An explicit KO-degree map and applications

The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-homotopy theory of the unit map from the motivic sphere spectrum to the Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We show that "Suslin matrices", which are explicit maps from odd dimensional split smooth affine quadrics to geometric models of the spaces appearing in Bott periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit map. As applications, we deduce that $K^{MW}_i(F) = GW^i_i(F)$ for $i \leq 3$, which can be thought of as an extension of Matsumoto's celebrated theorem describing $K_2$ of a field. These results provide the first step in a program aimed at computing the sheaf $\pi_{n}^{{\mathbb A}^1}({\mathbb A}^n \setminus 0)$ for $n \geq 4$.Comment: 36 Pages, Final version, to appear Journal of Topolog

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4Comment: Accepted for publication in ApJ. Some minor changes due to referee report, most notably that the clumping mechanism has been identified as the streaming instability of Youdin & Goodman (2005). Movies of the simulations are still available at http://www.mpia.de/homes/johansen/research_en.ph

Effects of Geochemical and Environmental Parameters on Abiotic Organic Chemistry Driven by Iron Hydroxide Minerals

Geological conditions play a significant role in prebiotic/abiotic organic chemistry, especially when reactive minerals are present. Previous studies of the prebiotic synthesis of amino acids and other products in mineral‐containing systems have shown that a diverse array of compounds can be produced, depending on the experimental conditions. However, these previous experiments have not simulated the effects of varying geochemical conditions, in which factors such as pH, iron redox state, or chemical concentrations may vary over time and space in a natural environment. In geochemical systems that contain overlapping gradients, many permutations of individual conditions could exist and affect the outcome of an organic reaction network. We investigated reactions of pyruvate and glyoxylate, two compounds that are central to the emergence of metabolism, in simulated geological gradients of redox, pH, and ammonia concentration. Our results show that the positioning of pyruvate/glyoxylate reactions in this environmental parameter space determines the organic product distribution that results. Therefore, the distribution pattern of amino acids and alpha‐hydroxy acids produced prebiotically in a system reflects the specific reaction conditions, and would be distinct at various locations in an environment depending on local geochemistry. This is significant for origin of life chemistry in which the composition and function of oligomers could be affected by the environmentally driven distribution of monomers available. Also, for astrobiology and planetary science where organic distribution patterns are sometimes considered as a possible biosignature, it is important to consider environmentally driven abiotic organic reactions that might produce similar effects

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

Multiple and Fast: The Accretion of Ordinary Chondrite Parent Bodies

Although petrologic, chemical and isotopic studies of ordinary chondrites and meteorites in general have largely helped establish a chronology of the earliest events of planetesimal formation and their evolution, there are several questions that cannot be resolved via laboratory measurements and/or experiments only. Here we propose rationale for several new constraints on the formation and evolution of ordinary chondrite parent bodies (and by extension most planetesimals) from newly available spectral measurements and mineralogical analysis of main belt S-type asteroids (83 objects) and unequilibrated ordinary chondrite meteorites (53 samples). Based on the latter, we suggest spectral data may be used to distinguish whether an ordinary chondrite was formed near the surface or in the interior of its parent body. If these constraints are correct, the suggested implications include that: i) large groups of compositionally similar asteroids are a natural outcome of planetesimal formation and, consequently, meteorites within a given class can originate from multiple parent bodies; ii) the surfaces of large (up to ~200km) S-type main-belt asteroids expose mostly the interiors of the primordial bodies, a likely consequence of impacts by small asteroids (D<10km) in the early solar system (Ciesla et al. 2013); iii) the duration of accretion of the H chondrite parent bodies was likely short (instantaneous or in less then ~10^5 yr but certainly not as long as 1 Myr); iv) LL-like bodies formed closer to the Sun than H-like bodies, a possible consequence of radial mixing and size sorting of chondrules in the protoplanetary disk prior to accretion.Comment: Accepted for publication in Ap

Frontiers of the physics of dense plasmas and planetary interiors: experiments, theory, applications

Recent developments of dynamic x-ray characterization experiments of dense matter are reviewed, with particular emphasis on conditions relevant to interiors of terrestrial and gas giant planets. These studies include characterization of compressed states of matter in light elements by x-ray scattering and imaging of shocked iron by radiography. Several applications of this work are examined. These include the structure of massive "Super Earth" terrestrial planets around other stars, the 40 known extrasolar gas giants with measured masses and radii, and Jupiter itself, which serves as the benchmark for giant planets.Comment: Accepted to Physics of Plasmas special issue. Review from HEDP/HEDLA-08, April 12-15, 200

The secondary eclipse of CoRoT-1b

The transiting planet CoRoT-1b is thought to belong to the pM-class of planets, in which the thermal emission dominates in the optical wavelengths. We present a detection of its secondary eclipse in the CoRoT white channel data, whose response function goes from ~400 to ~1000 nm. We used two different filtering approaches, and several methods to evaluate the significance of a detection of the secondary eclipse. We detect a secondary eclipse centered within 20 min at the expected times for a circular orbit, with a depth of 0.016+/-0.006%. The center of the eclipse is translated in a 1-sigma upper limit to the planet's eccentricity of ecosomega<0.014. Under the assumption of a zero Bond Albedo and blackbody emission from the planet, it corresponds to a T_{CoRoT}=2330 +120-140 K. We provide the equilibrium temperatures of the planet as a function of the amount of reflected light. If the planet is in thermal equilibrium with the incident flux from the star, our results imply an inefficient transport mechanism of the flux from the day to the night sides.Comment: 6 pages, to appear in A&A, submitted 18 march 2009, accepted 7 July 200