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

Assessing impacts to groundwater from CO2-flooding of SACROC and Claytonville oil fields in West Texas

Comparison of groundwater above two Permian Basin oil fields (SACROC Unit and Claytonville Field) near Snyder, Texas should allow us to assess potential impacts of 30 years of CO2-injection. CO2-flooding for enhanced oil recovery (EOR) has been active at SACROC in Scurry County since 1972. Approximately 13.5 million tons per year (MtCO2/yr) are injected with withdrawal/recycling amounting to ~7MtCO2/yr. It is estimated that the site has accumulated more than 55MtCO2; however, no rigorous investigation of overlying groundwater has demonstrated that CO2 is trapped in the subsurface. Mineralogy of reservoir rocks at the Claytonville field in southwestern Fisher County is similar to SACROC. CO2-EOR is scheduled to begin at Claytonville Field in Fisher County in early 2007. Here we have the opportunity to characterize groundwater prior to CO2-injection and establish baseline conditions at Claytonville. Methods of this study will include: (1) examination of existing analyses of saline to fresh water samples collected within an eight-county area encompassing SACROC and Claytonville, (2) additional groundwater sampling for analysis of general chemistry plus field-measured pH, alkalinity, and temperature, stable isotopic ratios of hydrogen (D/H), oxygen (18O/16O), and carbon (13C/12C), and (3) geochemical equilibrium and flowpath modeling. Existing groundwater data are available from previous BEG studies, Texas Water Development Board, Kinder Morgan CO2 Company, and the U. S. Geological Survey. By examining these data we will identify regional groundwater variability and focus additional sampling efforts. The objective of this study is to look for potential impacts to shallow groundwater from deep CO2-injection. In the absence of conduit flow from depth, we don’t expect to see impacts to shallow groundwater, but methodology to demonstrate this to regulators needs to be established. This work is a subset of the Southwest Regional Partnership on Carbon Sequestration Phase 2studies funded by the Department of Energy (DOE) in cooperation with industry and government partners.Bureau of Economic Geolog

Evolution of Exoplanets and their Parent Stars

Studying exoplanets with their parent stars is crucial to understand their population, formation and history. We review some of the key questions regarding their evolution with particular emphasis on giant gaseous exoplanets orbiting close to solar-type stars. For masses above that of Saturn, transiting exoplanets have large radii indicative of the presence of a massive hydrogen-helium envelope. Theoretical models show that this envelope progressively cools and contracts with a rate of energy loss inversely proportional to the planetary age. The combined measurement of planetary mass, radius and a constraint on the (stellar) age enables a global determination of the amount of heavy elements present in the planet interior. The comparison with stellar metallicity shows a correlation between the two, indicating that accretion played a crucial role in the formation of planets. The dynamical evolution of exoplanets also depends on the properties of the central star. We show that the lack of massive giant planets and brown dwarfs in close orbit around G-dwarfs and their presence around F-dwarfs are probably tied to the different properties of dissipation in the stellar interiors. Both the evolution and the composition of stars and planets are intimately linked.Comment: appears in The age of stars - 23rd Evry Schatzman School on Stellar Astrophysics, Roscoff : France (2013

Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks

Planetesimals in gaseous protoplanetary disks may grow by collecting dust particles. Hydrodynamical studies show that small particles generally avoid collisions with the planetesimals because they are entrained by the flow around them. This occurs when $St$, the Stokes number, defined as the ratio of the dust stopping time to the planetesimal crossing time, becomes much smaller than unity. However, these studies have been limited to the laminar case, whereas these disks are believed to be turbulent. We want to estimate the influence of gas turbulence on the dust-planetesimal collision rate and on the impact speeds. We used three-dimensional direct numerical simulations of a fixed sphere (planetesimal) facing a laminar and turbulent flow seeded with small inertial particles (dust) subject to a Stokes drag. A no-slip boundary condition on the planetesimal surface is modeled via a penalty method. We find that turbulence can significantly increase the collision rate of dust particles with planetesimals. For a high turbulence case (when the amplitude of turbulent fluctuations is similar to the headwind velocity), we find that the collision probability remains equal to the geometrical rate or even higher for $St\geq 0.1$, i.e., for dust sizes an order of magnitude smaller than in the laminar case. We derive expressions to calculate impact probabilities as a function of dust and planetesimal size and turbulent intensity

Twisting algebras using non-commutative torsors

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchange

Inverse scattering at fixed energy for layered media

AbstractIn this article we show that exponentially decreasing perturbations of the sound speed in a layered medium can be recovered from the scattering amplitude at fixed energy. We consider the unperturbed equation utt = c02(xn)δu in ℝ×ℝ, where n ≥ 3. The unperturbed sound speed, c0(xn), is assumed to be bounded, strictly positive, and constant outside a bounded interval on the real axis. The perturbed sound speed, c(x), satisfies ¦c.(x) - co(xn)¦ < C exp(−δ¦x¦) for some δ > 0. Our work is related to the recent results of H. Isozaki (J. Diff. Eq. 138) on the case where c0 takes the constant values c+ and c− on the positive and negative half-lines, and R. Weder on the case c0 = c+ for xn > h, c0 = ch, for 0 < xn, < h, and c0 = c− for xn < 0 (IIMAS-UNAM Preprint 70, November, 1997)

A correlation between the heavy element content of transiting extrasolar planets and the metallicity of their parent stars

Nine extrasolar planets with masses between 110 and 430M are known to transit their star. The knowledge of their masses and radii allows an estimate of their composition, but uncertainties on equations of state, opacities and possible missing energy sources imply that only inaccurate constraints can be derived when considering each planet separately. Aims: We seek to better understand the composition of transiting extrasolar planets by considering them as an ensemble, and by comparing the obtained planetary properties to that of the parent stars. Methods: We use evolution models and constraints on the stellar ages to derive the mass of heavy elements present in the planets. Possible additional energy sources like tidal dissipation due to an inclined orbit or to downward kinetic energy transport are considered. Results: We show that the nine transiting planets discovered so far belong to a quite homogeneous ensemble that is characterized by a mass of heavy elements that is a relatively steep function of the stellar metallicity, from less than 20 earth masses of heavy elements around solar composition stars, to up to 100M for three times the solar metallicity (the precise values being model-dependant). The correlation is still to be ascertained however. Statistical tests imply a worst-case 1/3 probability of a false positive. Conclusions: Together with the observed lack of giant planets in close orbits around metal-poor stars, these results appear to imply that heavy elements play a key role in the formation of close-in giant planets. The large masses of heavy elements inferred for planets orbiting metal rich stars was not anticipated by planet formation models and shows the need for alternative theories including migration and subsequent collection of planetesimals.Comment: Astronomy and Astrophysics 0 (2006) in pres

Rainy downdrafts in abyssal atmospheres

Results from Juno's microwave radiometer indicate non-uniform mixing of ammonia vapor in Jupiter's atmosphere down to tens of bars, far beneath the cloud level. Helioseismic observations suggest solar convection may require narrow, concentrated downdrafts called entropy rain to accommodate the Sun's luminosity. Both observations suggest some mechanism of non-local convective transport. We seek to predict the depth that a concentrated density anomaly can reach before efficiently mixing with its environment in bottomless atmospheres. We modify classic self-similar analytical models of entraining thermals to account for the compressibility of an abyssal atmosphere. We compare these models to the output of high resolution three dimensional fluid dynamical simulations to more accurately model the chaotic influence of turbulence. We find that localized density anomalies propagate down to ~3-8 times their initial size without substantially mixing with their environment. Our analytic model accurately predicts the initial flow, but the self-similarity assumption breaks down after the flow becomes unstable at a characteristic penetration depth. In the context of Jupiter, our findings suggest that precipitation concentrated into localized downdrafts of size ~20km can coherently penetrate to on the order of a hundred kilometers (tens of bars) beneath its initial vaporization level without mixing with its environment. This finding is consistent with expected convective storm length-scales, and Juno MWR measurements of ammonia depletion. Compositional gradients of volatiles beneath their cloud levels may be common on stormy giant planets. In the context of the Sun, we find that turbulent downdrafts in abyssal atmospheres cannot maintain their coherence through the Sun's convective layer, a potential challenge for the entropy rain hypothesis.Comment: 20 pages, 16 figures. Accepted by A&