SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page

Polarizabilities of the 87Sr Clock Transition

In this paper, we propose an in-depth review of the vector and tensor polarizabilities of the two energy levels of the 87Sr clock transition whose measurement was reported in [P. G. Westergaard et al., Phys. Rev. Lett. 106, 210801 (2011)]. We conduct a theoretical calculation that reproduces the measured coefficients. In addition, we detail the experimental conditions used for their measurement in two Sr optical lattice clocks, and exhibit the quadratic behaviour of the vector and tensor shifts with the depth of the trapping potential and evaluate their impact on the accuracy of the clock

SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension

We prove that if $t \mapsto u(t) \in \mathrm {BV}(\R)$ is the entropy solution to a $N \times N$ strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields $$u_t + f(u)_x = 0,$$ then up to a countable set of times $\{t_n\}_{n \in \mathbb N}$ the function $u(t)$ is in $\mathrm {SBV}$, i.e. its distributional derivative $u_x$ is a measure with no Cantorian part. The proof is based on the decomposition of $u_x(t)$ into waves belonging to the characteristic families $$u(t) = \sum_{i=1}^N v_i(t) \tilde r_i(t), \quad v_i(t) \in \mathcal M(\R), \ \tilde r_i(t) \in \mathrm R^N,$$ and the balance of the continuous/jump part of the measures $v_i$ in regions bounded by characteristics. To this aim, a new interaction measure \mu_{i,\jump} is introduced, controlling the creation of atoms in the measure $v_i(t)$. The main argument of the proof is that for all $t$ where the Cantorian part of $v_i$ is not 0, either the Glimm functional has a downward jump, or there is a cancellation of waves or the measure $\mu_{i,\mathrm{jump}}$ is positive

Spinel Harzburgite-Derived Silicate Melts Forming Sulfide-Bearing Orthopyroxenite in the Lithosphere. Part 1: Partition Coefficients and Volatile Evolution Accompanying Fluid- and Redox-Induced Sulfide Formation

We report abundances of major trace and volatile elements in an orthopyroxenite vein cutting a sub-arc, mantle-derived, spinel harzburgite xenolith from Kamchatka. The orthopyroxenite contains abundant sulfides and is characterized by the presence of glass (formerly melt) both interstitially and as inclusions in minerals, comparable with similar veins from the West Bismarck arc. The glass formed by quenching of residual melts following crystallization of abundant orthopyroxene, amphibole, and minor olivine and spinel. The interstitial glass has a low-Ti, high-Mg# andesite composition, with a wide range of H2O and S contents but more limited F and Cl variations. We calculate trace element partition coefficients using mineral and glass data, including those for halogens in amphibole, which agree with experimental results from the literature. Despite having a similar, high-Mg# andesite composition, the orthopyroxene-hosted glass inclusions usually contain much more H2O and S than the interstitial glass (4–7 wt% and ∼2,600 ppm, respectively). The initial vein-forming melts were oxidized, recording oxygen fugacity conditions up to ∼1.5 log units above the fayalite–magnetite–quartz oxygen buffer. They intruded the sub-arc mantle lithosphere at ≥1,300°C, where they partially crystallized to form high-Mg# andesitic derivative melts at ca. 1,050–1,100°C. Comparison with literature data on glass-free orthopyroxenite veins from Kamchatka and the glass-bearing ones from West Bismarck reveals fundamental similarities indicating common parental melts, which were originally produced by low-degree melting (≤5%) of spinel harzburgite at ≥1,360°C and ≤1.5 GPa. This harzburgite source likely contained ≤0.05 wt% H2O and a few ppm of halogens. Volatile evolution inferred from glass compositions shows that (i) redox exchange between S6+ in the original melt and Fe2+ in the host mantle minerals, together with (ii) the formation of an S-bearing, (H2O, Cl)-rich hydrothermal fluid from the original melt, provides the conditions for the formation of abundant sulfides in the orthopyroxenites during cooling. During this process, up to 85% of the original melt S content (∼2,600 ppm) is locally precipitated as magmatic and hydrothermal sulfides. As such, melts derived from spinel harzburgite sources can concentrate chalcophile and highly siderophile metals in orthopyroxenite dykes and sills in the lithosphere

The Effect of Polyhydramnios on Cervical Length in Twins: A Controlled Intervention Study in Complicated Monochorionic Pregnancies

Objective: To test the hypothesis that cervical shortening in polyhydramnios reflects the degree of excess amniotic fluid, and increases with normalisation of amniotic fluid volume. Study Design: Prospective cohort study of 40 women with monochorionic twins undergoing interventional procedures between 16-26 weeks. Cervical length was assessed via transvaginal sonography pre-procedure, 1 and 24 hours postprocedure, and results compared between amnioreduction and control procedures. Amniotic fluid index (AFI) was measured pre- and post-procedure. Results: Pre-procedural cervical length correlated with AFI (linear fit = 5.07 -0.04x, R2 = 0.17, P = 0.03) in patients with polyhydramnios (n = 28). Drainage of 2000ml fluid (range 700-3500ml), reduced AFI from 42cm to 21cm (P>0.001). Their pre-procedural cervical length did not change at one (mean Δ:-0.1cm, 95%CI, -0.4 to 0.2) or 24 hours (0.2cm, -0.1 to 0.6) after amnioreduction. There was no change in cervical length at control procedures. Conclusion: Cervical shortening in twins with polyhydramnios does not appear to be an acute process; cervical length can be measured before or after therapeutic procedures. © 2008 Engineer et al

A clock network for geodesy and fundamental science

Leveraging the unrivaled performance of optical clocks in applications in fundamental physics beyond the standard model, in geo-sciences, and in astronomy requires comparing the frequency of distant optical clocks truthfully. Meeting this requirement, we report on the first comparison and agreement of fully independent optical clocks separated by 700 km being only limited by the uncertainties of the clocks themselves. This is achieved by a phase-coherent optical frequency transfer via a 1415 km long telecom fiber link that enables substantially better precision than classical means of frequency transfer. The fractional precision in comparing the optical clocks of three parts in $10^{17}$ was reached after only 1000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than with any other existing frequency transfer method. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.Comment: 14 pages, 3 figures, 1 tabl

Genome-Wide Studies of Histone Demethylation Catalysed by the Fission Yeast Homologues of Mammalian LSD1

In order to gain a more global view of the activity of histone demethylases, we report here genome-wide studies of the fission yeast SWIRM and polyamine oxidase (PAO) domain homologues of mammalian LSD1. Consistent with previous work we find that the two S. pombe proteins, which we name Swm1 and Swm2 (after SWIRM1 and SWIRM2), associate together in a complex. However, we find that this complex specifically demethylates lysine 9 in histone H3 (H3K9) and both up- and down-regulates expression of different groups of genes. Using chromatin-immunoprecipitation, to isolate fragments of chromatin containing either H3K4me2 or H3K9me2, and DNA microarray analysis (ChIP-chip), we have studied genome-wide changes in patterns of histone methylation, and their correlation with gene expression, upon deletion of the swm1+ gene. Using hyper-geometric probability comparisons we uncover genetic links between lysine-specific demethylases, the histone deacetylase Clr6, and the chromatin remodeller Hrp1. The data presented here demonstrate that in fission yeast the SWIRM/PAO domain proteins Swm1 and Swm2 are associated in complexes that can remove methyl groups from lysine 9 methylated histone H3. In vitro, we show that bacterially expressed Swm1 also possesses lysine 9 demethylase activity. In vivo, loss of Swm1 increases the global levels of both H3K9me2 and H3K4me2. A significant accumulation of H3K4me2 is observed at genes that are up-regulated in a swm1 deletion strain. In addition, H3K9me2 accumulates at some genes known to be direct Swm1/2 targets that are down-regulated in the swm1¿ strain. The in vivo data indicate that Swm1 acts in concert with the HDAC Clr6 and the chromatin remodeller Hrp1 to repress gene expression. In addition, our in vitro analyses suggest that the H3K9 demethylase activity requires an unidentified post-translational modification to allow it to act. Thus, our results highlight complex interactions between histone demethylase, deacetylase and chromatin remodelling activities in the regulation of gene expression

Field test of quantum key distribution in the Tokyo QKD Network

A novel secure communication network with quantum key distribution in a metropolitan area is reported. Different QKD schemes are integrated to demonstrate secure TV conferencing over a distance of 45km, stable long-term operation, and application to secure mobile phones.Comment: 21 pages, 19 figure

SBV regularity of Systems of Conservation Laws and Hamilton-Jacobi Equation

We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper