cycles

Photoperiod Regulates Corticosterone Rhythms by Altered Adrenal Sensitivity via Melatonin-Independent Mechanisms in Fischer 344 Rats and C57BL/6J Mice

Most species living in temperate zones adapt their physiology and behavior to seasonal changes in the environment by using the photoperiod as a primary cue. The mechanisms underlying photoperiodic regulation of stress-related functions are not well understood. In this study, we analyzed the effects of photoperiod on the hypothalamic-pituitary-adrenal axis in photoperiod-sensitive Fischer 344 rats. We first examined how photoperiod affects diurnal variations in plasma concentrations of adrenocorticotropic hormone (ACTH) and corticosterone. ACTH levels did not exhibit diurnal variations under long- and short-day conditions. On the other hand, corticosterone levels exhibited a clear rhythm under short-day condition with a peak during dark phase. This peak was not observed under long-day condition in which a significant rhythm was not detected. To analyze the mechanisms responsible for the photoperiodic regulation of corticosterone rhythms, ACTH was intraperitoneally injected at the onset of the light or dark phase in dexamethasone-treated rats maintained under long- and short-day conditions. ACTH induced higher corticosterone levels in rats examined at dark onset under short-day condition than those maintained under long-day condition. Next, we asked whether melatonin signals are involved in photoperiodic regulation of corticosterone rhythms, and rats were intraperitoneally injected with melatonin at late afternoon under long-day condition for 3 weeks. However, melatonin injections did not affect the corticosterone rhythms. In addition, photoperiodic changes in the amplitude of corticosterone rhythms were also observed in melatonin-deficient C57BL/6J mice, in which expression profiles of several clock genes and steroidgenesis genes in adrenal gland were modified by the photoperiod. Our data suggest that photoperiod regulates corticosterone rhythms by altered adrenal sensitivity through melatonin-independent mechanisms that may involve the adrenal clock

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

Escherichia coli contamination of the river Thames in different seasons and weather conditions

Contamination of public water ways with sewage represents a serious environmental and health risk. We monitored pollution of the river Thames by enumerating the indicator organism Escherichia coli. Samples were taken from a site in central London near Waterloo Bridge in different seasons. E. coli were quantified using a membrane filtration method, and correlated with the tidal variations of the river and meteorological data on rainfall and temperature. More frequent and severe incidents of pollution occurred in the autumn. Heavy rainfall resulted in sharp peaks of E. coli contamination that implies a potential increase of numbers of pathogenic micro-organisms. Sixty percent of all samples were found to be in excess of the accepted upper limit of pollution set by European Union (EU) legislation for bathing water. This study demonstrated that frequent sewage pollution of the Thames results in high numbers of E. coli and incidents of detectable levels of pathogenic bacteria demonstrating the need for regular monitoring of bacterial pollution

Rapid detection of Escherichia coli in water using a hand-held fluorescence detector

The quantification of pathogenic bacteria in an environmental or clinical sample commonly involves laboratory-based techniques and results are not obtained for 24–72 h after sampling. Enzymatic analysis of microbial activity in water and other environmental samples using fluorescent synthetic substrates are well-established and highly sensitive methods in addition to providing a measure of specificity towards indicative bacteria. The enzyme b-D-glucuronidase (GUD) is a specific marker for Escherichia coli and 4-methylumbelliferone-b-D-glucuronide (MUG) a sensitive substrate for determining the presence of E. coli in a sample. However, currently used procedures are laboratory-based and require bench-top fluorimeters for the measurement of fluorescence resulting from the enzyme–substrate reaction. Recent developments in electronic engineering have led to the miniaturisation of fluorescence detectors. We describe the use of a novel hand-held fluorimeter to directly analyse samples obtained from the River Thames for the presence of E. coli. The results obtained by the hand-held detector were compared with those obtained with an established fluorescent substrate assay and by quantifying microbial growth on a chromogenic medium. Both reference methods utilised filtration of water samples. The miniaturised fluorescence detector was used and incubation times reduced to 30 min making the detection system portable and rapid. The developed hand-held system reliably detected E. coli as low as 7 cfu/mL river water sample. Our study demonstrates that new handheld fluorescence measurement technology can be applied to the rapid and convenient detection of bacteria in environmental samples. This enables rapid monitoring to be carried out on-site. The technique described is generic and it may, therefore, be used in conjunction with different fluorescent substrates which allows the assessment of various target microorganisms in biological samples