Stability of the Brascamp-Lieb constant and applications

We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp-Lieb inequality which have arisen recently in harmonic analysis

Sub-wavelength lithography over extended areas

We demonstrate a systematic approach to sub-wavelength resolution lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of $\lambda/[2(N+1)]$ by using a particular $2 M$-photon, multi-mode entangled state, where $N < M$, and banks of birefringent plates. By preparing a statistically mixed such a state one can form any pixel pattern on a $(N+1) 2^{M-N} \times (N+1) 2^{M-N}$ pixel grid occupying a square with a side of $L=2^{M-N-1}$ wavelengths. Hence, there is a trade-off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under non-ideal conditions, albeit with somewhat poorer performance.Comment: 8 pages, 8 figures, 1 table. Written in RevTe

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure

Crystal structure of rhodopsin in complex with a mini-G_o sheds light on the principles of G protein selectivity

Selective coupling of G protein (heterotrimeric guanine nucleotide–binding protein)–coupled receptors (GPCRs) to specific Gα-protein subtypes is critical to transform extracellular signals, carried by natural ligands and clinical drugs, into cellular responses. At the center of this transduction event lies the formation of a signaling complex between the receptor and G protein. We report the crystal structure of light-sensitive GPCR rhodopsin bound to an engineered mini-Go protein. The conformation of the receptor is identical to all previous structures of active rhodopsin, including the complex with arrestin. Thus, rhodopsin seems to adopt predominantly one thermodynamically stable active conformation, effectively acting like a “structural switch,” allowing for maximum efficiency in the visual system. Furthermore, our analysis of the well-defined GPCR–G protein interface suggests that the precise position of the carboxyl-terminal “hook-like” element of the G protein (its four last residues) relative to the TM7/helix 8 (H8) joint of the receptor is a significant determinant in selective G protein activation

Saving Super-Earths:Interplay between Pebble Accretion and Type I Migration

Overcoming type I migration and preventing low-mass planets from spiralling into the central star is a long-studied topic. It is well known that outward migration is possible in viscously heated disks relatively close to the central star because the entropy gradient can be sufficiently steep for the positive corotation torque to overcome the negative Lindblad torque. Yet efficiently trapping planets in this region remains elusive. Here we study disk conditions that yield outward migration for low-mass planets under specific planet migration prescriptions. In a steady-state disk model with a constant α-viscosity, outward migration is only possible when the negative temperature gradient exceeds ∼0.87. We derive an implicit relation for the highest mass at which outward migration is possible as a function of viscosity and disk scale height. We apply these criteria, using a simple power-law disk model, to planets that have reached their pebble isolation mass after an episode of rapid accretion. It is possible to trap planets with the pebble isolation mass farther than the inner edge of the disk provided that α crit 0.004 for disks older than 1 Myr. In very young disks, the high temperature causes the planets to grow to masses exceeding the maximum for outward migration. As the disk evolves, these more massive planets often reach the central star, generally only toward the end of the disk lifetime. Saving super-Earths is therefore a delicate interplay between disk viscosity, the opacity profile, and the temperature gradient in the viscously heated inner disk

Explaining millimeter-sized particles in brown dwarf disks

Context. Planets have been detected around a variety of stars, including low-mass objects, such as brown dwarfs. However, such extreme cases are challenging for planet formation models. Recent sub-millimeter observations of disks around brown dwarf measured low spectral indices of the continuum emission that suggest that dust grains grow to mm-sizes even in these very low mass environments. Aims. To understand the first steps of planet formation in scaled-down versions of T-Tauri disks, we investigate the physical conditions that can theoretically explain the growth from interstellar dust to millimeter-sized grains in disks around brown dwarf. Methods. We modeled the evolution of dust particles under conditions of low-mass disks around brown dwarfs. We used coagulation, fragmentation, and disk-structure models to simulate the evolution of dust, with zero and non-zero radial drift. For the non-zero radial drift, we considered strong inhomogeneities in the gas surface density profile that mimic long-lived pressure bumps in the disk. We studied different scenarios that could lead to an agreement between theoretical models and the spectral slope found by millimeter observations. Results. We find that fragmentation is less likely and rapid inward drift is more significant for particles in brown dwarf disks than in T-Tauri disks. We present different scenarios that can nevertheless explain millimeter-sized grains. As an example, a model that combines the following parameters can fit the millimeter fluxes measured for brown dwarf disks: strong pressure inhomogeneities of ~40% of amplitude, a small radial extent ~15 AU, a moderate turbulence strength α_(turb) = 10^(-3), and average fragmentation velocities for ices v_f = 10 m s^(-1)

Transpacific transport of ozone pollution and the effect of recent Asian emission increases on air quality in North America: an integrated analysis using satellite, aircraft, ozonesonde, and surface observations

We use an ensemble of aircraft, satellite, sonde, and surface observations for April–May 2006 (NASA/INTEX-B aircraft campaign) to better understand the mechanisms for transpacific ozone pollution and its implications for North American air quality. The observations are interpreted with a global 3-D chemical transport model (GEOS-Chem). OMI NO&lt;sub&gt;2&lt;/sub&gt; satellite observations constrain Asian anthropogenic NO&lt;sub&gt;x&lt;/sub&gt; emissions and indicate a factor of 2 increase from 2000 to 2006 in China. Satellite observations of CO from AIRS and TES indicate two major events of Asian transpacific pollution during INTEX-B. Correlation between TES CO and ozone observations shows evidence for transpacific ozone pollution. The semi-permanent Pacific High and Aleutian Low cause splitting of transpacific pollution plumes over the Northeast Pacific. The northern branch circulates around the Aleutian Low and has little impact on North America. The southern branch circulates around the Pacific High and some of that air impacts western North America. Both aircraft measurements and model results show sustained ozone production driven by peroxyacetylnitrate (PAN) decomposition in the southern branch, roughly doubling the transpacific influence from ozone produced in the Asian boundary layer. Model simulation of ozone observations at Mt. Bachelor Observatory in Oregon (2.7 km altitude) indicates a mean Asian ozone pollution contribution of 9&amp;plusmn;3 ppbv to the mean observed concentration of 54 ppbv, reflecting mostly an enhancement in background ozone rather than episodic Asian plumes. Asian pollution enhanced surface ozone concentrations by 5–7 ppbv over western North America in spring 2006. The 2000–2006 rise in Asian anthropogenic emissions increased this influence by 1–2 ppbv