A new variational approach to the stability of gravitational systems

We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are nonincreasing functions of their microscopic energy are nonlinearly stable by the flow. This was proved at the linear level by several authors based on the pioneering work by Antonov in 1961. Since then, standard variational techniques based on concentration compactness methods as introduced by P.-L. Lions in 1983 have led to the nonlinear stability of subclasses of stationary solutions of ground state type. In this paper, inspired by pioneering works from the physics litterature (Lynden-Bell 94, Wiechen-Ziegler-Schindler MNRAS 88, Aly MNRAS 89), we use the monotonicity of the Hamiltonian under generalized symmetric rearrangement transformations to prove that non increasing steady solutions are local minimizer of the Hamiltonian under equimeasurable constraints, and extract compactness from suitable minimizing sequences. This implies the nonlinear stability of nonincreasing anisotropic steady states under radially symmetric perturbations

The potential of triterpenoids as chemotaxonomic tools to identify and differentiate genuine, adulterated and archaeological balsams

International audiencePlant exudates have been extensively used in the past for different applications related to their olfactory, physical or medical properties. Their identification in archaeological samples relies, notably, on the characterisation of chemotaxonomic molecular markers but is often hampered by the severe alteration of their typical genuine molecular signature due to ageing. Among these exudates, those recovered from Styrax, Liquidambar and Myroxylon tree species – defined as balsams – have been exploited in the past for their pleasant scent and medical properties. They are characterised by a large variety of aromatic compounds, especially of the cinnamate and benzoate series, which can be used to assess their botanical source. These compound series may, however, be subject to alteration over time during exposure to environmental conditions in the case of archaeological material. As a result, their reliability as chemotaxonomic markers to characterise and discriminate archaeological balsams is problematic and questionable. We have, therefore, carried out a comparative analysis of various extant balsams (Styrax officinalis, S. paralleloneurum, S. tonkinensis, Liquidambar styraciflua, L. orientalis and Myroxylon balsamum var. pereirae) using gas chromatography–mass spectrometry to search for more solid lipid markers. The results revealed that a distinction between styrax, liquidambars, Peru and Tolu balsams is possible based on the distribution of pentacyclic triterpenes. The predominance of uncommon 6‑oxygenated derivatives of oleanolic acid among triterpenoids could be specifically related to styrax resins. Liquidambar gums were characterised by the predominance of oleanonic acid together with uncommon 3-epi oleanolic and ursolic acids, whereas Peru balsam was rich in cinnamic and benzoic acids, but devoid of triterpenoids. Thanks to the high specificity of some of these triterpenes, already known for their low volatility and robustness towards alteration processes, they should be considered as reliable molecular tools for the unambiguous identification of archaeological balsams. In addition to archaeological applications, these triterpenic markers might also find an application for the detection of counterfeit balsams

Synthesis of 26-methyl cholestane and identification of cryostanes in mid- Neoproterozoic sediments

International audienceThe biomarker distributions of mid-Neoproterozoic sediments (800–717 million yr, Ma) from various locations are characterized by the occurrence, besides cholestane isomers, of a novel series of C28 steranes, whereas classical C-24 alkylated steranes are absent. These unusual C28 steranes, termed cryostanes, seem to be restricted to pre-Snowball Earth sediments. We report their conclusive identification as 26-methyl cholestanes based on comparison of gas chromatographic (GC) behavior and mass spectrum of the last eluting cryostane isomer with those of a 26-methyl 5α(H),14α(H),17α(H),20R-cholestane standard obtained by way of synthesis. Sterols methylated at C-26 seem to be restricted to some demosponges and, based on molecular clock estimates, demosponges may have emerged in the time interval 800–700 Ma. A sponge origin of cryostanes is thereby conceivable, making cryostanes the oldest molecular markers for animals. However, other biological sources need to be explored, including the wide variety of eukaryotic protists

The transformation of transport policy in Great Britain? 'New Realism' and New Labour's decade of displacement activity

In a 1999 paper, Goodwin announced ‘the transformation of transport policy in Great Britain’. His central point was that consensus was emerging among policy makers and academics based on earlier work including Transport: The New Realism, which rejected previous orthodoxy that the supply of road space could and should be continually expanded to match demand. Instead a combination of investment in public transport, walking and cycling opportunities and – crucially – demand management should form the basis of transport policy to address rising vehicle use and associated increases in congestion and pollution / carbon emissions. This thinking formed the basis of the 1997 Labour government’s ‘sustainable transport’ policy, but after 13 years in power ministers neither transformed policy nor tackled longstanding transport trends. Our main aim in this paper is to revisit the concept of New Realism and re-examine its potential utility as an agent of change in British transport policy. Notwithstanding the outcome of Labour’s approach to transport policy, we find that the central tenets of the New Realism remain robust and that the main barriers to change are related to broader political and governance issues which suppress radical policy innovation

The effects of diagenetic aromatization on the carbon and hydrogen isotopic composition of higher plant di- and triterpenoids: evidence from buried wood

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The Orbital Stability of the Ground States and the Singularity Formation for the Gravitational Vlasov Poisson System

International audienceWe study the gravitational Vlasov Poisson system $f_t+v\cdot\nabla_x f-E\cdot\nabla_vf=0$ where $E(x)=\nabla_x \phi(x)$, $\Delta_x\phi=\rho(x)$, \rho(x)=\int_{\RR^N} f(x,v)dxdv, in dimension $N=3,4$. In dimension $N=3$ where the problem is subcritical, we prove using concentration compactness techniques that every minimizing sequence to a large class of minimization problems attained on steady states solutions are up to a translation shift relatively compact in the energy space. This implies in particular the orbital stability {\it in the energy space} of the spherically symmetric polytropes what improves the nonlinear stability results obtained for this class in \cite{Guo,GuoRein,Dol}. In dimension $N=4$ where the problem is $L^1$ critical, we obtain the polytropic steady states as best constant minimizers of a suitable Sobolev type inequality relating the kinetic and the potential energy. We then derive using an explicit pseudo-conformal symmetry the existence of critical mass finite time blow up solutions, and prove more generally a mass concentration phenomenon for finite time blow up solutions. This is the first result of description of a singularity formation in a Vlasov setting. The global structure of the problem is reminiscent to the one for the focusing non linear Schrödinger equation $iu_t=-\Delta u-|u|^{p-1}u$ in the energy space $H^1(\R^N)$

Betulin-related esters from birch bark tar: Identification, origin and archaeological significance

Birch bark tar, an organic material frequently encountered during archaeological excavations, has been identified from its lipid composition on the cracks of a ceramic dated to the late Neolithic. Lipids of this black substance were dominated by a characteristic triterpenoid assemblage of lupane-related triterpenoids from birch bark together with their thermal degradation products formed during preparation of the tar. Among the latter, four main series of unusual triterpenoid esters have been detected and were postulated to correspond to esters of Delta2-betulin and Delta2-dihydrobetulin based on their mass spectra and hydrolysis experiments. Their conclusive identification has been achieved by synthesis of reference compounds. These compounds most likely originate from the esterification between triterpenoid alcohols related to betulin and fatty acids from suberin formed upon heating of birch bark tar. They could be considered as markers of intense heating during birch bark tar preparation using the “single pot“ procedure

Orbital stability of spherical galactic models

International audienceWe consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture is the stability of spherical models which are nonincreasing radially symmetric steady states solutions. This conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by Antonov in 1961. In a previous work, we derived the stability of anisotropic models under {\it spherically symmetric perturbations} using fundamental monotonicity properties of the Hamiltonian under suitable generalized symmetric rearrangements first observed in the physics litterature. In this work, we show how this approach combined with a {\it new generalized} Antonov type coercivity property implies the orbital stability of spherical models under general perturbations

Characterization and analysis of a Commiphora species germinated from an ancient seed suggests a possible connection to a species mentioned in the Bible

A seed recovered during archaeological excavations of a cave in the Judean desert was germinated, with radiocarbon analysis indicating an age of 993 CE– 1202 calCE. DNA sequencing and phylogenetic analysis identified the seedling as belonging to the angiosperm genus Commiphora Jacq., sister to three Southern African Commiphora species, but unique from all other species sampled to date. The germinated seedling was not closely related to Commiphora species commonly harvested for their fragrant oleoresins including Commiphora gileadensis (L.) C.Chr., candidate for the locally extinct “Judean Balsam” or “Balm of Gilead” of antiquity. GC-MS analysis revealed minimal fragrant compounds but abundance of those associated with multi-target bioactivity and a previously undescribed glycolipid compound series. Several hypotheses are offered to explain the origins, implications and ethnobotanical significance of this unknown Commiphora sp., to the best of our knowledge the first identified from an archaeological site in this region, including identification with a resin producing tree mentioned in Biblical sources and possible agricultural relationship with the historic Judean Balsam