Study of bi-orthogonal modes in magnetic butterflies

We present a bi-orthogonal decomposition of the temporal and latitudinal distribution of solar magnetic fields from synoptic magnetograms. Results are compared with a similar decomposition of the distribution of sunspots since 1874. We show that the butterfly diagrams can be interpreted as the result of approximately constant amplitudes and phases of two oscillations with periods close to 22 years. A clear periodicity of 7 years can also be identified in the most energetic modes of both spatio-temporal series. These results can be used to obtain relevant information concerning the physics of the solar dynamo.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

39Ar‐40Ar “ages” and origin of excess 40Ar in Martian shergottites

Abstract— We report new ³⁹Ar‐⁴⁰Ar measurements on 15 plagioclase, pyroxene, and/or whole rock samples of 8 Martian shergottites. All age spectra suggest ages older than the meteorite formation ages, as defined by Sm‐Nd and Rb‐Sr isochrons. Employing isochron plots, only Los Angeles plagioclase and possibly Northwest Africa (NWA) 3171 plagioclase give ages in agreement with their formation ages. Isochrons for all shergottite samples reveal the presence of trapped Martian ⁴⁰Ar (⁴⁰Ar_xs), which exists in variable amounts in different lattice locations. Some ⁴⁰Ar_xs is uniformly distributed throughout the lattice, resulting in a positive isochron intercept, and other ⁴⁰Ar_xs occurs in association with K‐bearing minerals and increases the isochron slope. These samples demonstrate situations where linear Ar isochrons give false ages that are too old. After subtracting ⁴⁰Ar*that would accumulate by ⁴⁰K decay since meteorite formation and small amounts of terrestrial ⁴⁰Ar, all young age samples give similar ⁴⁰Ar_xs concentrations of ?1–2 × 10^?6cm³/g, but a variation in K content by a factor of ?80. Previously reported NASA Johnson Space Center data for Zagami, Shergotty, Yamato (Y‐) 000097, Y‐793605, and Queen Alexandra Range (QUE) 94201 shergottites show similar concentrations of ⁴⁰Ar_xs to the new meteorite data reported here. Similar ⁴⁰Ar_xs in different minerals and meteorites cannot be explained as arising from Martian atmosphere carried in strongly shocked phases such as melt veins. We invoke the explanation given by Bogard and Park (2008) for Zagami, that this ⁴⁰Ar_xs in shergottites was acquired from the magma. Similarity in ⁴⁰Ar_xs among shergottites may reveal common magma sources and/or similar magma generation and emplacement processes.     

Lensing, reddening and extinction effects of Mg ii absorbers from z= 0.4 to 2

Using a sample of almost 7000 strong Mg  ii absorbers with   W ₀ > 1 Å  and  0.4 < z < 2.2  detected in the SDSS DR4 data set, we investigate the gravitational lensing and dust extinction effects they induce on background quasars. After carefully quantifying several selection biases, we isolate the reddening effects as a function of redshift and absorber rest equivalent width, W ₀. We find the amount of dust to increase with cosmic time as  τ( z ) ∝ (1 + z )^−1.1±0.4  , following the evolution of cosmic star density or integrated star formation rate. We measure the reddening effects over a factor of 30 in E ( B − V ) and we find that  τ∝ ( W ₀)^1.9±0.1  , providing us with an important scaling for theoretical modelling of metal absorbers. We also measure the dust-to-metal ratio and find it similar to that of the Milky Way. In contrast to previous studies, we do not detect any gravitational magnification by Mg  ii systems. We measure the upper limit  μ < 1.10  and discuss the origin of the discrepancy. Finally, we estimate the fraction of absorbers missed due to extinction effects and show that it rises from 1 to 50 per cent in the range  1 < W ₀ < 6 Å  . We parametrize this effect and provide a correction for recovering the intrinsic  ∂ N /∂ W ₀  distribution.     

Rotational dynamics of a solar system body under solar radiation torques

The rotational dynamics of a small solar system body subject to solar radiation torques is investigated. A set of averaged evolutionary equations are derived as an analytic function of a set of spherical harmonic coefficients that describe the torque acting on the body due to solar radiation. The analysis also includes the effect of thermal inertia. The resulting equations are studied and a set of possible dynamical outcomes for the rotation rate and obliquity of a small body are found and characterized.     

Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories.     

Mineralogy and petrogenesis of lunar magnesian granulitic meteorite Northwest Africa 5744

Lunar meteorite Northwest Africa (NWA) 5744 is a granulitic breccia with an anorthositic troctolite composition that may represent a distinct crustal lithology not previously described. This meteorite is the namesake and first‐discovered stone of its pairing group. Bulk rock major element abundances show the greatest affinity to Mg‐suite rocks, yet trace element abundances are more consistent with those of ferroan anorthosites. The relatively low abundances of incompatible trace elements (including K, P, Th, U, and rare earth elements) in NWA 5744 could indicate derivation from a highlands crustal lithology or mixture of lithologies that are distinct from the Procellarum KREEP terrane on the lunar nearside. Impact‐related thermal and shock metamorphism of NWA 5744 was intense enough to recrystallize mafic minerals in the matrix, but not intense enough to chemically equilibrate the constituent minerals. Thus, we infer that NWA 5744 was likely metamorphosed near the lunar surface, either as a lithic component within an impact melt sheet or from impact‐induced shock.     

Wet Fault or Dry Fault? A Laboratory Approach to Remotely Monitor the Hydro-Mechanical State of a Discontinuity Using Controlled-Source Seismics

Stress variation and fluid migration occur in deformation zones, which are expected to affect seismic waves reflected off or propagating across such structures. We developed a basic experimental approach to monitor the mechanical coupling with respect to seismic coupling across a single discontinuity between a granite sample in contact with a steel platen. Piezoceramics located on the platen were used to both generate and record the P and S wave fields reflected off the discontinuity at normal incidence. This way, normal (B _n ) and tangential (B _t ) compliances were calculated using Schoenberg’s linear slip theory (Schoenberg, J Acoust Soc Am 68:1516–1521, 1980) when the roughness, the effective pressure (P _eff, up to 200 MPa), and the nature of the filling (gas or water) vary. We observe that increasing the effective pressure decreases B _n and B _t , which is interpreted as the effect of the closure of the voids at the interface, permitting more seismic energy to be transmitted across the interface. Values of B _n are significantly higher than those of B _t at low P _eff (<60–80 MPa) in dry conditions, and significantly drop under water-saturated conditions. The water filling the voids therefore helps to transmit the seismic energy of compressional waves across the interface. These results show that the assumption B _n  ≈ B _t commonly found in some theoretical approaches does not always stand. The ratio B _n /B _t actually reflects the type of saturating fluids and the effective pressure, in agreement with other experimental studies. However, we illustrate that only the relative variations of this ratio seem to be relevant, not its absolute value as suggested in previous studies. Consequently, the use of B _n against B _t plots may allow effective pressure variation and the nature of the pore fluid to be inferred. In this respect, this experimental approach at sample scale helps to pave the way for remotely monitoring in the field the hydro-mechanical state of deformation zones, such as seismogenic faults, fractured reservoirs, or lava conduits.     

The Geology and Petroleum Resources of Kansas: A Review From Alpha to Omega or From the Pleistocene to the Precambrian

The geological story of Kansas is told through the rocks that are present. It is a simple story in generalities but complex in detail. Knowing the story, gives insight into understanding the occurrence and location of possible economic valuable minerals, such as petroleum. This is a brief review of Kansas geology with respect to the known occurrence of oil and gas. Kansas is part of the Midcontinent oil province with oil having been discovered 150 years ago and commercial production commencing in 1873. Although many prospects remain in Kansas, the state has gone from the number 1 producer in the U.S. in 1916 to 8th today. Exploration for new oil and gas production therefore is going to have to be more imaginative and utilize new approaches and techniques to find the elusive petroleum. There are possibilities however for the prospector who can search diligently. Although the big fields probably have been discovered, the prospects today are deeper, in more undetectable traps, and in essentially untested places.