Understanding the behavior of Prometheus and Pandora

We revisit the dynamics of Prometheus and Pandora, two small moons flanking Saturn's F ring. Departures of their orbits from freely precessing ellipses result from mutual interactions via their 121:118 mean motion resonance. Motions are chaotic because the resonance is split into four overlapping components. Orbital longitudes were observed to drift away from predictions based on Voyager ephemerides. A sudden jump in mean motions took place close to the time at which the orbits' apses were antialigned in 2000. Numerical integrations reproduce both the longitude drifts and the jumps. The latter have been attributed to the greater strength of interactions near apse antialignment (every 6.2 yr), and it has been assumed that this drift-jump behavior will continue indefinitely. We re-examine the dynamics of the Prometheus-Pandora system by analogy with that of a nearly adiabatic, parametric pendulum. In terms of this analogy, the current value of the action of the satellite system is close to its maximum in the chaotic zone. Consequently, at present, the two separatrix crossings per precessional cycle occur close to apse antialignment. In this state libration only occurs when the potential's amplitude is nearly maximal, and the “jumps” in mean motion arise during the short intervals of libration that separate long stretches of circulation. Because chaotic systems explore the entire region of phase space available to them, we expect that at other times the Prometheus-Pandora system would be found in states of medium or low action. In a low action state it would spend most of the time in libration, and separatrix crossings would occur near apse alignment. We predict that transitions between these different states can happen in as little as a decade. Therefore, it is incorrect to assume that sudden changes in the orbits only happen near apse antialignment.     

QUEST on DASI: a South Pole CMB polarization experiment

QUEST on DASI is a ground-based, high-sensitivity, high-resolution (ℓ_max2500) experiment designed to map CMB polarization at 100 and 150 GHz and to measure the power spectra from E-modes, B-modes from lensing of the CMB, and B-modes from primordial gravitational waves. The experiment comprises a 2.6 m Cassegrain optical system, equipped with an array of 62 polarization-sensitive bolometers (PSBs), located at the South Pole. The instrument is designed to minimize systematic effects; features include differencing of pairs of orthogonal PSBs within a single feed, a rotatable achromatic waveplate, and axisymmetric rotatable optics. In addition the South Pole location allows both repeatable and highly controlled observations. QUEST on DASI will commence operation in early 2005.     

Magnetic remanence in the Murchison meteorite

Abstract— The Murchison meteorite is a carbonaceous chondrite containing a small amount of chondrules, various inclusions, and matrix with occasional porphyroblasts of olivine and/or pyroxene. It also contains amino acids that may have served as the necessary components for the origin of life. Magnetic analyses of Murchison identify an ultrasoft magnetic component due to superparamagnetism as a significant part of the magnetic remanence. The rest of the remanence may be due to electric discharge in the form of lightning bolts that may have formed the amino acids. The level of magnetic remanence does not support this possibility and points to a minimum ambient field of the remanence acquisition. We support our observation by showing that normalized mineral magnetic acquisition properties establish a calibration curve suitable for rough paleofield determination. When using this approach, 1–2% of the natural remanence left in terrestrial rocks with TRM and/or CRM determines the geomagnetic field intensity irrespective of grain size or type of magnetic mineral (with the exception of hematite). The same method is applied to the Murchison meteorite where the measured meteorite remanence determines the paleofield minimum intensity of 200–2000 nT during and/or after the formation of the parent body.     

Origin of chaos in the Prometheus-Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr⁻¹, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr⁻¹ arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.     

Observations on the ecological importance of salt marshes in the Cumberland Basin,a macrotidal estuary in the Bay of Fundy

The Cumberland Basin, a 118 km² estuary at the head of the Bay of Fundy which has an average tidal range of about 11m, contains large tracts of salt marsh (15% of the area below highest high water). Low marsh (below about 0·9 m above mean high water) is composed almost exclusively of Spartina alterniflora while the vegetation on high marsh is more diverse but dominated by Spartina patens. Because of its higher elevation, high marsh is flooded infrequently for short periods by only extreme high tides. Low marsh is inundated much more frequently by water as much as 4m deep for periods as long as 4 h per tide. Temporal variability in the occurrence of extreme tides influences the flooding frequency of high marsh for any given month and year. Using a modification of Smalley's method, the mean annual net aerial primary production (NAPP) of low and high marsh is estimated to be 272 and 172 g C m^?2, respectively. Vegetation turnover times average 1·0 and 2·0 y for low and high marsh, respectively. Because of abundant tidal energy, much of the low marsh production appears to be exported and distributed widely about the estuary. Since high levels of turbidity suppress phytoplankton production, salt marshes produce approximately half of the carbon fixed photosynthetically in the Cumberland Basin. It is concluded that salt marshes play a major ecological role in the Cumberland Basin.     

On the structure of oscillatory boundary layers

An empirical analysis is performed on the most detailed, recent measurements of turbulent oscillatory boundary layer flow. The measurements show that throughout elevations where the flow can be considered horizontally uniform, one deficit model is sufficient for describing the fundamental mode. Some general properties of the non dimensional velocity deficit D₁(z) appear with striking consistency. First of all the identity $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦ ≡}\text{Arg}\text{D}{}_{\mathrm{<mtext>1</mtext>}}$, which is a theoretical result for smooth laminar flow, seems to hold with great accuracy for a large range of turbulent flow conditions as well. This is of principal theoretical interest because all previous analytical eddy viscosity models as well as numerical mixing length models predict a consistent and fairly large difference between Arg D₁ and $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦}$. If the identity between $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦}$ and Arg D₁ extends all the way to the bed, it means that the bed shear stress leads the free stream velocity by 45 degrees. It is also found that the structure of smooth turbulent oscillatory flows as measured by Kalkanis (1964) corresponds to a sharp maximum in the normalized energy dissipation rate.