Probing the Protosolar Disk Using Dust Filtering at Gaps in the Early Solar System

Jupiter and Saturn formed early, before the gas disk dispersed. The presence of gap-opening planets affects the dynamics of the gas and embedded solids and halts the inward drift of grains above a certain size. A drift barrier can explain the absence of calcium aluminium rich inclusions (CAIs) in chondrites originating from parent bodies that accreted in the inner solar system. Employing an interdisciplinary approach, we use a $\mu$-X-Ray-fluorescence scanner to search for large CAIs and a scanning electron microscope to search for small CAIs in the ordinary chondrite NWA 5697. We carry out long-term, two-dimensional simulations including gas, dust, and planets to characterize the transport of grains within the viscous $\alpha$-disk framework exploring the scenarios of a stand-alone Jupiter, Jupiter and Saturn \textit{in situ}, or Jupiter and Saturn in a 3:2 resonance. In each case, we find a critical grain size above which drift is halted as a function of the physical conditions in the disk. From the laboratory search we find four CAIs with a largest size of $\approx$200$\,\mu$m. \Combining models and data, we provide an estimate for the upper limit of the $\alpha$-viscosity and the surface density at the location of Jupiter, using reasonable assumptions about the stellar accretion rate during inward transport of CAIs, and assuming angular momentum transport to happen exclusively through viscous effects. Moreover, we find that the compound gap structure in the presence of Saturn in a 3:2 resonance favors inward transport of grains larger than CAIs currently detected in ordinary chondrites.Comment: 16 pages, 10 figures, updated to match published version in Astrophysical Journa

Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Ordering of Energy Levels in Heisenberg Models and Applications

In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture for the Heisenberg model with arbitrary spins and coupling constants on a chain. In this paper we give a pedagogical introduction to this result and also discuss some extensions and implications. The latter include the property that the relaxation time of symmetric simple exclusion processes on a graph for which FOEL can be proved, equals the relaxation time of a random walk on the same graph. This equality of relaxation times is known as Aldous' Conjecture.Comment: 20 pages, contribution for the proceedings of QMATH9, Giens, September 200

Primitive decompositions of Johnson graphs

A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.Comment: 35 page

Magnesium and ⁵⁴Cr isotope compositions of carbonaceous chondrite chondrules – Insights into early disk processes

AbstractWe report on the petrology, magnesium isotopes and mass-independent 54Cr/52Cr compositions (μ54Cr) of 42 chondrules from CV (Vigarano and NWA 3118) and CR (NWA 6043, NWA 801 and LAP 02342) chondrites. All sampled chondrules are classified as type IA or type IAB, have low 27Al/24Mg ratios (0.04–0.27) and display little or no evidence for secondary alteration processes. The CV and CR chondrules show variable 25Mg/24Mg and 26Mg/24Mg values corresponding to a range of mass-dependent fractionation of ∼500ppm (parts per million) per atomic mass unit. This mass-dependent Mg isotope fractionation is interpreted as reflecting Mg isotope heterogeneity of the chondrule precursors and not the result of secondary alteration or volatility-controlled processes during chondrule formation. The CV and CR chondrule populations studied here are characterized by systematic deficits in the mass-independent component of 26Mg (μ26Mg∗) relative to the solar value defined by CI chondrites, which we interpret as reflecting formation from precursor material with a reduced initial abundance of 26Al compared to the canonical 26Al/27Al of ∼5×10−5. Model initial 26Al/27Al values of CV and CR chondrules vary from (1.5±4.0)×10−6 to (2.2±0.4)×10−5. The CV chondrules display significant μ54Cr variability, defining a range of compositions that is comparable to that observed for inner Solar System primitive and differentiated meteorites. In contrast, CR chondrites are characterized by a narrower range of μ54Cr values restricted to compositions typically observed for bulk carbonaceous chondrites. Collectively, these observations suggest that the CV chondrules formed from precursors that originated in various regions of the protoplanetary disk and were then transported to the accretion region of the CV parent asteroid whereas CR chondrule predominantly formed from precursor with carbonaceous chondrite-like μ54Cr signatures. The observed μ54Cr variability in chondrules from CV and CR chondrites suggest that the matrix and chondrules did not necessarily formed from the same reservoir. The coupled μ26Mg∗ and μ54Cr systematics of CR chondrules establishes that these objects formed from a thermally unprocessed and 26Al-poor source reservoir distinct from most inner Solar System asteroids and planetary bodies, possibly located beyond the orbits of the gas giants. In contrast, a large fraction of the CV chondrules plot on the inner Solar System correlation line, indicating that these objects predominantly formed from thermally-processed, 26Al-bearing precursor material akin to that of inner Solar System solids, asteroids and planets

Flow-to-fracture transition in a volcanic mush plug may govern normal eruptions at Stromboli

Stromboli is a model volcano for studying eruptions driven by degassing. The current paradigm posits that Strombolian eruptions represent the bursting of gas slugs ascending through melt‐filled conduits, but petrological observations show that magma at shallow depth is crystalline enough to form a three‐phase plug consisting of crystals, bubbles, and melt. We combine a 1‐D model of gas flushing a crystalline mush with a 3‐D stress model. Our results suggest that localized gas segregation establishes hot conduits of mobile magma within a stagnant plug. The plug is prone to tensile failure controlled by gas overpressure and tectonic stress, with failure most likely beneath the observed vent locations. We hence argue that Strombolian eruptions are related to plug failure rather than flow. Our proposed three‐phase model of the shallow plumbing system may provide a promising framework for integrating geophysical, petrological, and morphological observations at Stromboli and in open‐system volcanism more generally

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.Comment: 7 pages including 3 figure