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

Measurement of the scalar third-order electric polarizability of the Cs ground state using coherent-population-trapping spectroscopy in Ramsey geometry

The ac-Stark shift induced by blackbody radiation is a major source of systematic uncertainty in present-day cesium microwave frequency standards. The shift is parametrized in terms of a third-order electric polarizability α(3)0 that can be inferred from the static electric-field displacement of the clock transition resonance. In this paper, we report on an all-optical coherent-population-trapping pump-probe experiment measuring the differential polarizability Δα(3)0=α(3)0(F=4)−α(3)0(F=3) on a thermal Cs atomic beam, from which we infer α(3)0(F=4)=2.023(6)stat(9)systHz/(kV/cm)2, which corresponds to a scalar Stark shift parameter ks=−2.312(7)stat(10)systHz/(kV/cm)2. The result agrees within two standard deviations with a recent measurement in an atomic fountain, and rules out another recent result obtained in a Cs vapor cell

Petrology and geochronology of "muscovite age standard" B4M

Muscovite B4M, distributed in 1961 as an age standard, was ground under ethanol. Five grain size fractions were obtained and characterized by X-ray diffraction. They display a mixing trend between a phengitic (enriched in the fraction 20 µm). High-pressure phengite is preserved as a relict in retrograde muscovite. Electron microprobe analyses of the distributed mineral separate reveal at least four white mica populations based on Si, Al, Mg, Na, Fe and F. Rb/K ratios vary by one order of magnitude. Rb–Sr analyses link the mineralogical heterogeneity to variable Rb/Sr and 87Sr/86Sr ratios. The grain size fractions define no internal isochron. Relict fine-grained phengite gives older ages than coarse-grained retrograde greenschist facies muscovite. The inverse grain size–age relationship also characterizes 39Ar/40Ar analyses. Cl/K anticorrelates with step ages: Cl-rich coarse muscovite is younger than Cl-poor fine relict phengite. Sr and Ar preserve a similar isotopic inheritance despite peak metamorphism reaching 635±20 °C. A suitable mineral standard requires that its petrological equilibrium first be demonstrated. Relicts and retrograde reaction textures are a guarantee of isotopic disequilibrium and heterogeneous ages within single crystal at the micrometre scale

Hamilton Jacobi Equations with Obstacles

We consider a problem in the theory of optimal control proposed for the first time by Bressan. We characterize the associated minimum time function using tools from geometric measure theory and we obtain, as a corollary, an existence theorem for a related variational proble

CPT-pump-probe measurement of the Cs clock transition DC Stark shift

We report progress in measuring the third order electric polarizability of the Cs ground states using a Ramsey pump-probe experiment on coherent population trapped (CPT) atoms in a thermal atomic beam. We give a short description of the apparatus as well as the Fourier transform method used to monitor the phase and frequency of the Ramsey signal. Analysis of a typical data set is shown, proving the consistency of the method. We show that the motional magnetic field phase shift can be used to test the reliability of the electric field modeling. Finally, we give a preliminary value for the Cs ground state polarizability and compare it to previous published values of the DC Stark shift

High frequency guided wave propagation in monocrystalline silicon wafers

Monocrystalline silicon wafers are widely used in the photovoltaic industry for solar panels with high conversion efficiency. The cutting process can introduce micro-cracks in the thin wafers and lead to varying thickness. High frequency guided ultrasonic waves are considered for the structural monitoring of the wafers. The anisotropy of the monocrystalline silicon leads to variations of the wave characteristics, depending on the propagation direction relative to the crystal orientation. Full three-dimensional Finite Element simulations of the guided wave propagation were conducted to visualize and quantify these effects for a line source. The phase velocity (slowness) and skew angle of the two fundamental Lamb wave modes (first anti-symmetric mode A0 and first symmetric mode S0) for varying propagation directions relative to the crystal orientation were measured experimentally. Selective mode excitation was achieved using a contact piezoelectric transducer with a custom-made wedge and holder to achieve a controlled contact pressure. The out-of-plane component of the guided wave propagation was measured using a noncontact laser interferometer. Good agreement was found with the simulation results and theoretical predictions based on nominal material properties of the silicon wafe

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