Solar activity during the Holocene: the Hallstatt cycle and its consequence for grand minima and maxim

Cosmogenic isotopes provide the only quantitative proxy for analyzing the long-term solar variability over a centennial timescale. While essential progress has been achieved in both measurements and modeling of the cosmogenic proxy, uncertainties still remain in the determination of the geomagnetic dipole moment evolution. Here we improve the reconstruction of solar activity over the past nine millennia using a multi-proxy approach. We used records of the 14C and 10Be cosmogenic isotopes, current numerical models of the isotope production and transport in Earth's atmosphere, and available geomagnetic field reconstructions, including a new reconstruction relying on an updated archeo-/paleointensity database. The obtained series were analyzed using the singular spectrum analysis (SSA) method to study the millennial-scale trends. A new reconstruction of the geomagnetic dipole field moment, GMAG.9k, is built for the last nine millennia. New reconstructions of solar activity covering the last nine millennia, quantified in sunspot numbers, are presented and analyzed. A conservative list of grand minima and maxima is provided. The primary components of the reconstructed solar activity, as determined using the SSA method, are different for the series based on 14C and 10Be. These primary components can only be ascribed to long-term changes in the terrestrial system and not to the Sun. They have been removed from the reconstructed series. In contrast, the secondary SSA components of the reconstructed solar activity are found to be dominated by a common ~2400-yr quasi-periodicity, the so-called Hallstatt cycle, in both the 14C and 10Be based series. This Hallstatt cycle thus appears to be related to solar activity. Finally, we show that the grand minima and maxima occurred intermittently over the studied period, with clustering near highs and lows of the Hallstatt cycle, respectively.Comment: In press in Astronomy & Astrophysics, doi: 10.1051/0004-6361/20152729

Core-flow constraints on extreme archeomagnetic intensity changes

Recent studies (Ben-Yosef et al., 2009; Shaar et al., 2011) propose extreme archeomagnetic intensity changes (termed spikes) in the range ~4-5μT/year c.a. 1000 BC in the Near East, around 40 to 50 times larger than values typical of the present-day. In order to investigate whether such extreme changes are consistent with a model of the source region of the magnetic field, namely the fluid flow at the surface of Earth's core, we construct upper bounds for instantaneous magnetic intensity change at an arbitrary site on the Earth's surface. These bounds are constrained by the amount of kinetic energy available to sustain the change, taken here to be a prescribed value for the root-mean-squared surface velocity of 13 km/yr as inferred from the current state of the core. Further, we focus attention on two end-members of optimised core surface flow structure: unrestricted and purely-toroidal. As the derivation of the bounds demands complete knowledge of the geomagnetic field at the core surface, we model the unknown field by means of a Monte Carlo approach, extending to high degree the CHAOS-4 (epoch 2010 AD) and CALS10k1.b (epoch 1000 BC) geomagnetic field models.Using 2000 realisations for each family of stochastic field models, we find that optimised core flows are always large-scale and that they tend to generate a non-dipole, quadrupole-dominated secular variation at the Earth's surface. The dependence of the upper bounds as a function of site location reflects the large-scale structure of the intensity itself: stronger field permits more rapid change. For the site in the Near East, purely-toroidal flows have upper bounds of approximately 0.62 ± 0.02μT/year, whereas unrestricted flows increase this bound to 1.20 ± 0.02μT/year. We favour the former as more geophysically sound, on the account of a large body of previous results from core surface flow inversions and consistency with the existence of a stratified layer at the top of the core. Even if we allow for a generous threefold increase in the prescribed rms velocity (and a concomitant threefold increase in the bound), we conclude that the reported occurrences of extreme intensity changes as suggested in the Near East are not compatible with the commonly accepted structure of core-surface flow. However, it may be that an explanation for spikes lies beyond our current perception of core-dynamics and future work would be further motivated by seeking corroborative evidence of rapid intensity change from sites elsewhere on Earth's surface; we therefore also discuss the form that the secular variation would take in the case of simultanenous archeomagnetic spikes

The SPICE carbon isotope excursion in Siberia: a combined study of the upper Middle Cambrian-lowermost Ordovician Kulyumbe River section, northwestern Siberian Platform

An integrated, high-resolution chemostratigraphic (C, O and Sr isotopes) and magnetostratigraphic study through the upper Middle Cambrian–lowermost Ordovician shallowmarine carbonates of the northwestern margin of the Siberian Platform is reported. The interval was analysed at the Kulyumbe section, which is exposed along the Kulyumbe River, an eastern tributary of the Enisej River. It comprises the upper Ust’-Brus, Labaz, Orakta, Kulyumbe, Ujgur and lower Iltyk formations and includes the Steptoean positive carbon isotopic excursion (SPICE) studied here in detail from upper Cambrian carbonates of the Siberian Platform for the first time. The peak of the excursion, showing δ13C positive values as high as+4.6‰and least-altered 87Sr/86Sr ratios of 0.70909, is reported herein from the Yurakhian Horizon of the Kulyumbe Formation. The stratigraphic position of the SPICE excursion does not support traditional correlation of the boundary between theOrakta and Labaz formations at the Kulyumbe River with its supposedly equivalent level in Australia, Laurentia, South China and Kazakhstan, where the Glyptagnostus stolidotus and G. reticulatus biozones are known to immediately precede the SPICE excursion and span the Middle–Upper Cambrian boundary. The Cambrian–Ordovician boundary is probably situated in the middle Nyajan Horizon of the Iltyk Formation, in which carbon isotope values show a local maximum below a decrease in the upper part of the Nyajan Horizon, attributed herein to the Tremadocian Stage. A refined magnetic polarity sequence confirms that the geomagnetic reversal frequency was very high during Middle Cambrian times at 7–10 reversals per Ma, assuming a total duration of about 10 Ma and up to 100 magnetic intervals in the Middle Cambrian. By contrast, the sequence attributed herein to the Upper Cambrian on chemostratigraphic grounds contains only 10–11 magnetic intervals

Relating L-Resilience and Wait-Freedom via Hitting Sets

The condition of t-resilience stipulates that an n-process program is only obliged to make progress when at least n-t processes are correct. Put another way, the live sets, the collection of process sets such that progress is required if all the processes in one of these sets are correct, are all sets with at least n-t processes. We show that the ability of arbitrary collection of live sets L to solve distributed tasks is tightly related to the minimum hitting set of L, a minimum cardinality subset of processes that has a non-empty intersection with every live set. Thus, finding the computing power of L is NP-complete. For the special case of colorless tasks that allow participating processes to adopt input or output values of each other, we use a simple simulation to show that a task can be solved L-resiliently if and only if it can be solved (h-1)-resiliently, where h is the size of the minimum hitting set of L. For general tasks, we characterize L-resilient solvability of tasks with respect to a limited notion of weak solvability: in every execution where all processes in some set in L are correct, outputs must be produced for every process in some (possibly different) participating set in L. Given a task T, we construct another task T_L such that T is solvable weakly L-resiliently if and only if T_L is solvable weakly wait-free

Three distinct reversing modes in the geodynamo

© 2016, Pleiades Publishing, Ltd.The data that describe the long-term reversing behavior of the geodynamo show strong and sudden changes in magnetic reversal frequency. This concerns both the onset and the end of superchrons and most probably the occurrence of episodes characterized by extreme geomagnetic reversal frequency (>10–15 rev./Myr). To account for the complexity observed in geomagnetic reversal frequency evolution, we propose a simple scenario in which the geodynamo operates in three distinct reversing modes: i—a “normal” reversing mode generating geomagnetic polarity reversals according to a stationary random process, with on average a reversal rate of ∼3 rev./Myr; ii—a non-reversing “superchron” mode characterizing long time intervals without reversal; iii—a hyper-active reversing mode characterized by an extreme geomagnetic reversal frequency. The transitions between the different reversing modes would be sudden, i.e., on the Myr time scale. Following previous studies, we suggest that in the past, the occurrence of these transitions has been modulated by thermal conditions at the core-mantle boundary governed by mantle dynamics. It might also be possible that they were more frequent during the Precambrian, before the nucleation of the inner core, because of a stronger influence on geodynamo activity of the thermal conditions at the core-mantle boundary

Archeomagnetic intensity variations during the era of geomagnetic spikes in the Levant

Observational records of rapidly varying magnetic fields strongly constrain our understanding of core flow dynamics and Earth's dynamo. Archeomagnetic analyses of densely sampled artefacts from the Near-East have suggested that the intensity variation during the first millennium BCE was punctuated with two geomagnetic spikes with rates of change of intensity exceeding 1 μT/yr, whose extreme behaviour is challenging to explain from a geodynamo perspective. By applying a new transdimensional Bayesian method designed to capture variations on both long and short timescales, we show that the data considered only at the fragment (thermal-unit) level require a complex intensity variation with no less than six spikes, each with an approximate duration of between 30 and 100 years. However, the nature of the inferred intensity evolution and the number of spikes detected are fragile and highly dependent on the specific treatment of the archeomagnetic data. No spikes are observed when the data are considered only at the level of a group of fragments from the same archeological context, with a minimum of three different artefacts per context. Furthermore, the number of spikes decreases to zero when increasing the error budget for the intensity at the fragment level within reasonable levels of 3–6 μT and the data age uncertainty up to 50 years. Of the six spikes found, the most resilient when increasing the error budget was dated at ~970 BCE. However, we show that even this spike sensitively depends on the age model proposed for data from the Levant archeological site Timna-30 and disappears when considering a single Gaussian age prior distribution for these data and a moderate minimum intensity error. Thus, depending on the choices made, the Near-Eastern data are compatible with a broad range of time-dependence, from six spikes at one extreme to zero spikes on the other. An error of 6 μT at the fragment level produces a spikeless model with strong similarity with the reconstruction from the SHAWQ-Iron Age global model with rates of change of ~0.2–0.3 μT/yr

Strong Equivalence Relations for Iterated Models

The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical representation, has become standard for applying topological reasoning to distributed computing. Its modular structure makes it easier to analyze than the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS). It is known that AS and IIS are equivalent with respect to \emph{wait-free task} computability: a distributed task is solvable in AS if and only if it solvable in IIS. We observe, however, that this equivalence is not sufficient in order to explore solvability of tasks in \emph{sub-models} of AS (i.e. proper subsets of its runs) or computability of \emph{long-lived} objects, and a stronger equivalence relation is needed. In this paper, we consider \emph{adversarial} sub-models of AS and IIS specified by the sets of processes that can be \emph{correct} in a model run. We show that AS and IIS are equivalent in a strong way: a (possibly long-lived) object is implementable in AS under a given adversary if and only if it is implementable in IIS under the same adversary. %This holds whether the object is one-shot or long-lived. Therefore, the computability of any object in shared memory under an adversarial AS scheduler can be equivalently investigated in IIS

Non-universal equilibrium crystal shape results from sticky steps

The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) using the Monte Carlo method, where p=(dz/dx, dz/dy)$, and represents the thermal averag |p| dependence of , we derive a |p|-expanded expression for the non-universal surface free energy f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f_{eff}(p).Comment: 31 pages, 21 figure

Analysis of geomagnetic field intensity variations in Mesopotamia during the third millennium BC with archeological implications

We present new archeointensity results obtained at two multi-layer archeological sites, Tell Atij and Tell Gudeda (northeastern Syria), dated from the Early Bronze Period in the third millennium BC. The archeointensity data were obtained using the experimental protocol developed for the Triaxe magnetometer. In total, 68 fragments (204 specimens) of 151 fragments analyzed passed our selection criteria, allowing average intensity values to be estimated for 14 archeological layers, nine at Tell Atij and five at Tell Gudeda. Based on the available archeological constraints, the different archeological layers of Tell Atij and Tell Gudeda were dated between ∼2900 BC and ∼2600 BC and between ∼2550 BC and ∼2325 BC, respectively. The Tell Atij data show a significant increase in intensity over the dated period, while the results from Tell Gudeda exhibit a V-shape evolution. Using high-quality data available from Syria, the Levant and Turkey, a regional geomagnetic field intensity variation curve spanning the entire third millennium BC was constructed using a trans-dimensional Bayesian method. It clearly shows two intensity peaks, around 2600 BC and at ∼2300 BC, associated with variation rates of ∼0.1-0.2 μT/yr. This indicates that the occurrence of century-scale intensity peaks with rates of variation comparable to or even slightly higher than the maximum rates observed in the modern geomagnetic field is an ubiquitous feature of the geomagnetic secular variation. From an archeological point of view, the new archeointensity data strengthen the hypothesis that the successive occupation of Tell Atij and Tell Gudeda was synchronous with the two first urban phases of Mari, making possible a sustained trade network between these settlements during the third millennium BC. We further suggest that the end of Mari's first urban phase, contemporaneous with the abandonment of Tell Atij, might have been caused by a regional drought episode around 2600 BC. More generally, the Bayesian approach used to estimate the new reference intensity variation curve offers promising chronological constraints for archeological purposes

Facet ridge end points in crystal shapes

Equilibrium crystal shapes (ECS) near facet ridge end points (FRE) are generically complex. We study the body-centered solid-on-solid model on a square lattice with an enhanced uniaxial interaction range to test the stability of the so-called stochastic FRE point where the model maps exactly onto one dimensional Kardar-Parisi-Zhang type growth and the local ECS is simple. The latter is unstable. The generic ECS contains first-order ridges extending into the rounded part of the ECS, where two rough orientations coexist and first-order faceted to rough boundaries terminating in Pokrovsky-Talapov type end points.Comment: Contains 4 pages, 5 eps figures. Uses RevTe