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

Squeezed tensor non-Gaussianity in non-attractor inflation

We investigate primordial tensor non-Gaussianity in single field inflation, during a phase of non-attractor evolution when the spectrum of primordial tensor modes can be enhanced to a level detectable at interferometer scales. Making use of a tensor duality we introduced in arXiv:1808.10475, we analytically compute the full bispectrum of primordial tensor fluctuations during the non-attractor era. During this epoch the shape of the tensor bispectrum is enhanced in the squeezed limit, its amplitude can be amplified with respect to slow-roll models, and tensor non-Gaussianity can exhibit a scale dependence distinctive of our set-up. We prove that our results do not depend on the frame used for the calculations. Squeezed tensor non-Gaussianity induces a characteristic quadrupolar anisotropy on the power spectrum of the stochastic background of primordial tensor perturbations. As a step to make contact with gravitational wave experiments, we discuss the response function of a ground based Michelson interferometer to a gravitational wave background with such a feature.Comment: 34 pages, 4 figure

Potential pitfalls of modelling ribosomal RNA data in phylogenetic tree reconstruction: Evidence from case studies in the Metazoa

<p>Abstract</p> <p>Background</p> <p>Failure to account for covariation patterns in helical regions of ribosomal RNA (rRNA) genes has the potential to misdirect the estimation of the phylogenetic signal of the data. Furthermore, the extremes of length variation among taxa, combined with regional substitution rate variation can mislead the alignment of rRNA sequences and thus distort subsequent tree reconstructions. However, recent developments in phylogenetic methodology now allow a comprehensive integration of secondary structures in alignment and tree reconstruction analyses based on rRNA sequences, which has been shown to correct some of these problems. Here, we explore the potentials of RNA substitution models and the interactions of specific model setups with the inherent pattern of covariation in rRNA stems and substitution rate variation among loop regions.</p> <p>Results</p> <p>We found an explicit impact of RNA substitution models on tree reconstruction analyses. The application of specific RNA models in tree reconstructions is hampered by interaction between the appropriate modelling of covarying sites in stem regions, and excessive homoplasy in some loop regions. RNA models often failed to recover reasonable trees when single-stranded regions are excessively homoplastic, because these regions contribute a greater proportion of the data when covarying sites are essentially downweighted. In this context, the RNA6A model outperformed all other models, including the more parametrized RNA7 and RNA16 models.</p> <p>Conclusions</p> <p>Our results depict a trade-off between increased accuracy in estimation of interdependencies in helical regions with the risk of magnifying positions lacking phylogenetic signal. We can therefore conclude that caution is warranted when applying rRNA covariation models, and suggest that loop regions be independently screened for phylogenetic signal, and eliminated when they are indistinguishable from random noise. In addition to covariation and homoplasy, other factors, like non-stationarity of substitution rates and base compositional heterogeneity, can disrupt the signal of ribosomal RNA data. All these factors dictate sophisticated estimation of evolutionary pattern in rRNA data, just as other molecular data require similarly complicated (but different) corrections.</p

Effects of Restrained Sampling Space and Nonplanar Amino Groups on Free-Energy Predictions for RNA with Imino and Sheared Tandem GA Base Pairs Flanked by GC, CG, iGiC or iCiG Base Pairs

Guanine-adenine (GA) base pairs play important roles in determining the structure, dynamics, and stability of RNA. In RNA internal loops, GA base pairs often occur in tandem arrangements and their structure is context and sequence dependent. Calculations reported here test the thermodynamic integration (TI) approach with the amber99 force field by comparing computational predictions of free energy differences with the free energy differences expected on the basis of NMR determined structures of the RNA motifs (5′-GCGGACGC-3′)2, (5′-GCiGGAiCGC-3′)2, (5′-GGCGAGCC-3′)2, and (5′-GGiCGAiGCC-3′)2. Here, iG and iC denote isoguanosine and isocytidine, which have amino and carbonyl groups transposed relative to guanosine and cytidine. The NMR structures show that the GA base pairs adopt either imino (cis Watson−Crick/Watson−Crick A-G) or sheared (trans Hoogsteen/Sugar edge A-G) conformations depending on the identity and orientation of the adjacent base pair. A new mixing function for the TI method is developed that allows alchemical transitions in which atoms can disappear in both the initial and final states. Unrestrained calculations gave ΔG° values 2−4 kcal/mol different from expectations based on NMR data. Restraining the structures with hydrogen bond restraints did not improve the predictions. Agreement with NMR data was improved by 0.7 to 1.5 kcal/mol, however, when structures were restrained with weak positional restraints to sample around the experimentally determined NMR structures. The amber99 force field was modified to partially include pyramidalization effects of the unpaired amino group of guanosine in imino GA base pairs. This provided little or no improvement in comparisons with experiment. The marginal improvement is observed when the structure has potential cross-strand out-of-plane hydrogen bonding with the G amino group. The calculations using positional restraints and a nonplanar amino group reproduce the signs of ΔG° from the experimental results and are, thus, capable of providing useful qualitative insights complementing the NMR experiments. Decomposition of the terms in the calculations reveals that the dominant terms are from electrostatic and interstrand interactions other than hydrogen bonds in the base pairs. The results suggest that a better description of the backbone is key to reproducing the experimental free energy results with computational free energy predictions

Probing the inflationary particle content: extra spin-2 field

We study how inflationary observables associated with primordial tensor modes are affected by coupling the minimal field content with an extra spin-2 particle during inflation. We work with a model that is ghost-free at the fully non-linear level and show how the new degrees of freedom modify standard consistency relations for the tensor bispectrum. The extra interacting spin-2 field is necessarily massive and unitarity dictates its mass be in the $m \gtrsim H$ range. Despite the fact that this bound selects a decaying solution for the corresponding tensor mode, cosmological correlators still carry the imprints of such "fossil" fields. Remarkably, fossil(s) of spin $\geq 1$ generate distinctive anisotropies in observables such as the tensor power spectrum. We show how this plays out in our set-up.Comment: 25 pages, 3 figure

Effect of short-term ageing temperature on bitumen properties

© 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Properties of asphalt mixtures after ageing are fundamental parameters in determining long-term performance (e.g. durability) of these materials. With increasing popularity of reduced temperature mixtures, such as warm-mix asphalt, WMA, the question remains how a reduction in short-term ageing affects the properties after long-term ageing of bituminous materials. This paper aims to improve our understanding of the effect of asphalt manufacturing temperature on ageing and the resulting mechanical properties of bituminous binder by studying the effect of short- and long-term ageing of different bitumen samples as a function of short-term ageing temperatures. For this purpose, round robin experiments were conducted within the RILEM technical committee (TC) 252 chemo-mechanical characterisation of bituminous materials by 10 laboratories from 5 countries using four binders of the same grade (70/100 pen) from different crude sources. The short-term ageing was carried out using the standard procedure for rolling thin film oven test (RTFOT), but varying the temperatures. Long-term ageing was carried out using the standard procedure for pressure aging vessel (PAV) in addition to RTFOT. For the mechanical characterisation, rheological data were determined by using the dynamic shear rheometer (DSR) and conventional tests, with needle penetration and softening point using the ring and ball method. The results show that although different short-term ageing temperatures showed a significant difference in the mechanical properties of the binders, these differences vanished after long-term ageing with PAV