Boussinesq dynamics at a cloud edge: Theory and simulation

A consequence of air becoming increasingly less dense with altitude is that the vertical displacement of air against gravity results in up and down oscillatory motion -- much like the restoring force of a spring trying to maintain its equilibrium. This gravity-driven buoyancy effect is what sustains the vertical atmospheric motions known as gravity waves. Just as density decreases with height, the atmosphere is also stratified in its other thermodynamic properties. It becomes lower in pressure and generally cooler with height. When air is displaced vertically, with respect to this stratification, it alters the local thermodynamic state. Additionally, when moisture is included it can exist in either its vapour phase or as suspended liquid water droplets, the latter of which defines the presence of cloud. Altering the moist thermodynamic state can lead to the condensation and evaporation of water. In this way, gravity waves can impact the formation and dynamics of cloud. In this thesis, a simplified model is developed extending the classical Boussinesq approximation for gravity waves to include the effects of vapour-liquid phase change. The result is a mathematical framework that couples the fluid dynamics of gravity waves to the thermodynamics of moisture giving a theory that describes the geometrical evolution of cloud. From this model a particular wave-cloud interaction is identified which has a gravity wave trapped in the clear region below a cloud layer. This is commonly known as a waveguide or wave duct. In this setting, vertical motions of the wave lead to the phase change of water at the cloud-edge boundary resulting in a newly identified mechanism for wave propagation on the edge of cloud. This dynamical solution is constructed within the full physics numerical model ``cm1.\u27\u27 This represents a first analytically derived moist dynamical solution realized within a numerical weather model. A quantitative comparison of the cm1 computed and approximate Boussinesq solutions show a high degree of agreement in the dynamics. This validates that the moist physics of cm1 are true to the Boussinesq dynamical analysis and illustrates that the cloud-trapped wave-duct solution is achievable in idealized atmospheric conditions

Human middle temporal cortex, perceptual bias, and perceptual memory for ambiguous three-dimensional motion

When faced with inconclusive or conflicting visual input human observers experience one of multiple possible perceptions. One factor that determines perception of such an ambiguous stimulus is how the same stimulus was perceived on previous occasions, a phenomenon called perceptual memory. We examined perceptual memory of an ambiguous motion stimulus while applying transcranial magnetic stimulation (TMS) to the motion-sensitive areas of the middle temporal cortex (hMT+). TMS increased the predominance of whichever perceptual interpretation was most commonly reported by a given observer at baseline, with reduced perception of the less favored interpretation. This increased incidence of the preferred percept indicates impaired long-term buildup of perceptual memory traces that normally act against individual percept biases. We observed no effect on short-term memory traces acting from one presentation to the next. Our results indicate that hMT+ is important for the long-term buildup of perceptual memory for ambiguous motion stimuli

Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation (Hansen 2009, Walsh et al. 2011) has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk--a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies--the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as `primitive' bodies). We find here that the planets will accrete on order 1-2% of their total mass from primitive planetesimals scattered onto planet-crossing orbits during the formation of the planets. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. While the radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system, we find that the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event

The Phase Diagram of 1-in-3 Satisfiability Problem

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure

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http://archive.org/details/effectoffalsecon00walsNAN

Debris disks as signposts of terrestrial planet formation. II Dependence of exoplanet architectures on giant planet and disk properties

We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple unstable gas giants. We previously showed that the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and debris disks. Here we present new simulations that show that this connection is qualitatively robust to changes in: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk. We discuss how variations in these parameters affect the evolution. Systems with equal-mass giant planets undergo the most violent instabilities, and these destroy both terrestrial planets and the outer planetesimal disks that produce debris disks. In contrast, systems with low-mass giant planets efficiently produce both terrestrial planets and debris disks. A large fraction of systems with low-mass outermost giant planets have stable gaps between these planets that are frequently populated by planetesimals. Planetesimal belts between outer giant planets may affect debris disk SEDs. If Earth-mass seeds are present in outer planetesimal disks, the disks radially spread to colder temperatures. We argue that this may explain the very low frequency of > 1 Gyr-old solar-type stars with observed 24 micron excesses. Among the (limited) set of configurations explored, the best candidates for hosting terrestrial planets at ~1 AU are stars older than 0.1-1 Gyr with bright debris disks at 70 micron but with no currently-known giant planets. These systems combine evidence for rocky building blocks, with giant planet properties least likely to undergo destructive dynamical evolution. We predict an anti-correlation between debris disks and eccentric giant planets, and a positive correlation between debris disks and terrestrial planets.Comment: Astronomy and Astrophysics, in press. Movies from simulations are at http://www.obs.u-bordeaux1.fr/e3arths/raymond/movies_debris.htm

Scanning-probe Single-electron Capacitance Spectroscopy

The integration of low-temperature scanning-probe techniques and single-electron capacitance spectroscopy represents a powerful tool to study the electronic quantum structure of small systems - including individual atomic dopants in semiconductors. Here we present a capacitance-based method, known as Subsurface Charge Accumulation (SCA) imaging, which is capable of resolving single-electron charging while achieving sufficient spatial resolution to image individual atomic dopants. The use of a capacitance technique enables observation of subsurface features, such as dopants buried many nanometers beneath the surface of a semiconductor material. In principle, this technique can be applied to any system to resolve electron motion below an insulating surface. As in other electric-field-sensitive scanned-probe techniques, the lateral spatial resolution of the measurement depends in part on the radius of curvature of the probe tip. Using tips with a small radius of curvature can enable spatial resolution of a few tens of nanometers. This fine spatial resolution allows investigations of small numbers (down to one) of subsurface dopants. The charge resolution depends greatly on the sensitivity of the charge detection circuitry; using high electron mobility transistors (HEMT) in such circuits at cryogenic temperatures enables a sensitivity of approximately 0.01 electrons/Hz[superscript ½] at 0.3 K[superscript 5].National Science Foundation (U.S.) (DMR-0305461)National Science Foundation (U.S.) (DMR-0906939)National Science Foundation (U.S.) (DMR-0605801)Michigan State University. Institute for Quantum Science

A low mass for Mars from Jupiter's early gas-driven migration

Jupiter and Saturn formed in a few million years (Haisch et al. 2001) from a gas-dominated protoplanetary disk, and were susceptible to gas-driven migration of their orbits on timescales of only ~100,000 years (Armitage 2007). Hydrodynamic simulations show that these giant planets can undergo a two-stage, inward-then-outward, migration (Masset & Snellgrove 2001, Morbidelli & Crida 2007, Pierens & Nelson 2008). The terrestrial planets finished accreting much later (Klein et al. 2009), and their characteristics, including Mars' small mass, are best reproduced by starting from a planetesimal disk with an outer edge at about one astronomical unit from the Sun (Wetherill 1978, Hansen 2009) (1 AU is the Earth-Sun distance). Here we report simulations of the early Solar System that show how the inward migration of Jupiter to 1.5 AU, and its subsequent outward migration, lead to a planetesimal disk truncated at 1 AU; the terrestrial planets then form from this disk over the next 30-50 million years, with an Earth/Mars mass ratio consistent with observations. Scattering by Jupiter initially empties but then repopulates the asteroid belt, with inner-belt bodies originating between 1 and 3 AU and outer-belt bodies originating between and beyond the giant planets. This explains the significant compositional differences across the asteroid belt. The key aspect missing from previous models of terrestrial planet formation is the substantial radial migration of the giant planets, which suggests that their behaviour is more similar to that inferred for extrasolar planets than previously thought.Comment: 12 pages, 4 figures + Supplementary Material 46 pages, 10 figure