The dressed nonrelativistic electron in a magnetic field

We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the $x_{3}$-axis and with a quantized electromagnetic field. When the interaction between the electron and photons is turned off, the electronic system is assumed to have a ground state of finite multiplicity. Because of the translation invariance along the $x_{3}$-axis, we consider the reduced Hamiltonian associated with the total momentum along the $x_{3}$-axis and, after introducing an ultraviolet cutoff and an infrared regularization, we prove that the reduced Hamiltonian has a ground state if the coupling constant and the total momentum along the $x_{3}$-axis are sufficiently small. Finally we determine the absolutely continuous spectrum of the reduced Hamiltonian.Comment: typos correction

Nonuniform viscosity in the solar nebula and large masses of Jupiter and Saturn

I report a novel theory that nonuniform viscous frictional force in the solar nebula accounts for the largest mass of Jupiter and Saturn and their largest amount of H and He among the planets, two outstanding facts that are unsolved puzzles in our understanding of origin of the Solar System. It is shown that the nebula model of uniform viscosity does not match the present planet masses. By studying current known viscosity mechanisms, I show that viscosity is more efficient in the inner region inside Mercury and the outer region outside Jupiter-Saturn than the intermediate region. The more efficient viscosity drives faster radial inflow of material during the nebula evolution. Because the inflow in the outer region is faster than the intermediate region, the material tends to accumulate in Jupiter-Saturn region which is between the outer and intermediate region. It is demonstrated that the gas trapping time of Jovian planets is longer than the inflow time in the outer region. Therefore the gas already flows to Jupiter-Saturn region before Uranus and Neptune can capture significant gas. But the inflow in the Jupiter-Saturn region is so slow that they can capture large amount of gas before the gas can flow further inward. Hence they have larger masses with larger H and He content than Uranus and Neptune. I also extend the discussion to the masses of the terrestrial planets, especially low mass of Mercury. The advantages of this theory are discussed.Comment: 4 pages, 1 figure, A&A Letters accepte

Interpreting the yield of transit surveys: Are there groups in the known transiting planets population?

Each transiting planet discovered is characterized by 7 measurable quantities, that may or may not be linked together (planet mass, radius, orbital period, and star mass, radius, effective temperature, and metallicity). Correlations between planet mass and period, surface gravity and period, planet radius and star temperature have been previously observed among the known transiting giant planets. Two classes of planets have been previously identified based on their Safronov number. We use the CoRoTlux code to compare simulated events to the sample of discovered planets and test the statistical significance of these correlations. We first generate a stellar field with planetary companions based on radial velocity discoveries and a planetary evolution model, then apply a detection criterion that includes both statistical and red noise sources. We compare the yield of our simulated survey with the ensemble of 31 well-characterized giant transiting planets, using a multivariate logistic analysis to assess whether the simulated distribution matches the known transiting planets. Our multivariate analysis shows that our simulated sample and observations are consistent to 76%. The mass vs. period correlation for giant planets first observed with radial velocity holds with transiting planets. Our model naturally explains the correlation between planet surface gravity and period and the one between planet radius and stellar effective temperature. Finally, we are also able to reproduce the previously observed apparent bimodal distribution of Safronov numbers in 10% of our simulated cases, although our model predicts a continuous distribution. This shows that the evidence for the existence of two groups of planets with different intrinsic properties is not statistically significant.Comment: 17 page

Ion structure in warm dense matter: benchmarking solutions of hypernetted-chain equations by first-principle simulations

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential

Precision Beam Position Monitor for EUROTeV

In the framework of EUROTeV, a Precision Beam Position Monitor (PBPM) has been designed, manufactured and tested. The new PBPM, based on the inductive BPM presently used in the CERN CLIC Test Facility (CTF3), aims to achieve a resolution of 100 nm and an accuracy of 10 μm in a 6 mm aperture. A dedicated test bench has been designed and constructed to fully characterize and optimize the PBPM. This paper describes the final design, presents the test bench results and reports on the beam tests carried out in the CERN CTF3 Linac

A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation

The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the numerically accessible "planetary" parameter regime, and can easily be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.Comment: Submitted to Ap

Napoléon et la vitesse

Guillot G. Napoléon et la vitesse. In: Bulletin de l'Académie Vétérinaire de France tome 122 n°10, 1969. pp. 947-958

Scaling exponents for fracture surfaces in homogenous glass and glassy ceramics

We investigate the scaling properties of post-mortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular a roughness exponent $\zeta\simeq 0.75$ in homogeneous glass and $\zeta\simeq 0.4$ in glassy ceramics. The ranges of length-scales over which these two scalings are observed are shown to be below and above the size of process zone respectively. A model derived from Linear Elastic Fracture Mechanics (LEFM) in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect damage screening occurring for length-scales below the size of the process zone