Weak gravitational lensing of finite beams

The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of the distribution of matter---the so-called Ricci-Weyl problem. In this letter, we propose a strong-lensing-inspired formalism to describe the lensing of finite beams. We address the Ricci-Weyl problem by showing explicitly that convergence is caused by the matter enclosed by the beam, regardless of its distribution. Furthermore, shear turns out to be systematically enhanced by the finiteness of the beam. This implies, in particular, that the Kaiser-Squires relation between shear and convergence is violated, which could have profound consequences on the interpretation of weak lensing surveys.Comment: 6 pages, 2 figures, v2: matches published version, some typos correcte

Modeling the shortening history of a fault tip fold using structural and geomorphic records of deformation

We present a methodology to derive the growth history of a fault tip fold above a basal detachment. Our approach is based on modeling the stratigraphic and geomorphic records of deformation, as well as the finite structure of the fold constrained from seismic profiles. We parameterize the spatial deformation pattern using a simple formulation of the displacement field derived from sandbox experiments. Assuming a stationary spatial pattern of deformation, we simulate the gradual warping and uplift of stratigraphic and geomorphic markers, which provides an estimate of the cumulative amounts of shortening they have recorded. This approach allows modeling of isolated terraces or growth strata. We apply this method to the study of two fault tip folds in the Tien Shan, the Yakeng and Anjihai anticlines, documenting their deformation history over the past 6–7 Myr. We show that the modern shortening rates can be estimated from the width of the fold topography provided that the sedimentation rate is known, yielding respective rates of 2.15 and 1.12 mm/yr across Yakeng and Anjihai, consistent with the deformation recorded by fluvial and alluvial terraces. This study demonstrates that the shortening rates across both folds accelerated significantly since the onset of folding. It also illustrates the usefulness of a simple geometric folding model and highlights the importance of considering local interactions between tectonic deformation, sedimentation, and erosion

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published versio

Live yeast as a possible modulator of polyunsaturated fatty acid biohydrogenation in the rumen

In dairy cows, several studies focused on the effects of sodium bicarbonate and fibre on ruminal linoleic acid (c9c12-C18:2) biohydrogenation (BH) whereas literature is scarce about the effect of live yeast, used as a feed additive. The objective of this in vivo study was to evaluate the capacity of two dietary feed additives, sodium bicarbonate and live yeast (Strain Sc47), and hay to modulate ruminal BH and particularly conjugated linoleic acids (CLA) and trans-monoenoic acids (t-C18:1) production. Four dry dairy cows fitted with ruminal cannula, were used in a 4×4 Latin square design. They were given a control diet (CD) at a daily feeding rate of 10.4 kg of dry matter/cow supplemented with 100 g/d of sodium bicarbonate or 5 g/d of live yeast or a hay diet formulated to provide the same main fatty acids (FA) as CD during a 14-d experimental period. Ruminal pH and redox potential were measured from 1 h before feeding to 8 h after, and ruminal fluid samples were taken at 5 h after feeding for volatile fatty acids, ammonia and fatty acid determination. In addition to the in vivo experiment, an in vitro experiment was carried out to ascertain the possible mode of action of live yeast on c9c12-C18:2 BH: ruminal fluid was obtained from a donor cow fed with hay and was incubated in batch cultures over 6 h with a 6-pH buffer using starch, urea and grape seed oil as substrates. Results gathered from both experiments suggested that live yeast supplement increased the accumulation of t-C18:1 compared to sodium bicarbonate and prevented the formation of C18:0 which is usually observed when hay is added to a high concentrate diet. The accumulation of t-C18:1 observed in presence of live yeast was probably due to an inhibition of the second reduction step as a result of a more complete isomerisation of c9c12-C18:2

Effect of live yeast on ruminal biohydrogenation. A preliminary in vitro approach

Introduction : Ruminant dietary feed additives such as live yeasts are used on field because of their ability to induce a better diet utilisation. Even if studies on their mode of action are still going on, references are scarce about live yeast diet supplementation and ruminal biohydrogenation (BH) of dietary lipids in dairy cows. During the ruminal BH, some interesting fatty acids (FA), like conjugated linoleic acids (CLA), are synthesised by bacteria, and then could be transferred to milk. This experiment studied live yeast influence on ruminal BH with an in vitro approach. Materials and methods: Ruminal fluid was sucked out from a rumen fistulated dry dairy cow receiving a hay-based diet (57% hay, 43% concentrates) and divided in 10 flasks containing substrates (starch, hay and urea) and a buffer solution (pH 7). In 5 flasks, live Saccharomyces cerevisiae (1010 CFU/g DM, BIOSAF Sc 47, Lesaffre Feed Additives, France) was dosed at 0.15g per flask. All flasks were incubated kept from light and air in a waterbath rotary shaker at 39°C. Two not incubated control flasks without added fat were realized to determine the initial FA amount. After 6h, the incubated flasks were placed into iced water to stop microbial activity and the content was lyophilized for FA extraction and quantification by gas chromatography. Rates and efficiencies of the three reactions composing BH of C18:2 were calculated1. Data were submitted to an analysis of variance. Results and Discussion : Rates and efficiencies of the 3 steps of BH were not significantly modified by live yeast. Composition of FA of control and treated flaks did not strongly differ. The percentage C16:1+C17:0anteiso was twice higher (P0.05), including C18:2 BH intermediates, like trans-11 or trans-10 isomers of CLA and trans-C18:1. Live yeast had no effect in such conditions on the extent of C18:2 (P=0.566) or C18:3 BH (P=0.838), 51% and 54% on average disappeared during incubation, respectively. Conclusion : The fermentative substrate containing hay and the pH were favorable to a high ruminal BH. Live yeast had no effect in such conditions but this work showed that yeast had no adverse effect on BH. Because of live yeast supplementation being advised in case of high concentrate diets inducing ruminal acidosis, further studies will be carried out to investigate live yeast effect on BH in such conditions

Use of resonance Raman spectroscopy to study the phase diagram of PbZr0.52Ti0.48O3

Evidence is presented for the first time that the sharp and continuous spectral changes observed in PbZr0.52Ti0.48O3 (PZT) between 350 and 10 K with the 647.1 nm wavelength are due to a resonance Raman effect. Such a phenomenon can be explained by means of a self-trapped exciton emission oxygen deficient complex (TiTi' - VO-) of PZT powder whose energy is close to the radiation line of the laser. This kind of approach should also be very useful to distinguish the phase transition sequence for other related ferro/ piezoelectric systems